How to learn math | Jordan Ellenberg and Lex Fridman

[@8rboy]

I started doing high school maths when I was 22. I am now 24 and this fall I will start my studies in mechanical engineering. It’s never too late

[@keith3499]

Best of luck to you!

[@thenameisshubhamsingh.]

I am 16 and haven't started yet. Thanks. I thought that it's too late!

[@8rboy]

@@keith3499 Thanks my guy!

[@8rboy]

@@thenameisshubhamsingh. Don’t worry, you have plenty of time. You will kill it 🤟🏻

[@joesteadman343]

Hey man I just gotta tell you something.... I'm proud of you. Good job, man! I need to follow your footsteps. Keep it up. We were given the chance to live this life as humans. We'll walk this Earth on a never ending journey to learn more.

[@AitoNitram]

I was 26 when I left the military to go back to school, I did a pretty rough prep. year of maths, physics and chemistry to be able to do engineering. I'm now in my third year of my five year long degree, going for a masters in engineering physics. I'm not the best at it, but it's going well and I'm enjoying it a lot!

[@cia9648]

Keep going, I see your profile pic is the engineer from studio ghibli!

[@deltax7159]

@@cia9648 going back as an adult is night and day. Congrats on the success. You will love graduate school. Really fun time.

[@graysonjurado4128]

What branch and why did you pursue the engineering physics career?

[@royalewithcheese9257]

@@AitoNitram same here! From Army airborne infantry to developmental math. Literally learning to properly work with fractions to Calculus 3 is crazy. Aerospace eng life🫡

[@WillNewton10]

Discovered math was cool at age 21. Finally at 33, went back to school and got a math degree. Just finished it.

[@junjunjunhahaha]

Congratulations on your math degree! Your dedication and perseverance are truly inspiring. Keep reaching for your dreams. 😊

[@davidc4408]

What career are you doing

[@WillNewton10]

@@davidc4408 software development, AI

[@siimseiin]

This comment really motivates me as being on the same path. Let me know if you wanna connection

[@WillNewton10]

​@@davidc4408software development, machine learning, AI

[@ReflectionOcean]

- Identify personal learning preferences to enhance math understanding (Start: 0:33) - Read math textbooks if that suits your learning style (Start: 0:44) - Explore Martin Gardner's books for a playful approach to math (Start: 0:54) - Solve contest-style problems from various books for motivation (Start: 1:24) - Watch well-produced educational videos for a different learning format (Start: 1:35) - Use real-world problems to drive your math learning journey (Start: 2:42) - Embrace the difficulty in math as part of the learning process (Start: 3:15) - Push through frustration and uncertainty to achieve understanding (Start: 4:34) - Learn to appreciate the post-challenge satisfaction in math (Start: 5:17) - Accept and navigate dead ends as part of the learning process (Start: 5:50)

[@SgtSnausages]

As a CS student in the late 1980s and early 1990s I would randomly attend courses I wasn't enrolled in out of the Math Dept. If I had an hour or two break between actual scheduled classes, I'd find a math class I could just randomly attend without actually registering for. This lead to a few questions from professors come mid-term / exam time ... as well as two invitations (both declined) to switch majors. Mathematics is Amazeballz. My Wife still makes jokes in my general direction because I read Math textbooks daily while on the shitter ...

[@royalewithcheese9257]

Started “learning” at 27-28. Started my Aerospace engineering journey at 29 in developmental math. 31 today and finally in calc 2 🗿. Perseverance conquers all!

[@fezzlol]

Hahaha same here, 29 starting on mechanical engineering. I new I wasn't alone. 😅

[@NITROUSOXIDE921]

keep going sir

[@Krim_101]

⁠@@fezzlol same here , 29 and starting civil engineering

[@entwist_]

Thanks lex I needed this one. 29 and did 2 semesters at community college and hated it. Been teaching myself since then with online courses and algebra and calculus are the current and next phases. Been tough but been pushing through.

[@briansanchez6699]

I hope you keep pushing man. Time goes by so fast. Stick with it and you’ll be so grateful you didn’t wait even one more semester

[@heyysan9860]

Bro I started at age 30 back in 2022 and now I’m transferring to uci for math major focused in data science. I did have some college experience before so after years of time off I started with cal 1 and it was tough and this is my last semester at cc and I’m taking differential equations. I hope my hard work inspires you to keep pushing and don’t give up. math is awesome and will open many opportunities for you in the future.

