Math People Are Elitist

[@ModeratelyAwesomeX]

I failed my first math class in university five times, then barely passed. I then spent a whole year (from May to September) studying math non-stop, 4 or so hours daily to pass my second math class, which was mostly calc 2. After that, the next two math classes I had I breezed through, calc 3 and tons of probability etc. hard work pays off.

[@Justin-gk8hu]

Was this all in your first year of university?

[@MasterGhostf]

Went through this as well. Had to take calc 1 and calc 2 twice. Need to retake Chem. But, I feel solid on math now.

[@ModeratelyAwesomeX]

@@Justin-gk8hu no, first year were my first two math classes are first and second semester of year 1 (i had to retake some of my classes due to being an exceptionally bad student at the time), second two were year 2/3 Exams work differently here, we have exam terms every few months, meaning it took me around 8 or so months of prep to pass my first maths exam(due to the sheer amount of times I failed the exam) and around 5 months to pass my second one.

[@Justin-gk8hu]

@@ModeratelyAwesomeX ohhh I see, so it's not like you have all your exams for all your classes in one period at the end of the year.. makes sense man, well I'm happy that you managed to make it all work out in the end. I'm currently in a situation where I had to retake some exams for the grist time, and even those exams I'm afraid I may not have passed all of them.. just finished my first year of college so I need to pass them the second time round to be allowed into my second year

[@ModeratelyAwesomeX]

@@Justin-gk8hu was a similar case with me, keep working on it and don't let go of it until you are sure you can pass, but also don't take it too hard because you still need friends and sunlight, I made a massive mistake twice during my education and kept on studying for so long (I'm generally very healthy and athletic) that I eventually got really sick due to the constant stress taking a toll on my immune system. Education is important, but health is number 1.

[@spacetimemalleable7718]

If you were an "elitist" before, these books will put you in your place. Try doing ALL the problems in the mentioned texts and you'll become humble or you're a genius. Whenever I feel really knowledegable, I simply get humbled rapidly after trying to understand and work problems in the books. There's always something much more to learn.

[@TheMathSorcerer]

"If you were an "elitist" before, these books will put you in your place"

[@annaclarafenyo8185]

Stop it, these books aren't that difficult, they are summarizing things from 100 years ago. This isn't "elitism", because knowing math doesn't put you in any elite, it just makes you smarter. Elite people are quite unintelligent, they just have money. Actual 'elites', i.e. rich people, are, as a rule, lousy at mathematics.

[@everythingisalllies2141]

Yet even though these guys knew a lot of Math, they still make silly errors, such as Einsteins nonsense theories, are just silly mistakes in Math due to his failure to understand simple Physics.

[@АмальФарук-в6д]

More unique, interesting, challenging problem I solve, better I feel about my math abilities. Those books had lots of them…

[@callmedeno]

Yup, I think a lot of people's notions would be cured by actually trying proof-base mathematics (not like following recipes). I went most of my adult life thinking I was maybe above average intelligence, but I quickly learned when I started self-studying math that I am very much bang average, and it translates into every other intellectual area for me. I realise I was, like many people these days, essentially bullshitting myself without the rubber ever having to meet the road (to reality).

[@joseluismoreyrajr.7598]

I failed college algebra 3 times, I got a D in Algebra 2 in highschool. I went to the basics and relearned math, now I am a math major going into senior year. I studied so much, to understand what math was trying to convey to me. So worth it.

[@GoToMan]

How did you go on about your highschool? How did you ‘study’ maths?

[@andrearueda2062]

that’s amazing!!!

[@joseluismoreyrajr.7598]

@@GoToMan i got serious about math in college. What I did to help me understand algebra is visualizing it. I loved using Desmos because I then understood why we did some things. Also I tried to understand why they wanted us to learn a certain formula or action. Once I broke it down and understood each part of what I’m trying to learn, it carried on to all my other math classes. Best advice I can give is find the logic behind why the math is done in that way.

[@antinatalope]

I learned more about math with programming than in school.

[@Dr_Ender]

@@antinatalope Same here, programming helped me out a lot with math. Something else that got my brain going was some games. A good example is factorio. Using math to plan out a juicy factory. I encourage people to look at things like that because imo i feel like theres not enough engaging things to do with math outside of pursuing a job field that requires more and more math and or just math exercises. I find it similar to working out, theres a lot of people who feel more encouraged, etc when working out using a vr headset and doing a work out type game. Thats just a opinion though so take it with a grain of salt.

[@dantonio95]

Although there is a certain degree of elitism among mathematicians, it's not necessarily the case for the most part. The problem in mathematics, however, is the lack of good exposition. Yes, you may convey lots of interesting stuff in a rigorous text, but you don't have to let rigor get in the way of clarity and good exposition.

[@dorol6375]

Math youtube channels are wonderful at this

[@SenatorSigma]

legendary mathematicians can do both. Euler was a good example of this and honestly anyone can translate and read his writings and they hold up fine today. Its hard to be rigorous and still write in an engaging and simple way.

[@zalanahara270]

a STRONG concur.

[@gorgolyt]

Agree. Formalisation is the end point, not the start. Presenting it as such just creates unnecessary obfuscation.

[@albertbatfinder5240]

I’ve met with elitism in many fields and the critical factor (since it’s necessary to form some definition of the word) is how willing people are to put their ego aside as they assist other people into their world. Mathematics is notorious for removing the scaffolding. Time and time again I’ve spent hours trying to get from step 1 to step 2 when texts could easily have spelt out intermediate steps. I got the impression it was displaying some form of weakness to explain the reasoning the author or teacher went through when they first set eyes upon the subject. It’s easy to see how musicians or visual artists or chefs could be elitist, and it’s just as easy to see how they can make it easy and enjoyable to welcome others into the fold. Mathematicians have a lot to learn in that respect, if even they care.

[@rareastatine85rareastatine97]

Engineer here, I feel you bro. I remember a specific problem from analysis, where (as the book said) I should easily see that a constant is pi/4. I spent almost a whole weekend, not figuring this out. The book said "from [very big and intimidating equation] it can be easily concluded that the constant must be pi/4. Because they said "easy" I thought I was missing a totally simple and obvious way to figure it out. I thought I was stupid. Then I asked a mathematician. He was also intriegued by the problem and we spent another half a day on it. Result: Much better than "easily concluded" would have been: "split the equation into partial fractions, then apply curl(curl(...)) on both sides to confirm that the constant is pi/4". Later that week the professor confirmed that this was in fact the intended way to do it. My opinion on this: Most math books are written by people who are experts. Their perspective is "this is primary school stuff, how can you possibly not know that?!?" Meanwhile the students perspective "I have never seen this, basic introduction please?." There is a nice cartoon about this problem:"how developers see users / how users see developers". A lot of people who would make excellent mathematicians (and engineers) are discouraged, because a lot of math books are written with the intention of refreshing the memory of someone who already knows the stuff, rather than for someone who wants to learn it. Furthermore most math books are top-down, rather than bottom-up. "We have a vehicle with 4 wheels. We see what we can learn about that. Then we think about a vehicle with n wheels." vs "Here is a set of rules for a vehicle with n wheels, if you want to look at the special case 4, you can do that yourself. It is so easy, trivial even, that we can not be bothered to give just the slightest hint at fancy pitfalls you might encoutner..."

[@beleakswordsteel]

THIS I'm in college algebra right now and I'm only a few weeks into the class and I've nearly filled up an entire notebook with just problems. Half way through another one through the notes about those problems. So much of my frustration so far has been the website we use completely dropping the ball on steps that it just assumes you know, or it'll trap you by throwing a differently organized problem at you than the what you prepared for and it gets overwhelming quickly dealing with it.

[@zorroaster8895]

@@maalikserebryakov good job proving their point

[@sarah_757]

I slogged through the engineering maths classes, utterly tortured myself for a C+. I even avoided a double major in Computer Science partially because of the required maths. Thankfully in the 15 years I've been a practicing engineer I've never had to derive anything... for which I, and my employers, are very grateful. Lol. I've recently realized I have anxiety, and on reflection, it's that scaffold removal that is such a problem when it comes to math. I, and my anxiety, need the reassurances that I can carefully and safely climb up each level of the scaffolding in the correct sequence and with the correct outcome before I feel confident I can skip a step. The textbook or the course instructor often start at two levels already skipped and go from there. Very disheartening: I'm mean, they tell me I'm smart, why do I struggle with math? Must be something wrong with me!

[@nathankayhan4358]

@@sarah_757 "I'm mean, they tell me I'm smart, why do I struggle with math?" There are different sorts of intelligence. I ace reading comprehension tests. I find them pretty easy because I have no problem reading the text, understanding it, and answering the questions. Clearly most people, including friends of mine who are excellent at math and science, don't find these tests so easy, because I'm always in the 99th percentile. But when it comes to math I'm mediocre. I even struggle with arithmetic, let alone algebra beyond the simple stuff. For some reason I can remember details about history but I can't remember my social security number! It's funny how different minds work.

