The Secret Weapon of Elite Mathematicians

Math is hard, for everyone, and everyone is going to struggle. By learning to embrace the struggle and welcome the challenges on a daily basis you can become better at mathematics and mentally stronger. Do you embrace the struggle? Do you have advice for people learning mathematics? If so, please leave a comment below.
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Thank you:)

[@21ruevictorhugo]

This reminds me of the Paul Halmos quote that the Math Sorcerer gave us a while back. “The only way to learn mathematics is to do mathematics. Being bad at it is just the first step towards being good at it.”

[@georgezevallos]

What va brilliant quote, thanks for sharing it!

[@byronwilliams7977]

Embracing the difficult not only applies to Mathematics, I'd say its key for life. Learning to dance in the rain is LIFE!.

[@21ruevictorhugo]

Here’s another idea in the same vein. Many of us have been told how smart we are since early childhood. Turns out this has a deadening effect. A professor at Stanford, Carol Dweck, studies this sort of thing and points out that if someone tells you you’re smart you become afraid to do something you find difficult because you feel afraid to fail and your parents might see that you’re not really smart and be disappointed. Anyway, she calls this the Fixed Mindset. She then defines another mindset she calls the ‘Growth Mindset’ where if you succeed you congratulate your child, or yourself, for doing good work.

[@jlswlf7408]

I listend to a huberman Lab podcast where he talked about that study. Its very interesting!

[@limonadovi]

Another problem being told that I'm smart is that I believe it's enough and don't practice hard. For me, my high IQ was enough to be outstanding in high school and undergraduate university. All of it was rather just fun. But the lack of really hard work kept me outside the group of really best and prevented me gathering deep and cutting edge knowledge. Now, decades later, pursuing academic carrier I really miss it. One more downside of being told smart that I don't necessarily believe it, but compare myself to the best ones. This gives the picture I'm not enough. Without getting used to hard work I won't practice hard to be better. For example, in high school in hungary there is a correspondence math contest organized by Kömal. 6-8 problems (say 8 for now) are announced monthly in a paper and you have a month to solve and submit it. I regurarly solved around 4-5 of the 8. I believed that solving 8 needs superhuman power. Once being refused in love I got depression and didn't have better idea than working on the problems longer. A little bit moreeffort and I've solved all 8. The next month again. Then the depression was over and I returned being lazy.

[@21ruevictorhugo]

@@limonadovi Yes. I was in that same situation, high IQ and finding everything easy. Then comes reality! 🤣

[@mj47_dreamer]

You know professor, some people just dont wanna see you grow its bad when its your own family and its worst when you are supported for nothing not even for being yourself. But i dont wanna let those things get to me...i cannot fall down to their level of toxicity. I'm grateful for these educational videos, its my dream and my right to live my life as a human being and i won't give it up for anything. Thanks❤

[@Bubs.]

You can do it! It helps so much to have family support, but if you do this by yourself you’ll gain tons of self confidence and belief in yourself that will take you far!

[@mj47_dreamer]

@@Bubs. Thanks for replying. I'll remember this. Means a lot!

[@victoria66872]

Living in the same situation, don't ever give up. Heal your inner child, and continue to grow. Good luck ❤

[@mj47_dreamer]

@@victoria66872 Thanks girl, Wish you the best as well...We gonna change! Amen

[@zeez7935]

I'm addicted to making every single exercise in the books even the easier ones, i think that's slowing my progress to learn new math.

[@cuad0130]

I feel this. I tend to be so hyper focused to complete them from start to finish as I think that by skipping some I might not learn what I could if otherwise

[@yannicko.5936]

I have the same issue what are the math sorcerers thoughts on this?

[@tomekstable]

Indeed, curious to hear the Sorcerer's thoughts on this! I'm scared of skipping any exercises when I'm self-studying.

[@CloudyCloudy211]

I think it'll pay off in the long run, there's nothing wrong with going slow and taking your time unless you have a deadline

[@Mebro-m6d]

I try to do exercises of the thing take 30 minute to learn in the book for 3 day.