[@idkanaccountname]

Same here- at 32, I had to do a review of pre algebra before hitting college level math (that I got a D in at CC). Now I’m finishing up calculus 1 at 33 years old. I say f**k it, we’ve got nothing to lose. I’m not going to go the rest of my life wondering what could’ve been possible if I had actually challenged myself

[@lloyddodgen]

I think the problem most people face when learning something difficult or achieving a level of mastery is that they approach it thinking about the amount of days, weeks, or months it will take them. They don't look at the possibility that this may take years to master or even become competent in and that the pursuit of that knowledge could take a lifetime even. They hope to hit the mountain top in 2021 and be done with it.

[@Thethriftynest]

Don't know if algebra should take a lifetime to learn

[@christhegamechanger]

" If most people would quit here and I don't , I will have an opportunity to discover something beautiful that others haven't yet."

[@douglasstrother6584]

Motivated by a new work assignment, I had to revisit Complex Analysis after many years. "Complex Variables" by John W. Dettman is a great read: the first part covers the geometry/topology of the complex space from a Mathematician's perspective, and the second part covers application of complex analysis to differential equations and integral transformations, etc. from a Physicist's perspective.

[@ZachGlavin2]

I started my engineering degree in the fall of 2021 as well. I was 25 then. It's never too late

[@wladislawortlieb8992]

I'm 21 and I was accepted to university. I'm also a little nervous about my age, but your example inspired me!

[@HaCkeMatician]

Math learning process, is a sort of art itself. You've to have a Compass. It's your passion.

[@bear532]

Was a bio and psych major and went to med school. Worked in the hospital lab department prior to med school for years (cytology/pathology). By the time I was halfway done with med school I had developed mild PTSD which led to depression, existential crisis, and ultimately led me to completely leave the medical/biology field. I was always in the advanced math classes growing up and math was my strongest subject. Hadn’t taken math since HS calculus. Decided to go into machine learning meaning I need to study math again. Took calc 2 at 33 after not touching math whatsoever since I was 18. I’ve never felt dumber in my life. I love it.

[@specialforce8486]

Way to go. Good luck ✌️

[@WisdomofHal]

Gosh, Lex really explained my frustration with math. From 4:05 on. I was soooo frustrated when I couldn’t grasp a concept. I’d go until I couldn’t handle it anymore, come back the next day and be able to solve the problem. Why, why does my brain work like that. 50% of the time I get it immediately, the other half comes after a solid night of sleep (if I can sleep). I do not enjoy the suffering but it pays off.

[@hamzamohamed7935]

Thank sooooo much for the question..... Mad my day..... Respect from Sudan

[@rngouveia]

I agree with Jordan that problems should drive learning. It has been true in my experience. But I would like to expand into this idea a little further. You should have a shallow understanding of the most things possible. Being at least able to describe what it is, how it works and why in an sentence or two which is relatively easy to do. This way, when you face a problem, you have a catalogue of possible solutions, and can investigate/learn them further. Because if you don't even know certain things exist and you would not think of using/learning them to solve something. I really think this is the basis of the biggest problems with the education system. You are required to learn subjects deeply, sequencially, without context or a reason why (which by the way is a very common question from students).

[@masonart4950]

Totally agree. The most useful well-rounded people on earth are typically jack-of-all-trades types. And it's very easy to delve further into a particular subject when you have a multi faceted, basic understanding of a diverse swath of subjects.

[@bobbobson4030]

Yep, you described the problem in a nutshell

[@Unstable_Diffusion89]

Breadth first then depth ad hoc when you need. I think when they introduce subjects, say calculus, they should spend some time cementing a high level tree/ graph of entities and their relations. Then you can go into the nodes in depth and do practice questions off of them, you have more context when you understand stand the bigger picture.

[@DillaCat]

How to learn math: *Enjoy the suffering*

[@lucynowacki3327]

I am 43 and starting to do my MSc.

[@Ludverc]

Hi, how do you do it if you you have a full time job? Or don't you have that?