[@lewman999]

I think elitism is the wrong word, but it's an underlying challenge in maths education (particularly at the early level), where you spend quite a lot of time "learning the language" without really doing anything with it. To take an analogy I read in an excellent book (I believe one of Jordan Ellenberg's books?) - it's like if an English class was focused entirely on things like spelling, grammar, proper sentence structure and so on, but you never read any books or never wrote anything of your own. Or if you had a PE class where you did nothing but drills and conditioning, without ever playing a game. It's like how people who've stopped studying maths at school often see it as mechanical and rigid, whereas people who go study maths degrees or do further research treat it as an art and see it as something really creative - because they get more chances to play the game, even if they have to do more drills along the way. Rigour in math is important because it *allows* you to explore more of the landscape and be more creative, just as a wider vocabulary and a stronger understand of grammar can help you become more eloquent and make your writing more impactful. But the way maths is presented as an early level makes rigour feel arbitrary and mysterious, because you stop before you get to the fun stuff - there's no payoff for all that rigour, so to speak.

[@kkuznetsov2424]

Beautifully put 🙌

[@susilgunaratne4267]

As one author said in an engineering book, "Mathematical training is important in engineering, ... , not in its abstract concepts & theoretical results but in its rigorous methodology."

[@fatboyRAY24]

Your comment reminds me of Karate Kid when Mr Miyagi had Daniel LaRusso wash cars for a few weeks before showing him any actual Karate. To some extent you really might have to enjoy the almost arbitrary process of waxing on and off before getting to the really good stuff such as vanquishing your mortal enemies with your limbs.

[@DctrBread]

The analogy with English is hardly hypothetical in my experience. I would say primary education as a whole tends to gradually morph towards repetition and banal tasks, and you're basically not capable of standing out unless you do the majority of your learning extracurricularly. This is how laypeople end up seeing math as mind-numbing, rather than trippy. Their experience was that math is essentially just mind-numbing arithmetic tasks, to the point where they learned multiplication and division by straight up memorizing a table of all the possible products of two integers less than 12 greater than 2. You'd think at least they'd teach us the first few prime numbers instead lol. Algebra would normally be people's introduction to generalized math, but the system insists on making it about rote calculation tasks too.

[@CynicalBastard]

@@DctrBread My experience, as well. Standard education, and expectations, especially in schools belonging to the "lower rungs" of society [cf. elitism] suffer from a lack of sufficient interesting-building material: that is to say, it's overtly "standardised". But in a sense, within the sphere of education, everything [topical, social, etc.] is in an "overdetermined" space of particulars. Everything is interpenetrating, and in this sense, we come to the concept [and only after] to "rigor". [...]

[@azimuth4850]

I feel like knowing a lot of math definitely makes one susceptible to "elitism". I am just barely breaking into undergraduate math and I can already feel that "wow, I'm pretty smart!" feeling creeping in when I finally understand some results. The key is to just have fun with it, make some fellow math friends, but don't look down on people who don't know math. It's a blessing to have the time to be able to study math for a living! I used to get annoyed at "less than clear" expositions, but then later I realized...that's exactly what you want once you get to a higher level. It's like boom, boom, boom, let's get to the next result. There's an exposition out there for literally everyone at every level. That's why I love your channel because you really help people find the resources they need (and all the encouragement is awesome too!).

[@mastershooter64]

it's actually the opposite, the more you learn, the more you realize how much you dont know!

[@dickrichard626]

The word "elitist" is almost always just used to belittle intelligence... There is nothing wrong with being smart and nothing wrong with being ignorant. Everyone isn't meant to be a genius and many people have mental deficiencies and on top of never trying to become smarter, they stay ignorant or just can't be smart for one reason or another. It's just frowned upon for a smart person to point out how and why someone else is a moron and so when they do, people call them an elitist, as if it's a bad thing that they are smart, but really this is just an anti-intelectual idea that assumes it's somehow better to be ignorant... All I know is I'd rather be an elitist then an imbecile. To each their own. It's just better to not mix people with drastically different mental compacities. This is straight up why the government is designed and functions under the assumption that most of the public is too stupid to deal with complicated matters. If you let dumb people talk and make decisions, they just create confusion and mess stuff up and waste time. Your smart phone wasn't invented by a bag of wind that hates intelecualism and has no understanding of physics, math and gets angry when things get too complicated. I've delt with this my whole life practically. My Father is an irrational idiot that believes he is highly inteligent, but he never make sense about anything and acts like all science and academic topics like math is a bunch of mumbo jumbo and a waste of time... It's called: "cognitive dissonance." He has conflicting ideas and opinions and also he becomes nonsensical, irrational, and maddened in responce to anything that gets too complex. 😆 🤣 😂, If calling him a moron makes me an elitist so be it.

[@Randorandom232]

Could it because ppl who study math are from better backgrounds as opposed to someone in a field like engineering or medicine?

[@qazwsx6340]

yeah definitely. high school maths is so little in scope compared to the whole world of maths, that after even 1 semester of studying maths at university no one else will even have a clue what you are doing. even after completing my undergrad degree i feel like know barely anything.

[@mathboy8188]

Would the feeling be any different if you were getting good at skiing? The first time you attacked and nailed a Black slope, you'd probably come away thinking "Wow, I'm getting pretty damn good at this." It's an appropriate and justified feeling, given the amount of time and effort you had to invest to get that good.

[@SkodaUFOInternational]

My father, a university math professor wouldn't consider me as a person until I got my BSc in computer science. My next one was a psychology BA. Now I am a child psychologist. Go figure.

[@birdsamora9925]

What

[@riceboybebop7018]

you didnt like career prospects of comp sci?

[@birdsamora9925]

@@riceboybebop7018 the you’re not a person part😂 but if that motivates this person then so be it

[@SkodaUFOInternational]

@@birdsamora9925 until I got my degree, nothing of what I thought of the world was important. My preferences, my opinions, simply did not matter. I was thought of as a nobody in the house I was growing up, which certainly messed with my mind. I didn't prove myself as a worthy person in front of my father until I got my degree. He pretty much thought about me as a worthless idiot until that very moment. Elitism has a dark side.

[@birdsamora9925]

@@SkodaUFOInternational that’s just so wild to me honestly but very interesting.

[@iheartalgebra]

A powerful opening sentence: "This is undoubtedly the most important function in mathematics." I thought it was an especially audacious statement the first time I opened this book, but I quickly came to agree

It's really important in math with numbers in it. Not quite sure about other parts of math. (Though it does pop up from time to time.)

[@VeteranVandal]

I'd say maybe behind of the linear of affine functions, but only because they are usually the simple examples on anything that isn't an exponential or a constant, those being the usual boring examples in almost anything involved in math, regardless of what you are doing. Exponentials are hidden in basic courses before university level courses for a reason. Unfortunately there's a lot of lay people that got into the 'not knowing math is cool' stupidity that deny the usefulness of math, but, luckily, examples involving money in a capitalist world make people accept importance without further questioning. Any time people are about to spout the dreadful 'that's gotta be useless in real life' I give the compound interest example, which I feel is the easiest exponential to grasp. There are literally many other applications that are way more interesting, but the example of compound interest really seems more intuitive to people in general.

[@aavalos7760]

@ What other parts of math involving 1-1 functions excludes this foundational identity?

[@abstractnonsense3253]

I remember talking to a med student and telling her that the lecture notes I had to study for a 1 semester course were around 80 pages long. She laughed mockingly. However, I explained to her that I could only get through 2 pages an hour, on average. Her jaw dropped.

[@travisbickle5829]

Gosh I remember med students during my time in Uni. They were the true elitists😅

[@agnosticmanquestionsall2409]

Med students don't know what it takes to do math. Medical studies are mainly biology and memory.

[@ExplosiveBrohoof]

2 pages an hour is a pretty good pace. As someone who reads very slowly anyway, I actually find quite a bit of comfort in mathematical texts.

[@abstractnonsense3253]

@@ExplosiveBrohoof It's a quiet contemplative joy.

[@jackyjack9660]

@@abstractnonsense3253 I use same thing be it maths or biochemistry... Slow pace reading makes me think of what I'm reading.. But i need to study for longer because some maths textbooks are very bulky and biochemistry books are fat.. Understanding the mechanism reaction SN1, SN2 etc in biochemical pathways needs slow pace study..

[@zhatar4214]

The problem I've faced with math during the middle part of school, was that we were only taught HOW and not WHY. I started school loving math and slowly turned into hating it, for me, the why, the story on how that was discovered and what problem does it solve, is very important. Then after that, practice, of course, but without the why, it's soulless.

[@sollinw]

To answer why, one has to answer the whys beyond why and all the whys beyond, not a linear thread and may be infinite, so people created religions, much easier to create one's reality than understanding the existing reality. No one knows y, that's why it's so seducing to solve a hard math problem after a hard while, it gifts u the feeling like u ve come closer to know why, to the truth that fills whole universe. Chances are human are not the ones that have come to the greatest understanding of it all, so we don't have that much time to have time to fight with eachother, and the good ones goes first? The more egoistic and stupidier survive

[@urosmarjanovic663]

Oh yeah... The one time I got that answer is when I did Analysis and Mechanics at the university. Basically concept of integral/differential calculus. From then on, everything opened.