[@xyblade4625]

This just reminded me of my time in the Marines. There’s a saying we have, and it’s called embrace the suck, knowing that every day may not be easy and it’s called embrace the suck knowing that each day it’s not going to be comfortable; you have to suffer from being able to reach that level of comfort it’s not going to be satisfied you have to suffer from being able to reach that level of comfortability.

[@anniesizemore3344]

I'm working my way through Blitzer's Intro & Intermediate Algebra for College Students. Its the best book anyone could ask for. I completed first 2 chapters and decided to skip around in the book since I was doing well. I skipped ahead to Chapter 8 Functions . Its basically calculus stuff in that chapter. So easy. Domain. Range. Output. Input. Vertical line test. So easy. Calculus is not as intimidating to me as it once was. I think I'll still have trouble with it, but its not that intimidating now. I'm also slowly working my way through James Stewart's Calculus. Preparing for online math classes

[@davidnelson4960]

Dude is jacked

[@calculus988]

No way!! I'm using that book now to study Algebra and trigonometry. It's the best book to learn math. I use Blitzer's

[@anniesizemore3344]

I@@calculus988 Algebra & Trigonometry is also published under the name Precalculus by Blitzer. Any of his books are fantastic. Good luck

[@aarongreenberg159]

All for accepting a challenge! Sometimes it's good to be able to ask for help, too.

[@chandankumarmohanta5666]

I am also on the track to embrace the mathematics rigour and difficulty. This is helping me to appreciate the mathematical beauty. Thank you for such a motivational video.

[@LoveAndLustInc]

I'm working through Khan Academy, so not the most difficult stuff, but I came to a question that I wouldn't quit. It took me 2 hours to finally find a way to solve it, and I jumped up for joy when I clicked enter and it said "Correct!" Those are the moments where it all seems worth it. A few days ago I was working through some Kinematics questions at the end of a chapter and I couldn't for the life of me figure out which formula to use, and after about 2 hours I had to conceed and look up how to do the question. It was a crushing blow. But those moments are just as important. They humble you, and make you work even harder, so you never get those questions wrong again.

[@hemrajue3434]

Mathematics is like a mountain. Accept the challenge and climb it if you wish.

[@davidnelson4960]

Dude is jacked

[@eli-shulga]

"Being in constant pain of friction", but in a healthy way :) So true for learning and applying programming too. Because you should be always in a state of solving a problem, which can be also just, understanding a concept. Once you do you proceed to the next problem. Actually also true for learning musical instrument or any other hand coordination based skill. Interesting to hear its tarlatans to math, but also makes a lot of sense.. Sometimes your videos are re enforcing stuff that are already felt in the guts. And yet ists still supper important to hear it from external source to help overcome our own silly brain that attempts to avoid this pain with self doubts and a bazillion of other cheesy tactics it throughs at us daily Thank you

[@aradarbel4579]

I didn't use to embrace the struggle, until I miserably failed calc 1. After a lot of thinking and self reflection it made me realize, that's really the fun part. If we could learn math from a book and completely understand it without any effort, it'd take all the fun out of learning! So ever since then I always try to think about where I am and enjoy the journey of learning.

[@alejandroaguilar3816]

I’m studying Lang’s Linear Algebra, every time I come across a theorem I refuse to read the proof and attempt to prove it myself. I’m also doing every single problem and don’t pass on to the next one until I’ve thoroughly solved it, I enjoy doing this so much, the amount of satisfaction I get after solving something I struggled with is truly unique.

[@olivermaclean8564]

Struggling at the right level is a great tool. Growth as a mathematician is stunted if everything is spoonfed or if you you're so far from understanding you don't even have the prerequisites for the prerequisites. The best mentors know how to keep you at the right level of lost

[@chriswilliams5291]

I enjoy solving math problems in the easiest way possible and sharing this information with other students to make passing their classes as easy as possible for them as well. And as a tutor I have gotten a lot of gratitude from those that I have shared this information. I guess it's different for students that plan to take the really hard math classes and enjoy the struggle like you said seems like a rare trait.