[@KhanyoMjamba]

I'm 40 and starting undergrad 😂

[@rafikitho]

that explanation about running was so beautiful. lol so true

[@hristoplamenov1942]

1:29 Prof. Ellenberg mentioned Bulgarian problems. Proud to hear it as a Bulgarian

[@strength9621]

I needed this, reinvigorated by a friend and my own passion , I am refreshing starting from Algebra 1 , my goal is to go beyond calculus through self learning. It’s never ever ever too late

[@helioliskfire5954]

I'm a lawyer taking a PhD in Math. I'm in government, and the economists I have to deal with are intimidated by my math background. Lolz. But of course, the lawyers couldn't care less. In fact, the lawyers I know couldn't even begin to understand what math is. I remember a law professor interrogated me in class, "But what comes after calculus? How could there be more math stuff to study after that?"

[@someonenotnoone]

Lawyers and many "philosophers" get stuck in very black and white zeroth order logic. Simple but very incomplete.

[@anti-youTV]

but what comes after calculus?

[@fidelogos7098]

I was hoping for some concrete advice, like 'start here' with a specific book, etc. I've been all over the place with my math studies and I've discovered there are gaps when I don't know a basic concept. I'd like to go back to square one and start again. I always loved 10th grade geometry, proving triangles congruent, etc, but connecting that with the Pythagorean theorem and the quadratic equation was almost an epiphany. It makes me wonder what other connections I might find. I'm a little slower these days (I'm 76), but it's still fascinating, almost like magic, that so much of the world can be explained by math.

[@TwoPyramid]

congrats, that's awesome.

[@antwanwimberly1729]

I had to study math in my spare time as a computer science major. What I learned is that you can be superb at math as a kid like I was,, it came natural. But by the end of junior high I sucked at math. I stopped taking it seriously. It was like it all just disappeared..I don’t mean the easy stuff I mean seeing advanced math like proofs, theorems, postulates, stuff I was exposed to in AP class and not knowing where to even begin. I had to relearn the language of math and really push myself over the years. Now it’s all finally clicking because I took it serious and I practice it daily. That’s the only way. Don’t learn math and get comfortable. Learn math and keep learning it! Make it stick!!

[@mandy28887]

I like maths. I don't love it. But mathematics is key to understanding the universe

[@mandy28887]

Philosophy is a set of ideas that can grow too moralistic and idealistic. Symmetry through mathematics and philosophy should be searched

[@mufflager9065]

@SubZee no way math is the language of the universe and ties everything together Philosophy never really explains anything just opinions

[@Hyumanity]

Both math and philosophy are needed to understand the universe, language and reasoning, respectively.

[@alexbramm8526]

mathematics only exist on our earth what if it's all just bullshit

[@mufflager9065]

@SubZee your point ? You haven’t made one yet

[@_GlobalNomad]

Great podcast

[@tracywilliams7929]

3:54 Math is Hard Chapter. Lex shares with a famous writer this sentiment about doing something that is hard. She said of writing that she hates to write, but loves having written! Lex might say the same about exercise or math study.

[@marshacd]

Superb! Right on the point! Not only good advice for students, but for math teachers at all levels. I had to learn these points on my own, and it took years.

[@ttrev007]

application really helps me or a good story on how and why the math was discovered. the pure rules don't make sense to me until it has a reality to it.

[@Pirake123]

For anyone here, I found Khan academy the best resource for learning math (1st and 2nd year level University level math). Khans' explanations are phenomenal, always started with intuitive explanations with diagrams, examples and then finally derivations. This is by far the most approachable method for people starting off.

[@ConsciousnessExplored]

I fucking love the internet and the digital commons of KZbin

[@MOliveira-m5h]