[@heilaarnezki8222]

try physics

[@Vivek10010]

You cant really teach the 'why' part in mathematics until you reach the physics concepts that require that specific mathematical concept.

[@pooodonklooopdoop5672]

@@Vivek10010 is that more the application, you can still explain why this and that works and stuff rather than memorising a series of steps.

[@gungholio3416]

What I've realized is that your success with math very much depends on your confidence. I have some anxiety issues regarding math that made it harder to learn. I'd end up crying even thinking about doing math. At it's peak when I was younger, I failed pre algebra 4 times. Since you might learn at a slower pace or have trouble with a concept, you come to the conclusion that you're just stupid, and you're not a math person- which in turn makes it more difficult to learn the math because you grow to resent it, because you always feel like an idiot and that really holds you back. I still greatly have trouble with my confidence in myself but once I thought of math as more of a skill to be worked upon then some concrete determination of intelligence, I began to understand concepts way better than previously. When your mind is clouded with self doubt, it's hard to focus, and you immediately assume you're going to fail because you're "too stupid." A change in mindset and a boost in much needed confidence is the most important thing to becoming better at math in my opinion and it is so depressing our schools fail to ever do this. I think that the kids that feel stupid that observe the kids who excel in math and play a great deal into giving math this elitist idea where only the naturally gifted can enter, and you never will. Math skill is so often tied to the ego and we write it off as some kind of natural ability when in reality that couldnt be farther from the truth. Seeing math as inaccessible for some people by design is an anti intellectual idea for everyone involved and yet our society, parents, and children believe this and the effects are destructive.

[@jment34]

I agree it takes emotional control wich makes the mind clear and gives confidence.

[@jahjahjah213]

This was eye opening, thank you

[@valhatan3907]

"I'd end up crying even thinking about math". That's hit hard. I remember literally sobbing at 2nd year in highschool when working to math assignment.

[@climatebabes]

True, because its basically exploration resulting in experiences. Without confidence you don't explore..

[@felicityc]

You described every field of learning, very good. Some people seem to never realize this

[@benjaminsmith4058]

When I think of elitism in mathematics, I think of the pedigree books where people trace their PhD mentor lineage back to Euler or Newton to validate their self-importance, or people who explicitly state "if x-proof isn't immediately self-evident to you, you have no future in math." Deliberately discouraging people from pursuing math is definitely a destructive form of elitism.

[@rabbitcreative]

> Deliberately discouraging people from pursuing math is definitely a destructive form of elitism. I saw a comment on YT about a year ago where someone said, "math is power, and not everyone should have that power". So, at the very least, that person was a gate-keeping scumbag.

[@adorp]

So, Euler is the Miyamoto Mushashi/Ip Man of maths? Ironically, Euler himself wrote one of the simplest and most accessible maths books ever. His elementary algebra is actually elementary. It begins with basic additions and subtractions, and has a very friendly storytelling style. It assumes that the reader knows nothing.

[@ianpullman203]

This is an incredibly powerful channel. I felt like I could just about keep up with trig and then had no clue with calc.I assumed I’m just one of those “not smart enough/doesn’t get it” people. Each of your videos has me intrigued and inspired to open up my old math books and have a crack at it again.

[@TheMathSorcerer]

💪💪

[@johnflorio3576]

I am a physicist so mathematics is my language. Like learning any language, it can be difficult at first and you have to stick with it. This I can confidently state: Mathematical intuition can only be developed through practice.

[@meteor8076]

Can you recommend some good books on math ?

[@johnflorio3052]

@meteor: Oh yes. “Calculus Made Easy” by Silvanus P. Thompson might be the most amazing math book ever. It lays out the methods to solve both differential and integral calculus in a most elegant way.

[@voidzennullspace]

*Ramanujan enters the chat*

[@urosmarjanovic663]

@@johnflorio3052 Sudden Fourier and Laplace appear.

[@fisyr]

One thing I consider very elitist in math is that a lot of content is hidden behind paywalls that regular people just wouldn't be able to afford. Especially if they don't know what to necessarily look for. Without having access to books from my library (and sometimes just doing plain piracy out of laziness), there is simply no way I could have completed my PhD. Sometimes I just needed to check one or two pages from a specific book/article and I'd have to pay like 30$ for having access to those said pages. I'd say though this is a problem with academia in general: a lot of science gets mystified because the sources are made inaccessible by publishers due to extravagant fees. Don't even get me started on undergrad college text books which is a scam on its own.

[@paxdei1988]

I never had this problem when I was enrolled at my university, since my enrollment granted me unlimited access to myriads of otherwise paywalled technical journal databases. Granted, I was doing ecology, so perhaps the same might not be true for maths; but it could also just be the way your particular institution operates.

[@hughcaldwell1034]

Yeah, Rebecca Watson has a good video on pay-walls in academia. It's a bloody crime.

[@fisyr]

@@paxdei1988 No I could access most of the stuff I needed too, with the exception of a few books. I also bought a few books I didn't have to, just because I'm a sucker for the Springer hard cover and just wanted to own certain books I considered essential. But that's more or less my point a person who is not in Academia and wants to do some kind of a research is really out of luck, because they'd have to spend hundreds of dollars just to access all the references in one small paper.

[@jessdoritowhale]

As someone who is more into the feild of art, I find myself realizing how similar older math people and old artists are. The way both side talk, the way both side approach new information and learning and skill, are very very similar. In the end, when both sides reach almost their absolute peak, ive found how humbleing they both talk and speak about their craft. Both feel like two sides of the same coin. Some of the smartest people i know talk like artists, and the most skilled artist i know talk aproach their crafts like mathematician.

[@jksmusicstudio1439]

I dont think that mathematicians are elitists, it's just that they are aware of the huge effort one has to put in in order to understand the subject. Someone outside that circle might think of the mathematics community as a closed one, but it's not due to some sense of superiority, it's just that it's actually very hard to become a mathematician. Once you get your degree no one will exclude you, instead almost everyone will be happy to have a new colleague working in the field.

[@theguire]

Having failed the mathematics entrance exam at a community college, I was required to pass a basic math class. After failing the self-directed option - twice - I enrolled in formal class to get through it. Took me three semester to pass the math competency requirement. My major was Liberal Arts, which required three more math classes - advanced algebra, trig, yadda-yadda. While I was scared I would not be able to pass thoses next classes, the foundational skills I learned made the math classes easy. I ended up with B.S. in Mathematics/Computer Science. But, it was a lot of work for me. Many Saturday nights I stayed home while my friends went to parties. I still have my five three ring binders of handwritten problems. Good times.

[@rawadosa90210]

Good on you mate.

[@andrearueda2062]

stories like this are so inspiring thanks for sharing

[@Saturnia2014]

Do you have any advice for somebody who has trouble concentrating on their math studies?

[@uku4171]

@@Saturnia2014 Do you have trouble concentrating overall or just the math studies?

[@LowestofheDead]

If math was taught more effectively and intuitively, you could've achieved even more. It's amazing that you put in that work and succeeded, but you had no choice because other people decided to design Math education the way it currently is (The same way that bureaucracy at your local DMV is poorly designed). It's similarly inspiring when a refugee escapes North Korea, but ideally there shouldn't be communist dictatorships to escape from in the first place.

[@bertrandbarrois3169]

Four months studying “Baby” Rudin cured me of any ambition to major in math, but taught me that I was cut out to be a math user instead. Rigorists are obsessed with airtight proofs, whereas users gain intuition by studying definitions, examples, and counterexamples. Ironically, the rigorous style inflicted upon math majors is opposed to the exploratory style by which discoveries are made. Euler was no rigorist. Some say that Bourbaki killed creativity, but there is still hope. Nonlinear dynamics (chaos) is messy enough to defy rigor.

[@surrealistidealist]

As I've come to see it now, Math itself doesn't have to be hard. It's just hard in general to do any great thing like Math because it requires a lot of work, and it's simply hard to do a lot of work. And then it's also hard to communicate the product of all of that work, especially if you're trying to distill it for an audience that doesn't have enough experience or familiarity with all of that work. But all that being said, it's toxic if successful people don't acknowledge how hard they had to work, how often they've had to learn from failure, how often they still make mistakes, how fallible they still are, and how many other people deserve credit for their development and progress. A lot of elitism boils down to that. Some people are only able to devote so much time and effort to math because, for various reasons, they're social outcasts who don't get as distracted by people. Elitism can occur if they interpret their success as a way of paying back any real or perceived unfairness they experienced from others. Mathematical maturity is also very powerful, and I'm sure there are ruling class interests that don't want to make it easy for the masses to match or surpass them in this regard. So that's likely a component to elitism, too.

[@alittax]

I like how well you've articulated your position. Did you study any Philosophy?

[@surrealistidealist]

@@alittax On my goodness! Thank you so much! Yes, I did study Philosophy. It was part of my double-major with Psychology. Sadly, I never finished my degree, but I hope to go back some day. 🙏

[@surrealistidealist]

@Ruben Vegas How much math did you learn before starting undergrad?