[@ronflypotato4242]

you touched my heart a little with this video I want to do a first degree in math, and I want to be a professor. I want to become a mathmetician and I often think I am not good enough for that. when you said that he didn't want to see/hear your solution. I am doing this things my all life so naturaly whenever there was a formula I wanted to crack it down even back than at the age of 10-12 I didn't want them to tell me the formula just what it is supposed to do and I will get there myself but it didn't have anything about difficulty(probably since I never read a book that I cannot understand just me thinking trying to imagine a solution and I loved that process) and I am sad because this was a crucial part of me and my life It is me, and I am without it very long time now( becuase I have reached my limit of doing mathematics alone 4 years ago when I was 17) it is not all that sad because I have now more things in life now but that one thing remembering that I wanted to be a mathematician will always stay part of me and always define me now that I want to get back to mathematics I am reading books and trying to understand solutions from math olympiads, I can more relate for that struggle/difficulty sometimes and it does get me frustrated and sometimes I have full weeks of not doing it because in order to do it,I need to work hard and concetrate for now math that challenges me is not my confront zoon anymore,not that frequently at least.

[@hikashia.halfiah3582]

Embracing the difficulty is about right, but there are multiple ways to do it. Hard struggle is only part of the story. No less important is patience, the sense of knowing when to slow down, and it's okay to admit that you don't understand it, and then reorganizing your life on what actually matters. Hard struggles all the time would burn you out, most of the time I prefer to treat it like I treat my lover, take my time knowing them well enough. Slowly but steadily at my own pace, when your knowledge of your lover reach a critical mass, you suddenly start to see them in a whole new perspective, and you become much more understanding and realize their charm beyond what a surface glance might suggest.

[@WitchidWitchid]

It's uncanny. I just encountered that feeling only moments ago. I was attempting to write a proof to a theorem and I was just sitting there drawing a blank about where to start. It is a scary feeling especially when I know that I do know more than enough relevant Mathematics to handle such a proof. Then I started focusing very hard on exactly what the theorem is stating and I was finally able to get some ideas as to how to approach the proof. I now feel much more confident that I'll.be able to crank out a proof when I get back to it shortly.

[@zhiychen1626]

I'm willing to embrace challenges and doing hard math now, but everytime I do math for over 4 hours I feel physically dizzy and disgusting and need long time to recover myself. I'm looking for some ways to relax myself fast but haven't found yet.

[@Caurt.]

Thx for making this

[@goldCrystalhaze]

In this video, I learned the most important lesson in my life. I've been in the situation that you describe, and that's the reason I didn't get my university degree. Had someone told me all the things you sai right here, I would have finished my school. I was caught up in a loop, starting to read math from a book, got stuck, drop the book for months, then try again, then same thing happened, until I felt I was no good at all, not being smart enough, and finally gave up. After this video, I'm going to start again on another basis this time. Thank you so much for your help!

[@yannicko.5936]

Dear Math Sorcerer, some of us have the issue that we do every single exercise in a book, and thus it takes a long time to go through a book and we are not sure whether this is the right approach. But otherwise we feel like we are missing out on essential lessons from the exercises. What are your thoughts on this?

[@blazed-space]

I have the same feeling when I am sitting in front of a programming problem attempting to design a solution!

[@calculus988]

I have to continue grinding at math. I really want to be a Mathematician

[@mrgms3892]

I remember, during my math A-Level finals there were a few questions I couldnt solve immeadiatly....it was the first time in years I realy felt joy working on high school math problems. I realy enjoyed said difficulty.