You know what it is. You have to be a physical person. My dad is a business guy and would try to say that I’m not mechanical even though I have a mechanical engineering degree and in that i liked the math the most meaning solving problems in my head verses tinkering with an object. But then I’m also much fitter than him and athletic. I’m good at guitar. And learn sports quickly. I’m good at physics because I’m physical and not lazy. When people think of mechanical engineering they think about making things easy like sitting on a bulldozer or driving a truck. They don’t think about working for the Olympic cycling team. Doing the math is physical because you’re staring with the definitions and working through the problems and fully understanding them. It’s like playing music vs the radio. I don’t like to listen to the radio but I love to try and learn new song and interact. The personality is like someone who would tether push a shovel all day and wheelbarrow than sit on a machine. Tesla took a job digging ditches and no one understands why. Business people are super lazy. They don’t like math. They like passively counting money and looking for easy A’s. An example is Jeff bezos starting Amazon. That’s an equivalent to the dirty jobs guy going to opera school and then using his voice for the home shopping network. Amazon Jeff bezos applied computer science to the home shopping network. That’s a dumber than real engineering projects but makes a ton of money. It’s just like Facebook is easy. It’s a database. It’s just the yellow pages with more abundant space. That’s not working hard at math. You have to like to push letters and number intrinsically to get good at math. I hate counting money and not working on something physical. It’s fine if it’s estimating for components of some product or a house. I hate the taxes and collecting rents. You have to do it to stop people from stealing because they think you’re stupid. Business people and politicians are like if you have a first grade class the ability to grade their own work. Everyone has absurd scores a million percent A + infinity’s.

[@zrmsraggot]

My personal approach is learning must be a responsability, not something you do in order to feed your ego

[@terrywalters5078]

Yes! We learn best when we have a problem we want to solve that requires you to learn.

[@johnnykhawand]

The Nicolas Bourbaki series are interesting to read and the story behind it is interesting

[@DinkanFollower]

They are interesting to read!! Every single one of them would be offended by this statement

[@zulqarnain_haider]

Thanks for advice

[@alansillitoNYC]

That's exactly how I feel about running. I thought it was just me. Thanks Lex.

[@specialforce8486]

He is so right. You've got to have a reason. I just started learning mathematics because I want to study AI and software engineering. I am loving maths now unlike before.

[@gerardomenendez8912]

Great question!

[@davidnowicki4024]

Lex, I thought it was just me that thought about not having the complete picture.

[@robinmcbride4057]

Math is the substrate to a life lived well. It disciplines the recursive problem-solving mind, and the word mathematic from the classical Greek 'mathema' translates as 'learning.' Math is lifelong, learning to solve living problems, maths mode of thought is the root of STEM, and realise that Science, comes from the Latin scientia meaning 'knowledge.' If we are truly homo-sapiens (wise-men) maths is the starting point.

[@zachzeurcher6450]

Hooking it to something is exactly it.

[@AbhikChakraborty1]

3:56 ❤ 2:56

[@jpined14]

Look at the lack of comments whenever there’s a math conversation. It’s one of the few topics you don’t get JR experts and armchair specialists with their self aggrandizing options.

[@bossgd100]

Lol

[@Dextermxck]

facts lol

[@ravichanana3148]

Very correct what Friedman says.

[@iangilbert4811]

At at aged 15 I remember thinking Math was really hard. At age 25 I picked up a math text book again. Now I'm aged 35, maths is still hard and I work at Burger King.

[@johndaly6732]

I think there’s an innate factor. Maybe fluid/spatial intelligence or some other combo plays a role. Some people just struggle with anything beyond basic arithmetic and others, like our guest here, are math gurus at age 12. Someone in between those extremes might be able to outwork someone else who innately is good at it, but even then there’s a limit.

[@agh1750]

My spatial intelligence is worse than anyone else's that I know yet I was able to complete a math degree.

[@RandomGuy-yf4wf]

No one is born with an innate understanding of complex math concepts. Doing math changes your brain, and even if your brain wasn't "predestined to be good" at math, it would become just that. I truly do believe that anyone can excel at math, as math is but an abstraction of real world. Sure, there are people with an early head start, but that doesn't mean you can't outrun them.

[@SimplyAlwaysAsleep]

@@RandomGuy-yf4wf It actually has more to do with how much you enjoy it. Andrew huberman talks about it. Of course, if you're naturally good at something you're more likely to enjoy it but it's not exactly causal. You can be average at something and still enjoy it. Ultimately that's the most important factor for determining how well one does in math because it's just like you said. Your brain changes due to neural plasticity, and the people that get a dopamine release from tackling hard problems that they can't solve, will do so willingly and are going to be able to focus on math for much longer and maintain high effectiveness as well. So those people just end up doing a lot of math, their brain changes and therefore they get good at math.