[@alittax]

​@@surrealistidealist I'm sure you could do it. If you can explain things so well, then that's a good sign that you can get the degree. Just be determined. Best of luck to you! :)

[@surrealistidealist]

@@alittax Thank you again so much!!! I'm going to give it all I've got!!! 💪❤️🙏💪❤️🙏💪❤️🙏💪❤️🙏

[@thebluriam]

The trouble with math(ematics) on the whole, is that "scalability" of the field has never been considered meaningfully. By "scalable", I mean that difficult elements of the field are not intentionally simplified for wider distribution of acceptance. Mathematics, as a culture, seems to have an inbuilt desire to maintain it's historical levels of unapproachable abstraction. The cultural behavior within Mathematics of naming methods and algorithms after the people who discover/invent them is a good example of dirty architecture presenting itself. It is very difficult to mnemonically comprehend systems if the nomenclature of the objects within the system is based on something which is completely disconnected from the conceptualization of what said object does/is/behaves/acts as/is related to/is for/etc. In my mind, Mathematicians aren't "elitists" exactly, but most of them just not clever/smart/wise/courageous enough to do the extra work of helping the beauty of what they perceive and play within to be transferred maximally to the rest of our human tribes. The exception to this previous statement is the guy behind 3Blue1Brown, he does a LOT of the extra work to de-abstract and refactor the concepts without losing any of the deeper modalities. 3Blue1Brown is the Carl Sagan and Richard Feynman of our time, at least in terms of being an interface between most of the human population and the abstract beauty of the deep realities of the universe.

[@konarkmadan4782]

Underrated comment right here. On one hand you got math professors who love math more than they love teaching. On the other hand you got indian youtubers who treat it like a chore. But 3b1b hits just right. Him and Tibees are definitely the Carl Sagan and Bob Ross of mathematics. *edit: grammar

[@thebluriam]

@@konarkmadan4782 Much appreciated

[@costakeith9048]

I agree in part, but I don't think the nomenclature is the problem. The thing with mathematics is that historically it was one of the humanities. All the great mathematicians wrote books and, historically, mathematics was learned by reading their books. If you go back to a mid 19th century work on mathematics they will cite theorems by citing the book and the author (the mathematician who wrote it), generally with a prober bibliographical citation including the page you can find it on; this is how all humanities were done and generally still are, except for mathematics. Then in the late 19th century there was an attempt to turn mathematics from a humanity into a science. This movement was spearheaded by Hilbert and was the inspiration for such mathematical abominations as the Principia Mathematica. This is when there was a big emphasis on axiomatic approaches to mathematics and an increased emphasis on rigor and, in my opinion, when mathematics got screwed up. People attempted to categorize and systematize mathematics and rigor, which previously was nothing more than argumentation to convince people of the correctness of your mathematical statements, was turned from a mere tool for mathematical discussion into an end in and of itself. This made mathematics far more esoteric and convoluted than it ever was before or it needed to be. I don't know what the best solution to this problem is, ideally we'd get all the works of the great mathematicians translated into history so that it would be easier to take a humanities approach to mathematics once again (though you still have the problem that, in the 20th century, mathematicians got lazy and became more likely to publish papers rather than books, as they had in previous centuries). But, as things stand, some works have been translated into English and others have not, so you really need to be able to read German and French to fully delve into the humanities approach today.

[@ILoveMaths07]

@@costakeith9048 Wow! Thanks for that info! The Math Sorcerer should read your comment and talk about this. I wish I could tag him.

[@IsomerSoma]

I absolutely agree with the naming convention, but hard disagree with your take on abstraction.

[@cypher1333]

Henri Cartan made it to age 104. Some mathematicians live a long time: Dirk Struik made it to 106; Walter Rudin lived to "only" 89. They all had good lives and while I encountered only Struik, I tend to think they were all good people. Struik was hardly an elitist: his Yankee Science in the Making is perhaps the best book in that field.

[@TheMathSorcerer]

Wow interesting information. Thank you for this comment.

[@anthonyjulianelle6695]

Leopold Vietoris; as in Meyer Vietoris, lived to be 110 years 309 days.

[@drjenburgess]

Thank you for emphasising the hard work that goes in, there's such a societal discourse around "maths geniuses" that really affects the perception. Such an interesting video and comments. I worked so hard at GCSE maths (exams age 16 in England) and wanted to get the top grade but couldn't (and I get quite bad 'maths anxiety'), my husband on the other hand barely had to put any work in to get the top grade and he took Maths A Level (17-18yo) early. I find it so interesting how these books look like they're written in a different language but if you can't read a book in a foreign language you'd never say "oh you're clearly not smart enough" we'd say "oh you just can't do that yet but you could if you wanted to". Similarly people who aren't good at English Literature (like if they find it hard to write essays on books for example) don't get told they're not smart enough (not commonly anyway, I'm sure someone somewhere has been!), It's just "oh they're not very interested in that". But if you keep getting questions wrong in maths it's like that says something about you and your value intrinsically as a person. Anyway I'm still not good at Maths (I find fairly basic algebra hard tbh) but I'm still trying, just to try and learn something new.

[@jment34]

I think it's the obscure and verbose sometimes antiquated type of language math books use. I remember reading somewhere that it's on purpose and a very old habit of competition. The others could not figure things out so easily. I know for a fact that it happens a lot in music theory. What mathematicians could do is work together with language specialists and put those concepts in simple plain english terms. Many complex books could be completely rewritten that way it won't scare many people away the way it does now.

[@kylejohnson8447]

No.

[@matthewsullivan3804]

Yeah.

[@arsenalfanatic09]

The problem is that mathematical notation and verbiage is very useful for explaining precise concepts compactly, and you would have trade-offs needing to devote more space to explain every theorem in depth. It would make a worse reference book for the trade-off of being a better learning book. Really you need to read an intro to mathematical logic or proofs book to get more out of a real analysis book, even if you already have background in performing calculus and think you're ready for more rigour. The way to study math theorems is to have a lot of paper next to you and make notes to try and follow along the logic, and go back if you don't get something. Many books are pretty decent about citing already proven/used theorems from earlier in the book, and the compact language helps you flip back to these earlier concepts if you got lost somewhere in a proof. You just can't get around having to devote 30 minutes or more per page of text. Also doesn't help that many books don't really outline what you need to be familiar with to get more out of the book.

[@talrefae97]

If the most notable (supposedly positive) features of a book is that its "really tough" and "not for the faint of heart" and "takes a lot of effort" to read, perhaps the elitism criticism isn't very far off… We live in a culture where being challenging and unapproachable is apparently a positive feature. These are not the goals of education. They're the goals of elitism.

[@drjenburgess]

Top comment, this is very insightful

[@bm-br3go]

It surprises me how many people use Rudins books for beginning graduate level classes given how abstract they are. Almost every book on analysis that I've read (beyond the basic measure theory and functional analysis) has been much more down-to-earth, and quite frankly more user friendly than the Rudin books. Also, in almost every hard problem in analysis one always starts off with the basic, familiar spaces. For Banach spaces it's L^1(R) and L^○○(R), and for hilbert spaces it's L^2(R) and l^2(R). An intimate familiarity with these spaces is, in my opinion, more valuable than spending weeks discussing F-spaces, Frechet-spaces, and locally convex spaces.

[@srikanthtupurani6316]

To do well in pure math one should be blissful and should be free from all kinds of pressures. Most of the students when they learn math from books like loney, Bernard and child are under the illusion that pure math is is similar to the math found in books like loney trigonometry or hall and knight. When they read books like rudin they feel it is totally different from what they thought. things we learn from books like loney, Bernard and child, hall and knight etc are very important if we want to excell in pure math. The skills we acquire from these books help us in doing pure math. We need those skills if we want to be comfortable with inequalities in pdes, multivariable calculus. These books are very important even though they don't follow a rigorous approach. We will not find any epsions and deltas in books like loney. But the skills we learn from these books are needed to grow as a pure mathematician.

[@TheMathSorcerer]

Great comment thank you!