[@CharliRay]

One year ago today o had a 3rd grade math education at 44 my schools were ghetto prisons and I simply was never taught math and I refused to learn as an adult I’ve dedicated the last full year of my life every single day studying math I’m up to quadratic equations and I am proficient in it and all that comes before it I e never been more proud of myself and it’s changed my life in so many ways I can apply it to my life in every aspect I did cry lie cheat myself and want to give up the first few months and knew I was cheating myself I’ve since got my high school diploma with a 188/200 145 to pass in the math I got a 102 the first try before studying . I’m starting college this month for fall semester and I don’t need prerequisite classes for math only for my grammar reading and language arts . Which I’ve never been exposed to scholars only street smart people . I used to think book worms were weak how wrong I was . Studying and learning is the hardest challenge I’ve ever had .

[@83jbbentley]

Mathmatics is a race of the strong and persistent.

[@douglasstrother6584]

One always has to learn "on their own" in that one has to figure out how to fit ideas into their own brain; this is the truly difficult solo work. Building your own "take" on a body of knowledge is something only you can do. Discussing ideas with others is irreplaceable for deep understanding: work hard on your own *and* go to the Professor's and TA's office hours, and organize small Problem Set Parties with classmates. Success in life demands clear communication of ideas: questions, argument, "Help me with this idea.", banter, brainstorming, etc. ... writing clearly.

[@maggieschroeder9531]

This is excellent. Deep philosophical wisdom too.

[@alanbaker6098]

The reward for grinding on a problem is the joy of finding a solution! The immense confidence that comes from stretching yourself into a new place of understanding! ‘The journey of a thousand miles begins with a single step’

[@michaelcunnane230]

I save difficult question number, which I failed to solve, in my notebook. The longest chapter I learn a topic is 6 months. I remember I attempt several times to answer one question that last me four days. Yes, i "respect" the questions like embracing.

[@stretch8390]

Feeling the first 25 seconds acutely with time series analysis right now, here's to hoping for the moment of clarity!

[@alphaomega3944]

Dang, this is coaching for life!

[@kennethfreeman2954]

I was stuck on a tough integral for two days. I'm in my first year of undergrad (math and astrophysics major) I was working on a math assignment, the flow went pretty smoothly until I had to stop in my tracks when I came across that integral. I didn't know how to approach it and whatever approach I had cone up with at the time failed. Two days later I decided to go to a friend's to get some help and on my way there it clicked after contemplating on it on the way. The two days of struggling and just thinking about that integral throughout the days helped me to understand it a lot better and eventually solving it.

[@aminmohammadi9308]

I don’t know how to thank you for these amazing videos 🙏🏼❤️

[@kevin-gg8ir]

You're so right! P.S. Your intuition is very helpful! 😁

[@shpleemcgert]

Tolerance for frustration is akin to fertile soil for your mind.

[@khana.713]

Contextualising pain is an essential skill.

[@jlswlf7408]

Your videos are motivating me so much to do math but Im done with my math exam for this semster so now I have to study the other subjects...Next semester I will be so ready to 'grind' math. Thanks for your videos!

[@eternalm.s6088]

Thank you Math Sorcerer, this video helped me today. I was doing some problems before eventually getting stuck and taking a break, hoping on to KZbin to find this video. This gave me the motivation to embrace the difficulty and find the method needed to solve my problem. Well timed and appreciate your content and motivation as usual.

[@shutupimlearning]

Embracing the difficulty is a must for me. Doing an Modern Algebra class right now and I'm going giddy with all the new concepts : modular congruences, invariant subspaces, Jordan normal form oh my!

[@user-fd2xx2ob9i]

You'll truly be free until embracing difficulties.

[@gio_hdz]

As a Computer Science major, I didn’t know this was a thing. I can definitely relate to this so much. In fact, this summer as I worked as a Software Engineer I chose to embrace so many topics outside of work. One of them having to continuously learn algorithms. I spent a good portion of my time learning and solving algorithmic problems even on top of work where I was solving real-world problems. I have a strong passion for CS since an early age if you’re wondering why I did this which I think takes a huge part on even embracing the difficulty. The amount of grind I did was evident that I like to solve problems but I think that if you see this “uncomfortable” path that you mentioned and continuously tackle it eventually you will have more eagerness to solve even more problems. Once you see yourself making significant learnings you just want to keep getting better, and to to me at that point it’s not even about embracing failure but rather having it to be part of my life now.