[@AustinfromNashville]

I thought I hated math; now that I'm an adult; turns out I was just a kid who hated school. That's the issue. People tell themselves over and over that they aren't good at math. No you just never wanted to do it. Hard to learn something when you don't give a crap about something

[@richtofen4888]

@@SimplyAlwaysAsleep Do you have a link to a clip of him talking about this?

[@KhojiInsaan]

I am 43 and wants to start Learning Mathematics again

[@davidnowicki4024]

Made me cry for the beauty of play..

[@elijaprice]

So the way to learn mathematics is to enter a hot dog eating contest. Gotcha.

[@mrjamesgrimes]

Why does it seem like his glasses are on his face but not on his face

[@iahkrishnashiva]

Interesting subject that I’ve been thinking about recently

[@omarelmaghat5050]

I read an introduction to manifolds, it was funny.

[@__hannibaalbarca__]

My Journey in math start when i see first time Computer in 1990, with my father : if you want understand this you should be excellent in mathematics.

[@sethawarren]

Sounds like programming advice. Build something that solves a problem for you. Learn what you need to build it.

[@hunterabdo1952]

الرياضيات التجريبية بنهج فيزيائي لها جانب في نجاح الاختراعات منذ بداية النهضة المجال الرياضيات

[@calvinrob4068]

This comment section is great for people who are learning math at unconventional stages e.g after many years out of education !

[@aniketbisht2823]

You gotta grind on them textbooks boi.

[@MikeStallings2023]

Khan Academy up through differential equations. It's free and will give you a good start.

[@melansaloon]

Is my interest in Lex Fridman clips a feature or a bug?

[@TheGerogero]

Lex "feature not a bug" Fridman

[@micheltchonang7556]

3:20 cool

[@misraaditya9213]

0:17 I saw what you did there ;)

[@jbvalle]

Saying stuff like I want to get into math is like you are saying I want to start learning tools. If you have a specific task or goal or something you want to build im a certain field, read the industry standard introductory book resources and you will be guided through the maths you need, this is were it really gets enjoyable because you get to see the purpose and functionality of a certain math tool or math field used for that industry. Math is such a broad field you don't have to learn all, learn the math tools you need to accomplish your goal and do this for every other tasks/goals you have

[@matta5749]

This is mostly only true for introductory level math and applied math. Research in the fields of pure mathematics mostly revolves around concepts that have no application outside math yet. It is perfectly valid to aspire to learn pure mathematics.

[@jbvalle]

@@matta5749 First of all nothing against inspiring people for pure maths, this wasn't my point. But I would be interested to know how you would advice/inspire a person to get into higher level pure maths, who is in the process of learning maths properly? It would also be interesting to know what higher level pure maths you have been diving into and why

[@Sol-gl3nl]

doing systems biology, wanting to do ML algorithims, not gonna be able to do either if i dont know algebra let alone linear algebra or differential equations.

[@jbvalle]

@@Sol-gl3nl Well coming back to my point. You have a specific application? Perfect! Lets take ML or sys bio, take an introductory level book, specific to this application, this will then guide you through the maths of lin algebra differential eq up to ML backpropagation etc for example, thats the purpose of introductory level books. And this is how you can get into this kind of higher level maths. Now you can a feeling how this foundational level maths is used in higher level maths. Now its not only pure maths with no application but you at least have a feeling why you need every single piece of the puzzle. I hope its clear

[@mikeolsen6814]

0:13 taking a bunch of meth 😂

[@spidey9504]

❤️ lex. peace world love forever. empathy gang

[@Leopar525]

Lol Lex giggling like on mushrooms is so funny 😂

[@mpumi1024]

I am answered. I will go hard at it

[@k9man163]

I can barely factor a polynomial.

[@creed4466]

mylab pearson that my teacher assigns us to do hw with ruins math for me.

[@Alsteraib985]

I am learning with Python

[@jackerylel]

Oh lex. Suffer to improve the world, to help people. Suffering for the sake of suffering, or for it's own enjoyment (running through blisters, or eating 36 hotdogs in a row) is a very naive life perspective. Ayn Rand's heroes don't run until they can't just to see their limits, they toil until exhaustion to build their dreams because they know the world will be a better place for it. You're hung up on suffering and it's kinda cringe bro. Accept that it exists and is a part of life, but dont love it or chase it.