[@algorithminc.8850]

I can think of many times over the years, where someone's day was made by simplifying the cryptic mess they were taught (typically by people who didn't really love math, or had the "I am smarter/better than you" attitude/illness). I love seeing the "lighbulb" go off, when they understand something new - and their confidence is bolstered. I remember being at a wedding, and a lady bought me a nice lunch after explaining how a LASER functions - making people happy with knowledge can get you fed! Sure, a lot of math is complex ... it is an equal oppotunity heartache ... but much of it is simpler than many teach it to be ... and there's nothing like when it clicks ... why we like your channel. Cheers

[@mike777881]

I did engineering undergrad then did comp sci for my masters. While I cant speak too much for math majors specifically, I think stem has a problem where the way it is traditionally taught is not conducive for understanding. In undergrad I would constantly leave lectures lost and while I was able to outperform the other students just enough to get a decent grade, I rarely felt like I was able to intuitively grasp the subjects. I had just assumed that these subjects were too difficult to understand intuitively. However, with computer science, you have a wide collection of online resources available that just aren't present for high level engineering classes. So in these debatably more difficult masters level CS courses, I actually was able to develop an intuition for the subject from these online videos. At this point I don't believe any subject is prohibitively difficult, just poorly explained. And I think traditionally most textbooks and courses aren't designed to optimize understandability, adding to the perception of the subject's elitism

[@Creationweek]

Yes, math is probably the most elitest subject. I barely understood math in high-school, c's in almost all of the classes D in trig and D in algebra 2. I have a degree in anthropology partly to avoid math, but started in on statistics and probability. I randomly started watching math youtube and really fell down a number theory rabbit hole. I taught myself calculus and i am currently working through linear algebra now. It isn't easy exactly, but it isn't difficult either It's very fun and relaxing. the issue to the reputation is the emphasis everyone places on the "work" "difficulty" "this isn't for the feint of heart". Math is just another domain of knowledge it isn't difficult, but like every domain it takes time to learn. It's not magic it's just a precise language to compare, one thing to another thing. If it was not eliteist the emphasis would be on the time investment required to obtain the tools not on any value judgement inherent to the subject itself. No one considers trade school "difficult" but it usually takes a tradesman 1-4 years to reach journeyman and 12-16 years to master the craft. math isn't any different.

[@alaxel3222]

I had a math teacher in high school who was a super elitist. I mostly remember him getting frustrated that a bunch of high school kids just didn't "get" algebra without him having to you know, actually teach it to them. It was a very surreal experience because he'd go on about stuff none of us understood, then we'd spend our time basically having to self-teach.

[@alexandertownsend3291]

I think you misunderstand what people mean when they say someone is elitist. Elite and elitist are not the same. If you are elite in the math world, that is fine in my book. The issue lies with elitist people. Here is a definition: a person, P, is elitist if they belittle, mock, or make fun of those who are not as skilled as them, if they insist that the other person is not a math person because they haven't reached P's level of skillfulness, and/or if they try to exclude other people from discussions who they see as lesser to them because of a perceived inherent mathiness quality, rather than encouraging other people to improve their skills so they can make substantive contributions to a discussion. So an elitist isn't just someone who is good at something or renowned for a thing, but decides to be an asshole about it. Elitist as an adjective usually refers to the attitudes of such people. One can be skilled without being an ass. I hope that helps.

[@billmorrigan386]

I think most people will agree with what you are saying or they will at least agree that the word elitist has such connotations. So, I don't think there's any misunderstanding here. I would also add that an elitist is not necessary a pro (let alone high level pro). He or she is just a snob or, to put it bluntly, the word a...hole also fits the bill. What's more, they are often incompetent and stupid in my opinion. Most professionals (in terms of skills, not in terms of earning money) are not like that including virtually all areas: scientists, composers, writers, athletes, pianists, etc. Quacks and dilettantes are like snobs and elitists, the worse they at their areas of expertise, the more snobbish they are. Just an opinion.

[@alexandertownsend3291]

@@billmorrigan386 That is often true. If you go to any math forum you will see people asking very valid questions only to be made fun of for not knowing the answer to "easy" question. The person doing the insulting is usually only slightly more knowledgeable than the other person in spite of acting like qa god among men. A common phrase I hear from elitists is, "can't you figure out anything on your own". A better way to say that would be, "You might be overthinking it. Keep trying. You can do it."

[@billmorrigan386]

@@alexandertownsend3291 Yes, it's exactly like that, even on stack exchange. Or sometimes they answer a simple question in a difficult way (which requires very advanced math), or they may even give a slightly wrong answer or with some inaccuracies. The latter is often attacked by other trolls. So, they keep answers short or cryptic (or just look up the information in some book, etc.)The whole internet is like that. You hit the bull's eye. What's more, I think it holds for other sciences too to a certain extent. Now I'm gonna add somewhat extreme statement (my opinion): the most extreme cases of such elitists, trolls and snobs are usually the moderators themselves.

[@TechnoW1zard]

After seeing and listening to this video, observing you derive pleasure from the smell of the math book: whether elitist or not, "math people" have a certain frame of mind and usually an above average emotionally stable background in their younger years. Probably from families with above average incomes. My parents got divorced when I was young and one of my parents really gave me a lot of math anxiety while trying to "help" me with math homework. Those events in my formative years still are a huge stumbling block to my math skills improving. I get all worked up in an emotional knot when faced with algebra and pre-calc

[@twentylush]

Not a math major but currently work often, in an academic setting, WITH math majors. I've interacted in broad spectrum with many across all disciplines and worked in teams where Kineseology students were working every day with ChemE and Stats students. In my experience there certainly are math elitists, but the correlation is not necessarily in how much rigor they have in their studies or how much they know about a certain subject, but rather how often they have worked with other disciplines and other people in general. I've met math undergrads who frankly seemed to be elitist out of clear lack of self-confidence and drive to be great, and math post-docs who intently listened to me talk about boring engineering project-related subject matter to the point of taking notes(which really blew my mind). Those who tend to be more personable, empathetic, and easy to work with always have a sense of wanting to know more. Those who tend to not listen, criticize, and are hard to work with always seem to think there is nothing more they can learn. The Dunning-Kruger effect might be totally pseudo-scientific but it is certainly useful to have something that describes this phenomenon :)

[@TheMathSorcerer]

Great comment, thank you!!!!!!!

[@JCCyC]

One way you become an elitist is thinking you're in some way "superior" because you're good at something. Writing a book and starting it by assuming the reader knows abstract algebra isn't that, it's just a practical decision about what audience you're focusing on in that particular work. Being aware you have skills X and Y and putting that to a useful purpose is perfectly OK, but you have to be constantly vigilant to not let get to your ego. Every human being who's a part of society is every bit as important as you. No more, no less. Never forget that.

[@TheMathSorcerer]

Wow, great comment:)

[@jayaprakash387]

Hey he made a video on your comment!

[@JCCyC]

@@jayaprakash387 Say WHAT?

[@JCCyC]

@@jayaprakash387 Holy crap!

[@martinhawrylkiewicz2025]

You are quite correct, the 3rd edition of Baby Rudin now has Dedekind cuts in the Appendix. I have all these books btw! My treasures!

[@TheMathSorcerer]

Awesome!!!

[@peterkistler3537]

I think elitism is present in any discipline, and it's most noticible in especially difficult or challenging disciplines. Math is no exception. I also think any type of elitism is always unjustified, and any discipline would benefit from less elitism about it, because it's so often used to gatekeep and prevent others from practicing the discipline. I think math is a great example of something beautiful that gets disregarded by newbies because the people entrenched in mathematics don't take enough time to introduce newbies to the coolest parts.

[@evanurena8868]

In addition to you're great points, I also think the gatekeeping elitst mentality stems from many parts of the world , especially America, who keep immaturely clinging on to a cultural attitude of a math hierarchy in which one must be arithmetically competent for seven years and do drills before they can delve into the logical foundations of proof and applications that generalize patterns of such numerical processes that are overall more central to math. Moreover, its why l personally believe algebra can be learned as early as fourth grade and is often more important then learning how to be a mental calculator that calculates big numerical quanities. Why do i have to waste my precious time for several years in grade school learning to multiply 3 or 4 digit numbers or decimals as opposed to learning how to formulate an algorithm or computer program like python or matlab that focuses on the numerical analysis of appling these numerical operations or the algebraic communitive property , (a prelude to abelian groups), of multiplying such numbers?

[@peterkistler3537]

@@evanurena8868 absolutely!

[@mmcmdcab]

This guy really feels what I feel about these books and math in general. The feeling of challenge and enrichment when studying these great references is unique, difficult to explain to other people. Thanks for sharing this experience with us. Thanks from Brazil

[@TheMathSorcerer]

Np, thank you for your comment:)

[@benhill3098]

Whenever I tell people that I'm a math major, they say, " Oh, you must be good at math." I tell them, "No, I'm not good. That's why I'm in this program; to get good." I, for one, am quite a humble learner and hope to stay that way 🙂

[@Daughter0fTh3King]

❤️ you must enjoy the process then!!

[@benhill3098]

@@Daughter0fTh3King I enjoy the challenge! 😄

[@AlejandroKar98k]

as an engineer student i really love to study mathematics in its pure form, sometimes i buy books like yours to see how many of it i can understand, oh boy my respects to everyone who can understand even the first chapter

[@peterodonnell4404]

My education is in computing and engineering, but some years ago I began to work as mathematics and science teacher. Since it was a school for foreign students, it was my job, primarily, to prepare students' language so that they would cope with their mathematics and science classes at their regular schools. That experience helped me think a lot about the problems all students face with mathematics, and I came to the conclusion that at least half the difficulty faced was understanding the *language* of mathematics. They would look at or listen to the problem, and very often simply couldn't understand its symbols or arrangements or language or semantics. They would not get so far as to think mathematically because they couldn't grasp the fundamentals of the communication. And it struck me that the language is seldom taught in mathematics class, let alone being the focus. Rather, it is presented as though it is self-evident. That observation led me to alter my mathematics teaching, and I have seen even self-described "non-mathematics" students suddenly beaming with confidence as they look at a complex expression and understand it. We would all do well to remember that mathematics is as much about communication as it is about solution.