[@satyavivekanandbattula1091]

thanks sir useful video

[@nikolaykolev5125]

Colleague of mine ( UK ) use the phrase " bite the bullet"

[@charliecho5392]

I thought you were just a David Goggins of math. You are much more than that, now that I watch you more haha. You give us lots of good strategies as opposed to technicalities that we are usually accustomed to on studying math.

[@girlsinacoma]

How many problems is too many? I’m going through 4 modern algebra books doing 80% of the problems and I usually learn something that wasn’t mentioned in the chapter.

[@Jenni_H]

That's how it is

[@benhill3098]

I do not go for either extreme. When I am working on a math problem, I try to do it myself. If I run into difficulties, I like to just get a hint. Some sources like Khan Academy allow you to get as many or as few hints as you want. I also like when I can find out if my answer is wrong without finding out the solution yet, like Khan Academy or Brilliant, or my courses at school, so I can keep working on it. If my best efforts are not enough, then I find out the solution, preferably one given in detail, step-by-step, like Mathway, or the previously mentioned sources. With books, I also make a good effort to find the solution myself, but I try to avoid spending hours on one problem. After some time, I find out the solution when one is available and move on. I am still in my undergrad studies in my math program, so I'll see how much more challenging things will get later on. Thanks for the video.

[@jacobharris5894]

I used to be all about doing every problem on my own but I think the fact of the matter is you have to find that balance between doing problems on your own and seeking help do too the fact your almost always under a time constraint. The time sink isn't always worth it and can make you fall behind. That being said the power of a good hint/sneak peak shouldn't be underestimated. If you can piece the rest of the solution together with some hints you understand the solution and you'll probably cement the key concepts in your mind quicker than if you simply read the whole solution and reworked it later.

[@Wandering_Horse]

I was trying to figure out 'Rationalizing the Denominator' just last night. I had to study the proof and example several times and it finally clicked. It was more of getting the concept then the actual mechanics of the problem. Then just this morning I was reading a random problem from Washingtons 'Basic Technical Mathematics' and the problem made zero sense, I reread it several times. Exclaiming in frustration it must be a printing error! Looks like I need to revisit that pesky problem once again and embrace the difficulty. PreCalc class starts Monday, woot!! :)

[@timferguson1526]

It’s like lifting weights!

[@kevin_heslip]

Can I make a video request? I’d like to know a lot more about complex numbers, quaternions, and octonions. There currently seems to be a vacuum of content surrounding this trio of topics on KZbin. Even if you can’t simplify the language very much, I’d still love to have an idea of the prerequisite maths.

[@TheMathSorcerer]

Great idea! Here is a video I have on the Quaternion Group: kzbin.info/www/bejne/pXykl2eXmaejrdU

[@ronaldjorgensen6839]

unknowing or chaos apart from solution is a form of the final variable needed for isolation of solution specified part of mental flow chart

[@sukantb1980]

It’s absolutely worth it

[@yousefmath_art4896]

I was one of those who refused to look at answers before I solve the problems on my own, I totally agree with you, but sometimes this method is very difficult and time consuming and may be slow down your progress, sometimes it's more wise to look at answers or ask someone for help

[@johnadriandodge]

Math is a beautiful language and art form!

[@johnadriandodge]

Math is a lot like programming and chess and all three are GREAT for our minds!

[@sr2291]

Anything math related os good for our minds!

[@Jenni_H]

The only problem in middle school was the fact that I had to show my work.. sometimes I just knew! Im 38 now and just completed Chemistry some of the worksheets I tried figure for myself, and do the equations 'old school', same as I did with statistics... find your niche because we all cannot rely on technology!

[@Bubs.]

I’m currently learning how to represent functions as a power series and I’m stuck on a problem (I think I have to use two antiderivatives to get it into the form I can use, but I’m not sure and I keep getting it wrong. Maybe it’s more simple than I’m thinking). Anyway your videos always have the motivation I need! I’m going back to the book to see if there’s some information I missed that can help me.