[@oguzhankocalioglu3180]

You are escaping from suffering. Don't.

[@jackerylel]

​@@oguzhankocalioglu3180 Nah I'm good haha. but if you enjoy suffering for the sake of suffering and are willing to sacrifice your well being for it, then I'd recommend that you re-direct your energy towards a more positive outcome. Or at least try to understand why you believe that you deserve to and should seek to suffer. life can be amazing, and it can be amazing all the time, its a choice you make at every moment.

[@oguzhankocalioglu3180]

@@jackerylel Yeah life can be positive. But most of it it doesnt. I am not negative or pessimistic or nihilist, i am just looking life with a state that hold realism and practicalism. "You said cringe" on the top of your comment; its not. You felt cringe, its about your emotions, ideas not Lex's. So you are in a state of running and avoiding the hard thruths about life; death, pain, discipline. You gotta carry the weight of suffer and pain. But like i said its not pessimistic, actually its about taking responsibility and keep moving forward. Not some masoschistic, meaningless suffer.

[@jackerylel]

@@oguzhankocalioglu3180 yea we agree then. Cringe is just an internet word, not my actual emotional response. Lex loves to say that there is a romantic side to suffering. That, in my opinion, is such a naive viewpoint that it makes him look like a fool in that moment. Struggling is okay, chasing suffering is not. Maybe I'm getting caught up on the words and Lex meant struggling and not suffering. But even then, he tends to glorify getting hurt to achieve a physical goal. that's going too far in my opinion.

[@kyleahague]

Why did we think math was lame in school?

[@slottibarfast5402]

The guy that started math at 22? So funny like five years is no time at all in the big picture. I'm 73 and though i took calc in college it is like starting over now even algebra and trig. Are rusty. I want to keep my mind going plus the news of the world is so bad and is going to get much worse as the oil runs out, not in my lifetime but certainly in the life of todays college grads. Then global warming, environmental degradation depletion of resources. I could be wrong but odds are i am right. So math is less depressing and equally useless.

[@Msid2021]

Prayers , Love and respect for you sir.❤

[@giuseppegnazzo3154]

2+2 equals 5 right?

[@clintceli9238]

Yes

[@sharilali8240]

1? No?

[@senseihitmanwayofkempo8305]

No more caculators n grade school learn the basics on paper then without papar... then the rezt is easy

[@FlameForgedSoul]

"I don't enjoy the suffering!" Dearest, he's Russian, let it go.

[@guanenteng4870]

mathematics is very difficult

[@emale03]

You need to quit running and workout with what you like.

[@practicecoach777]

Professor Leonard ❤ youtube Channel-Calculus, Stats, Algebra

[@speedy909CALI]

I love ur podcast my dude !!! But dam u need a hair cut 💇‍♂️. Hit my friends at thecutby in LA … tell them speedy sent you… they’ll hook u up proper !!!! That’s los Ang. Not Louisiana

[@ef6957]

Ellenberg? Fridman ?

[@UnknownUser-fg3fs]

Math is so hard

[@SamOlisson-tf1ic]

Ill boys 10 to shwell scoots on Time to clock when back at Arial smook is back down first famous évidence it factor name on Brooklyn Bad boys if rider it Will choked irik rames in Portland and Chicago 12={×3+1/9}=[12]>12TS=14+(8)(/9)

[@MrCananball]

I seriously don't get doing math. Machines can do it for us; And better. What's the point? \('-' )/

[@koshobai]

Sure, but we need to know the problems we're attempting to solve in order to set tasks for those computers. Not sure of there are exceptions or if I'm just making this up, but I would suppose that without manually working backward from a still-unsolved point, we can't move forward beyond that point.

[@goochipoochie]

Because if you don't know what you want to do, then you can't tell the computer what to do

[@MrCananball]

I see. That makes sense.

[@goochipoochie]

@@MrCananball 👌🏻🙌🏻

[@bluesrockfan36]

I think you have the wrong idea what math is, the creativity and abstract reasoning involved in higher mathematics. A machine can't do it. Not yet at least.

[@xxnotmuchxx]

textbooks + chatgpt