[@TheNAWorks]

These are going on my reading list. A few months ago, I was watching a physics video that referenced the book "Lorentzian Wormholes" by Matt Visser, and I was immediately intrigued by the title and incredible cover art; I had to get a copy. Well, when it arrived, and I opened it up for the first time, it was like hitting a brick wall! Far beyond the purview of my computer science/mathematics undergrad degree, to be sure. But it is still a beautiful book, and it has sparked a personal quest for me to learn enough to actually be able to read it. A little intro to analysis could help!

[@imacds]

The Baby Rudin book looks really fun, I will definitely check it out.

[@valor36az]

Sir what a great motivator, you described the grind so accurately .

[@mathopo237]

I won't say that Complex Analysis is complicated to read because it's rigorous. I would say that it's complicated to read because the author doesn't present all the details in the text. There are a lot of missing steps and you have to fill them out by yourself. Sometimes, the steps to fill out are not obvious! My comment also applies to Rudin's text.

[@TheMathSorcerer]

good comment, thank you:)

[@reishiboo]

I‘m still in school and I don’t even plan on studying math, but I loved seeing someone displaying his passion for math as a matter of course!

[@davidnoll9581]

Controversial take, but I think the concepts aren’t nearly as difficult as they are made out to be, and it’s more about memorizing vocab and conventions than anything. Once you’re introduced to the infinite series for the exponential and how it relates to Euler’s formula etc, it’s hard not to understand it… the problem is just that those explanations were for some reason not widely available outside of elite universities until a recent explosion of math KZbin videos. Modular arithmetic? Kids can learn a lot of it as easily as non-Modular. But we just don’t introduce it to them. In fact it might help with other arithmetic to teach it first

[@mettaursp309]

Yeah. To expand on this, the bane of my existence is when papers or pages use proprietary notations, use advanced steps from other fields of math as steps with no explanations, or otherwise don't just properly explain themselves. I said this in another comment somewhere here already, but there are a lot of times where I'll go do a quick fact check on something I already know on something like Wikipedia, but the notation used is often needlessly complex. If I spend enough time breaking it down I'll often find that I already know the meaning of what it is saying, but the presentation got in the way of conveying the information. I've found that places like Wikipedia in most cases are really bad for learning something and are only ever understandable for concepts I already know. There are some exceptions, but I've found it to be a very consistent rule of thumb. A lot of places where math information is posted is seriously lacking in communication skills.

[@stevemenegaz9824]

Good choice of books (mostly). Good mathermaticians are not elitists. They simply have put in the necessary hours with a lot of enthusiasm. If you study math in a diligent and thorough and intelligent manner, reading every word in every line and understanding it, it will get easier with time. Ahlfors book is very pleasant and is written to be understood. Cartan's book is beyond me. Richard Feynmann, both a great mathematician and physicist, is my inspiration.

[@3koningen]

On my shelf are: Foundations of modern analysis by Dieudonne and Einfurung in die differentialrechnung und integralrechnung by Landau, both among the worst of elitist math books possible. Look at what Courant, for instance, can accomplish in a very non elitist way.

[@user-sf9gs2pg1b]

A lot of math people I see are elitist online, but I also see a lot willing to help others learn. It really just depends on the person.

[@jamesn.5721]

I recently graduated with a BSc in Maths. For three years and counting into my masters, it genuinely feels like every different subfield within Maths has a very loud yet justifiable need to be as important if not perhaps more important than a closely related yet potentially entirely different subfield. I felt this through the similar mathematical language used across everything I use, yet how the language is used can vary massively. I had a module on percolation theory, one on PDEs, and another on mathematical biology, as an example. One uses ridiculously abstract concepts to justify solutions, another uses even more abstract concepts to prove statistical results. And while these subfields can all agree on many things including the methods and language used, they are on their own entirely unique fields. Yet, as obvious as it might seem, each field adopts the language so similarly yet quite differently, and in many cases being proficient in one more than the other can make it seem like the former is better or more higher potential if potentially less people are able to grasp it properly. When properly exposed to multiple fields within Maths as all maths under/post-grads, PhDs etc do, I don't think we mathematicians are elitist to each other (at my level at least, in a Masters course), but may understandably seem otherworldly and potentially 'elitist' when we lose the interest of attention of someone who may not have delved into Maths as much as we have. After all, Maths definitely isn't easy, as many have pointed out, and it is certainly difficult to share our love of this mysterious language the way we understand it to someone who have not seen it the way we have. P.S. To make sure the last part is conveyed properly, it certainly isn't the fact that we think non-mathematicians aren't capable of understanding what mathematicians do, but the methodology of the effort mathematicians put in to understand is definitely fairly unique but is certainly achievable with the right mindset, attitude and right amount of hardwork, as all mathematicians are willing to invest into throughout their academic careers. P.P.S. definitely a personal opinion based on what I have experienced at least in a European academic setting. Certainly I cannot speak for the rest of the academic community of Maths, as Im sure the amalgamation of different nationalities, cultures, people at different academic settings all around the world will produce different perspectives and undertones of how mathematicians are perceived.

[@LowestofheDead]

Do you think academic funding affects this? It would make sense if different subfields are competing to prove themselves as more worthy than others.

[@josephjagusah8668]

"Mathematicians are elitist because they're better than you." Fixed it for you.

[@Dutchsnake5]

I feel like the problem with mathematics in an educational setting is how often we're taught material in a class, and then subsequently the next class barely mentions much of the previous material. Sure, Calculus is just an evolution of basic Algebra, but it's not the most important part of that class. Not much of what you learn in Algebra, and even Pre-Calculus ever really builds into it unless you're taking several Calculus classes in a row. It's a very harsh and sharp learning curve for many as a result. What also can make it more complicated is how teachers/professors with these more complicated math subjects may be brilliant at them, but can't find the words to explain all of the mechanics that go into them. While it is no doubt the student's job to seek out information and study it in order to get better, having a teacher/professor who can comfortably explain their material in easier-to-digest wordings and lectures helps tenfold, and having a bad teacher/professor can really demotivate you from wanting to get better at it. Another fundamental issue of mathematics classes as a whole is the odd lack of freedom. This may just be a problem in classes before later Calculus, but a lot of teachers expect you to solve a problem in their way. The problem, of course, is that math has multiple different avenues that allow you to get the same answer in a logical way, effectively allowing different people to use a favored or multiple kinds of methods. Teachers that expect students to show their work on assignments, in my experience, would dock you for not writing absolutely every part of your problem solving correctly, or by using the "wrong" method. I understand the intention is to challenge students to solve problems in new ways that change how they think about the way they solve math problems, but it ends up alienating and confusing even more people since now they have to throw all their understanding out in favor of forcing themselves to think in a new way the professor expects them to, even if it doesn't help them fundamentally. I just think the field of mathematics needs to humble itself and re-think how they deliver their material in textbooks and lectures.

[@KC-dw6yz]

Am only math-adjacent (physicist) but it's cool to see the 'bibles' of mathematics (in particular both Rudins are so famous even we know about it)! If you want some equivalent 'standard reference' in physics you have Jackson's 'Electrodynamics', Sakurai's 'Modern Quantum Mechanics', or Landau's 'Mechanics'

[@mastershooter64]

I was failing math in 7th grade but then i found math channels on youtube in 8th grade and then I was doing linear algebra and multivariable calculus in 11th grade lol yea your perspective of the subject can make a huge difference

[@DiamondANDI]

Many math people get angry when somebody doesn't understand something that is obvious to them (because they are several levels above in terms of knowledge, not because it was always obvious to them). Then they act superior and often indirectly call you stupid, instead of explaining. I haven't met a mathematician that could explain math well, in terms of geometry or common life situations, which can definietly be done. My major is pure math btw, and I experienced this frequently at the beginning few years of my studies.

[@allenofatlanta]

I usually associate elitist/elitism with a social hierarchy. However, there are strata of academic orders. My thoughts are that people in general brandish these terms to absolve themselves of not understanding a subject. Or, in an alternate perspective, use it to place the subject upon a pedestal to enshrine as an unobtainable quest for many people. Whether it's reverence or fear enjoy the limelight of the respect afforded you for your efforts. Mathematicians should gleefully embrace similar to the notion that diamonds " are rare." That is the believe that increases their value!

[@billmorrigan386]

Could not agree more.