[@Bubs.]

Update: 2 antiderivatives was correct, just had a number or two off, the problem was kind of messy. I got through all my homework and quiz that would be due in like one minute, and i feel like I understand it. Feels good!

[@machina123]

I had two Math courses in 1st year of University (Algebra, Matrixes and Determinants, Vectors, Analytical geometry in space, Arrays, Functions (limits, continuous functions, derivatives, Taylor series, graph draw) in first semester and Multivariable functions and Integrals in second semester). Now in third I'm going to have discreate math. What do you recommend me to do to prepare to follow the course ? What should I revise ? I doubt I would need much of the topics I learned previously but I should start from somewhere. You as the person helped me to pass the exam in second semester with good grade (9/10) which, if you asked myself 10 years ago is unbelivable. Thank you.

[@aaronwong7340]

EMBRACE THE CHALLENGE!!!

[@Clew_]

"Do you have advice for people learning mathematics?" When I was in school. almost on every exam I was making "stupid" mistakes in simple mathematical operations and about year ago I've developed and published a mobile app, that shows simple random math.operations for 1 minute, and you have to solve as many math problems as possible. When i first played that game (a year ago), my highscore was about 28, now its 41. I don't want it to be seen like an adwert, so i will not tell the name of the app but if someone is interested let me know

[@zerodivider4333]

No pain, no gain.

[@qewiu830]

Professor, would you recommend going all-in on a single subject like math or biology, or do them both at the same time?

[@Real_LiamOBryan]

Do you have any recommendations for math and logic puzzle books or websites?

[@SequinBrain]

Look it up on utube, very often someone has a video on it. 3:20 good point, most of the time when I get stuck it's b/c it's late and I've already been studying for more than 2h. Time to quit & hit it tomorrow, I never figure it out in those conditions. Rest, regroup, we attack at dawn. You address the answers in the back of math texts in many of your videos. I wish there weren't copyright issues, b/c you could make a book from key problems in several of your math texts in your library called "Even Answers From Select Problems" where you fully work out 2-300 various problems that AREN'T answered in the answer sections. That would be a nice book to have. Sadly, legal tape probably would prevent its construction. For your bookshelf: Unless they're already sorted, shouldn't the Trading book and Stock Investing be on the same shelf? Or did I read one of them incorrectly?

[@Kim-ej2xm]

The deep learning is hard and exhausting too

[@Loots1]

Hi professor, may I ask for some advice, I'm using 'linear algebra friedberg' this September coming up, and i just got the book and it looks a little intimidating, I know you have gone through a lot of math books and I was wondering if you have any recommendations for things to review before my semester starts, just at first glance it looks like I need to review proofs but if you have any ideas or advice id appreciate it

[@Mebro-m6d]

I don't get it why some math books don't have the asnwers. It's okay to not having the solutions, but why no answers? Is it because not copy-paste the solutions of the homework problems?

[@willrose5424]

My instructor said one of the Blitzer Editions had an error. How does that effect students when textbooks are wrong? It's best to set a time frame before searching for the answers

[@davidnelson4960]

Embrace the pain and grow

[@omarashraf1713]

How can I send a question to math sorcerer?

[@davidnelson4960]

He rocks

[@davidnelson4960]

Some days peanuts Some days....

[@69erthx1138]

When math is always easy for you, you most likely are not gaining anything valuable, nor developing any new insight.

[@Number6_]

A book that cant answer its own problems is a useless book. There is a mismatch there. Either those questions should not be in that book or the book is badly written and edited. My professors were always veting text books, good people.

[@freepointsgals609]

Masochism.

[@johnadriandodge]

Dear Professor MS: considering you have that wild Einstein hair, but transforming in the opposite y value, do not dye your hair, allow it to turn WHITE!

[@byronwilliams7977]

Embracing the difficult not only applies to Mathematics, I'd say its key for life. Learning to dance in the rain is LIFE!.