[@luislopez-tx4tl]

This question and its responses are focusing a little too much on the individual and missing out on the institutional and societal level of what makes mathematics and a lot of the people in it elitist. Also for what is explained, I don't think elitism is the best term either. Oftentimes, you may have the potential to be great at mathematics (or anything really) but the demands of our lives often take a greater precedent over studying mathematics. Being able to sit and study for 1-4 hours on a given day isn't something any regular person in the U.S. can do. Most people can't afford to sit for an hour to just study mathematics let alone 2 or more. The language of the books is mentioned aside. What feeds into the elitism in mathematics is the social standing of the people 'doing' the mathematics. You're more likely to encounter someone that managed to complete a university degree (B.S) who comes from a middle/upper-middle-class family or higher than someone who is low income. And a lot of the values from people in the middle/upper-middle is the perceived idea of, 'if you work hard enough you'll make it. This is, on one hand, sorta true(barely), but misleading. You can work hard while staying at your parent's place and not worrying over finances while they do that work, meanwhile, someone who isn't middle-class can't afford to do that, and coming home from work to study mathematics is rather exhausting. Often people search for an example of someone who was in that circumstance and made it work ignoring the dozens, if not hundreds of people that it didn't work out. To diminish elitism in this or any field would require more than modifying textbooks.

[@jmcorpuz1]

This is a really good socio-economic view on this topic

[@PhrontDoor]

I love that display of the sheets covered in math.. I found that mistakes are about the most helpful part of math. Assume that you find, early on, that you quickly see that you can tackle this in TWO ways.. and you are newish, and just pick the 'wrong' one first. Firstly mistakes give you the opportunity to do MORE math. While you grind through to a possible dead-end, you've had to get there by doing more math. And each step might show you, more and more, precisely why this was the wrong path to have taken, and will hopefully show you how to know (next time) how to more easily make the RIGHT decision.

[@arnavrawat9864]

What you said about in the first part of video rings true. When you put a lot of effort into getting good at something, you feel accomplished. That creates a self image or an ego around yourself that you're a good mathematician. And that deserves respect. The elitism originates from that I think, wanting to be respected because of esteemed you consider yourself. As well as the desire to gatekeep the superior class you consider yourself to be.

[@virajkhatri7574]

this is NOT why Math is an Elitist field. Mathematics is for Elites only because it doesn't matter how good you are at math, your research papers won't matter if you don't have a PhD. If I solved the Navier Stokes problem, I would not get full credit if I did not have a PhD because no one would read my paper unless if I had a PhD reference who wants to steal credit from my paper.

[@dd-uf9nw]

I like mathematics mostly I self study but I can't say that I'm very good at it but i like the subject that's why despite failing so many times I don't regret or get frustrated .... And I have learnt most important thing is keep doing mathematics and keep practicing because I know much more now that I knew previously like any skill you can learn mathematics you just need time and focus. I also done some chapters from baby rudin and try to solve some exercises from it but I'm not completely satisfied i will go on second run and channel like yours has kept me motivated to do learn more so thank you for that.

[@Trixex]

They kind of are, just today I asked a math question on the internet and they told me that I shouldn't care about it because I'm a physicist.

[@jmguevarajordan]

Rudin and Cartan books are written in a bourbaki's style. Those books are very hard to read. They are presented as textbooks although they are not written in a pedagogical way (if you can find a figure in Rudin's books let me know). Ahlfors book is different from the other three. His book is more pedagogical, the ideas introduced in it are well motivated and its exercise are well selected. Ahlfors book has kept its position along the time as a solid and pedagogical introduction to complex variable. Ahlfors got a Field medal and that makes a difference. He wrote his book thinking in the students. Rudin and Cartan wrote for mathematicians or very advanced math students (an 'elitist' group of people).

[@joechamm]

I was taking a conference course with "Papa" Rudin (aka Real and Complex Analysis), and I couldn't believe how hard the book was for me. I would sleep through class to an A in my calculus courses, but this book made me want to cry at first. I have to check myself because it's very easy to feel elite because it's so far removed from almost everyone else's mathematical understanding and that sense of superiority tends to creep up on me. That's usually when I get brought down to earth. I was working on some problems at the pharmacy as I waited for them to fill an order and the pharmacy tech asked me what I was working on. I showed him the book, and he was like "Papa Rudin... nice"... Looking back it makes me laugh, because I was such an ass. I was thinking, this pharmacy tech isn't gonna have any idea how hard the thing I was doing was... lol, thankfully I've had plenty more experience like that to finally get it through my head I'm not as smart as I thought I was.

[@kevinthompson9953]

In the 3rd edition of "Principles of Mathematical Analysis" (baby Rudin) the Dedekind Cuts discussion is in an appendix to chapter one, and starts on page 27.

[@feraudyh]

I very much like your attitude to learning mathematics. Cartan's book Elementary Theory of Analytic Functions of one or several complex variables Is available in Dover Editions. I will say it's probably not the most accessible intro to the subject. I was quite happy with Erwin Kreisig's chapter on the subject. Henri Cartan wrote another classic called Cours de Calcul Différentiel in French. It starts off by assuming that all differentiation will be done in the context of Banach spaces, so it's not your average basic intro. It has been translated into English for Dover (again) but in two parts. There is a typo on the very first page of the French book and this got translated without correction into English, which means I don't have a high opinion of the translators. The error concerns the norm of the product of an element by a scalar. It should read something like || A V||=|A| ||V|| Where A is the scalar. One of the problems with Cartan's books is that he often just hints at the proof and the reader needs to fill in the details with pencil and paper.

[@ivankaramasov]

Rudin's Real and Complex Analysis is the best math book I've read. It is incredibly elegant and terse and therefore also pretty challenging. I decided to use this book also for complex analysis since I found it better than Ahlfors' book.

[@Αλέξανδρος56]

Nicolas Bourbaki actually left a legacy that makes french math books very hard to get through even to this day

[@sheenoreiki7843]

I felt relieved when I saw this Elitist series, I came to watch from the 2nd video, I always think that I am a slow and dumb idiot despite I am interested in it, up to recently I felt like a zombie and plan to give it up at some point. Until I heard you said Math is difficult, despite it does not improve my math knowledge, it at least somehow rekindled my spirit, I know I am highly unlikely to lead nor help someone in math, but at least I ain't falling behind if I could be useful, I don't know what to say other than a million times THANK YOU

[@metildajoseph5265]

Greetings Mr. Professor, Thanks for the Wonderful Insights into The World of Mathematics in all aspects. I agree with the fact that Mathematicians are Elite, Socially Detached and connected with subject - Mathematics in every aspects. With regards, RanjithJoseph (R.J)

[@virajkhatri7574]

Mathematics is not hard (especially if you love the subject), rather there is no respect for it outside of Elitists who believe knowledge should only be permitted to the 1% rich.

[@jacoboribilik3253]

Apostol's book Mathematic Analysis is also an excellent book and as rigorous as a math book could possibly get.

[@TheMathSorcerer]

Yes I love that book! I was looking at it a few days ago👍

[@johnflorio3576]

We used that book in graduate school. It was awesome!

[@lmntcrnstn4970]

Apparently, Kit-Wing Yu has written A Complete Solution Guide to Real and Complex Analysis I (a complete solution guide to all exercises from Chapters 1 to 9 in Rudin's Real and Complex Analysis) and A Complete Solution Guide to Real and Complex Analysis II.

[@radimnechut519]

Mathematics is hard, rigorous and exact. It demands a lot from you. But some of the kindest most humble and selfless people I have met were mathematicians. From high school to college. My maths professors always tried the most to teach me something, or to put it better, did the most to help me learn maths. I am studying chemistry. Professors I respect the most are my maths professors, and not for the subject they teach.

[@TheMathSorcerer]

great comment, thank you!!

[@ermiasawoke192]

Thank you, sir! Now I'm in the middle of Calculus. And it is a great motive.

[@justanotherguy469]

What it takes to get good at anything is love for that discipline. Studying math for me, is pure pleasure.

[@brandanvaquerano5809]

Thanks for letting me vicariously live through you while sniffing book paper.

[@dydx_]

Math reminds me so much of art. In does so in that it takes a shit ton of failure, headaches, humbling yourself over and over again and over and over again and over and ov... until one day you you reach that point where your pen appears to be gliding through all of it, like it became part of the motion, became the breeze itself. What I love so much about this analogy is how the correlation between these two fields is also partly causality. It was an architect who revolutionized art when he came up with the proper way to draw in perspective via calculations, and then later a painter who introduced his technique into art. Another similarity is how the competent and good in these fields are always labeled "geniuses" by those who lacked exposure to the fields. It's ambivalent, simultaneously pleasant and sad when your average person does not know about the vigorous studies you have undergone to reach such a point in your craft. The sweat it takes to even get to a level where you appear to be halfway competent is flabbergasting. I think math & art are referred to as high barrier of entry disciplines. I love math, but over the years my brain's pattern recognition aspect has found more pleasure in languages, yet this video somehow makes me wanna revisit the field again. Thanks for that!

[@andreshombriamate745]

Rudin wrote another famous work, "Functional Analysis", which is, in fact, much harder than "Real and Complex Analysis", but still one of the most accesible and self-contained books on the subject. I think it deserves the name of "Grandparent Rudin". Actually , all the books you showed were world-wide known. I have all of them, and also the other one I mentioned before , in their Spanish translation . In my opinion, Ahlford´s one is probably a little bit outdated, but the others are still first choices in the corresponding areas. Cartan´s book has the additional advantage of including all the properties of several complex variable functions that can easily be proved at an elementary level.

[@ivankaramasov]

I actually disagree that Rudin's Functional Analysis is the hardest of his books, but I don't think it is as well written as the others. When learning functional analysis I decided to use other books as for example Gert Pedersen's Analysis NOW which is also extremely terse and rigorous

[@andreshombriamate745]

@@ivankaramasov I haven´t read the book you mention. So, I´ve no oppinion about. The most complete "general text" in this area is a Soviet text "Theorems and Problems of Functional Analysis", written by Kirillov and Gvichiani. I have its French translation, which is still available in Abe Books (~40$) and the Russian edition (that I bought in what was still called Leningrad for less than a dollar). It covers also mesure theory and a brief but clear introduction to Fourier Analysis with 828 problems whose schematic solutions ("Indications" is the name of this part of the book) span over 80 pages. If you read Russian, as your nick suggests, the original title is (" Теоремы и задачи Функционального Анализа" Кириллов, Гвишиани, Изд. "Наука"- Москва).

[@ivankaramasov]

@@andreshombriamate745 Unfortunately, I don't speak Russian and I have stopped doing mathematics. But thanks for the tip anyway.

[@robertjenkins6132]

All 4 are analysis - blah. Not my cup of tea. I think "rigorous" is not necessarily the same thing as "difficult." If a textbook is difficult, it might be because it has a lot of prerequisites (which the reader might be missing), or because the author is excessively concise. As an author, maybe you want the reader to fill in some details: maybe it will be good mental exercise. But on the other hand, excessive concision might make the book unnecessarily difficult to read. So a balance is required. My favorite books are books that are both rigorous and easy to read, even if you occasionally have to fill in a few details here and there.

[@bruhsama3538]

Thank you for saying this it showed me what it takes to learn mathematics.

[@PerScientiaAdAstra]

..."Are math people elitist?" I'm unsure what the latest statistics show, but I'm willing to wager that mathematics majors still only make up a very small proportion of all graduates. Why? Probably because mathematics is, for most people, very hard work. But, more importantly, math requires a deep curiosity about how the world works. It requires inquisitiveness, dogged determination and much (for want of a less overused word) passion. Let's face it, there's a lot more money to be made persuing much easier degrees, so no budding mathematician goes into it for the remuneration. So why math? The pursuit of elitism for its own sake? By and large not likely. Some mathematical figures throughout history even pursued math to the detriment of their potential earnings. Some even lived frugal lives. While those less interested, or perhaps less capable, souls around them chose to chase wealth and status instead. All in the name of elitism? No. I believe every "math person" has within them a burning desire or thirst for the pursuit of truth and knowledge for the fundamental nature of the universe. This, above all else, is what drives most mathematicians to follow such a noble and compelling vocation. Are some math people elitist? Surely. But they are likely few and far between, and rightly so.

[@Miguel-pq9hz]

Gatekeeping? Yes, maybe. But you can always find more pedagogical approach to those books. These elitists' books have very specific audiences in mind and if you are not one of them, it is not anyone's fault. Also, there is more to maths other than the most obsessive-compulsive part of maths (analysis).

[@TheMathSorcerer]

Excellent comment !!!!

[@tauriqabdullah6130]

I started using paper with no lines and I love it!

[@TheMathSorcerer]

awesome!!!!

[@dong8912]

4:20 yep, instead of Dedekind cuts, the newer version instead has Ordered Sets and Fields in chapter 1.

[@TheMathSorcerer]

Cool👍

[@spectre7769]

I was decent at math back at grade 9, but due to mental health issues that only seem to get worse and worse, i essentially skipped 1-2 years of school. I don’t have a GCSE math grade, i barely got through AS level with a C (even with the advanced info bc covid) and now I have to force myself to understand this foreign language so I can get into uni for computer science. I have no other choice bc most unis require a maths at B grade or higher. It really doesn’t help that all my friends are straight A students and the type to still ace an exam even if they barely revise. Its just so hard to understand maths without knowing why it works the way it does, or why is something done in a certain way.

[@Victor-tl4dk]

I think math can definitely be elitist. People good at math can invest their time into it. That's elitist for a lot of people who have to deal with bad mindsets around them, things to do, and quick dopamine giving them real results. Math is a slow and humble thing that people considered "elite" can do more easily (ie. actually do it.)

[@joehinostro2459]

Nah people must pay attention as to not get carried away. People's feelings do matter. The issue is perspective. If you been studying math for a while, things that seem like common knowledge or basic may not be and explaining it to someone may alienate you from others. I speak on this from my own experience. All the books we read and dense text leaves us talking differently and thinking differently. Recently I have been making a mindful effort to use simple words and not to explain mathematical situations. Life is teaching me to just let people be. If they don't want to know, they don't need to know. From my own experience it is just a misunderstanding from both sides.

[@evanw5572]

I think that academia in general can be very elitist, but you're right in that inaccessibility due to requiring hard work to learn is not itself the problem. Hard work can make something inaccessible, but that's a problem for society in general (people not having time on their hands), not Math as an institution. What makes academia elitist is due to: -Internal inaccessibility caused by social status restrictions (e.g. getting into Harvard because you know the right people or because your parents are rich). -External inaccessibility caused by Mathematical study going towards topics & applications that primarily serve the ruling class, rather than ordinary people. One thing that has been nice in the past few years is youtube has made complex academic subjects a lot for accessible due to people making video essays.

[@khaiylahwiththestyla8722]

This is a very interesting question! I just finished an REU at an Ivy League school. Half of the mathematicians were from the school and the other half were not (I was part of the group who was not). From that experience I realized it all depends on how you’re taught math. The students from this school were taught math in a perspective that valued research over pedagogy and their mathematical communication skills reflected that. They weren’t clear in sharing ideas/proofs and treated others poorly. It felt like these very nice people had a switch flip in their brains when it was time to do math that said “if you don’t get it, you’re not worth the trouble of helping you get it.” But I think this was subconscious! (I assume) They simply reflected the poor behavior of their instructors who probably did the same wrt their instructors. Many higher-performing programs focus on research and choose their faculty according. The prioritization of research causes proofs to supersede people. Anyway, this is my long-winded way of describing the specific brand of elitism you find in math, in what communities you may find it, and why I think it’s found there.

[@mathformortals7043]

I'm not sure 'elitist' is the word I want to use but your video sparks a thought I've had before. There are a few popular math books that are good in terms of content covered and exercises given but they are TERRIBLE (and I mean SOOOO TERRIBLE) at teaching. Honestly, I don't like any of Rudin's books for actual learning. I like to consult them as references and also for picking up pieces of knowledge AFTER having learned the subjects elsewhere. There are many better books out there that are less terse and just have so much better exposition. Some of them are published for free too! I think the tradition of always assigning these books as main references is problematic in Math across the world. Frankly, those books can be used as syllabuses for what you should go find elsewhere.

[@insylogo]

oh god, your hand writing is almost identical to mine - it was giving me flashbacks to courses a decade ago to see you thumb through the pages

[@TheMathSorcerer]

Lol

[@brahimoukhouya3409]

I used to do math in french, now I'm eager to dive in deeper with these English textboxs. Thank you! Because I was tirelessly looking for challenging ones but I always get disappointed. And they sure seem interesting indeed.

[@mathdbase]

I was initially surprised when you said that a Rudin book was used at the level of Advanced Calculus. When I studied math over 40 years ago, we used Advanced Calculus by Buck (my professor recommended additional reading in Spivak's Calculus on Manifolds "for fun"). I had never heard of the "Baby Rudin" book, since we used Real Analysis by Rudin in the next level class. Around the same time, we used the Ahlfors Complex Analysis book and then later, Functional Analysis, also by Rudin, all at undergraduate level.

[@idiosinkrazijske.rutine]

Yes you are right about chosing the title of the video and these books illustrate it well. I would call whole this style the French style, Bourbaki and its members influenced this in particular.

[@idiosinkrazijske.rutine]

Remember that quote, that an analyst should be an analyst and not degenerated sort of topologist. I forgot who said it though but I understand his frustration.

[@swathi332]

I am pursuing mu Post Graduate studies in Math.. We have the principle of Mathematical Analysis book in our syllabus... I literally fell in love with this book.. It is a reader friendly book opt for self studies... It starts from so basic like what is a set? and go all the way through open sets, closed sets. Lovely book❤️

[@mitrikoudsi8060]

Great video! Thanks Sorcerer!!!

[@TheMathSorcerer]

Thank you!

[@ariston111]

Had probably a 4th/6th-grade education in math at the beginning of 2022. Studied for six months, working with a tutor that was studying for her P.h.D. I sometimes did 125 problems on a certain skill a night before the next session the following day. Had to go through most of Algebra-1 and Algebra-2. This fall, I am learning trig and taking a calculus-1 course. So far, my grade is 99.57% in the class. While being tutored in algebra-1 and algebra-2, I counted how many notebooks I was filling up for my practice problems. That only lasted so long until It was too many. I ordered bundles of notebooks from amazon multiple times, and they filled up pretty quickly. It is no joke with this stuff if you want to learn it. Literally, no joke - hard work pays off.