Learning CHESS vs Learning MATH

As a math professor, I've spent a lot of time thinking about how to learn math effectively. Recently I've been picking up the game of Chess, and those effective study habits from math are also great for learning chess, and vice versa. In this video I walk through and compare my study tips for the two disciplines.
0:00 Chess vs Math
0:39 Master the small details
2:04 Practice Yourself vs Learn from Experts
3:56 Review
4:54 Persistence
7:18 Memorization vs Understanding
11:04 Growth Mindset
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[@oliverquinonez3919]

The crossover I never thought I needed

[@biomec5690]

This is so true. No wonder mathematicians generally have a great aptitude for chess - it develops similar skills on logic and by applying core principles. I would love to play a game with you someday!

[@gamespotlive3673]

They're not similiar enough that there's a large correlation. Most great chess players are normal in math and vice-versa. Vishwathan Anand played 10s of professional mathematicians at the same time and won all but one (which he drew).

[@jacoboribilik3253]

@@gamespotlive3673 Being good at mathematics doesn't automatically make you a good chess player (or any board game for that matter). It takes a lot of training to get good at anything, but having a mathematical background certainly helps a lot. Mathematics is really at the end of the day the use of logic and some previously laid down principles to derive new results when dealing with ideal objects....chess imo is no different.

[@brendancoetzee5962]

Memorization is my absolute cryptonite. I rely mostly on understanding and then when I get to my tests I forget the foundations that made my understanding viable in the frist place. Lovely video. Thoroughly enjoyed it.

[@DrTrefor]

Yup, that's super common. Unglamorous, tedious, but pretty darned important!

[@abhijeetgore310]

@@DrTrefor sir please share ur chess.com id if exists 🙏

[@BboyKeny]

I had your exact problem and found a solution. Maybe it benefits you too ☺️ I use Anki (AnkiDroid on my phone). It's a flashcard app, since memorization very much linked to recollection. The more often you recall something from memory, the better you remember it. There are lots of collections available, from any school subject, to a lot of books. You can also make your own cards, for example tricks you learn on the job and want to remember it. It takes approximately 60 to 70 days to learn a new habit (I track my streak and give myself a reward once completed). When you habitually practice with flashcards a few minutes a day, you have no chance of forgetting.

[@DeathRipper97]

I've played chess a lot throughout school, but I was definitely in the too little memorization camp. I was really good as a kid at tournaments and stuff until everybody started putting more effort into really studying things. That part bored me and eventually drew me to give up chess. It's a beautiful game, I hope at some point my passion is reinvigorated to go and study it more deeply. That being said, there's definitely a connection between those good at chess and math and it's not just about somebody being a nerd. All of the kids in my chess club were good at math as well, some winning competitions. A lot of us ended up studying Computer Science. And since I study CS at Faculty of Mathematics, I know a bunch of people form Theoretical Math curriculum and they're all kickass at chess. For some reason, there is a huge overlap in those two interests. I also have a studying tip that I picked up from The Art of Learning that I found really great. Beginners should spend a lot of time studying endgame. In endgame, things are sort of simplified because you don't have as many pieces and as many possible moves. It makes it easier for a beginner to learn patterns because there's less noise. On top of that, it gives you a good idea of what your end goal is. Not every pawn is equally valuable in an endgame for instance, and that gives you insight on how you should build pawn islands and trade your pawns early game to really build up those advantages throughout the game.

[@DrTrefor]

I think that's really good advice. And a lot of beginnings I think struggle a lot at the endgame because if you play blitz online probably it doesn't get to close endgames all that often as everyone is blundering. But that is where you can really build your skills

[@brianwen5055]

Wow! This video has helped me revisit how I learn the two subjects and has motivated me to become intellectually curious about the details again.

[@benwilde1768]

So happy for you that you picked up chess. A great lesson for me on understanding came from the reality check of how easily you are thrown off by only one different move from your opening repertoire. And with that how important it is to truly experience and integrate in your mind every possible version of that problem to have a broad grasp of it and understand it for good.

[@briandwi2504]

Very positive point of view. Interesting to hear your views on this. I find it difficult to get a deep overview of chess, but I take your point about the small details being important, like what to do if you are attacked down a flank. It's a very difficult game to improve at, but, as with most things, persistence is the thing. You get good at what you do a lot.

[@swatimahapatra9806]

And this way I feel we are going to be able to relate each and every sector with that of learning math. The main idea which I could draw is that we are supposed to get into the depth of the matter with a deeper analysis done on a regular basis consistently to master the subject. Nice approach! :D

[@russelrussel419]

When i had my university exam i learned maths from your videos and now when i got bored and started playing chess.... There comes this video😍

[@garimasingh4426]

This is the first video i have seen from you and I watching this has made me want to learn maths again. I have never been good with maths but recently i have started to develop this interest/intrigue where i feel like i want to know more. I have finally found the place where I can start. Thank you so much. This is really helpful.

[@DrTrefor]

Glad I could help!

[@chiko4536]

As I was watching this I had an unfinished problem in front of me where I needed to find the eigenvalues of a 5x5 matrix which seems VERY tedious, but then you started talking about persistence and not being intellectually lazy and that really struck a chord with me, thanks prof!

[@DrTrefor]

Nice one! Ha although even I find 5x5 eigenvalues tedious lol

[@vivaldiantonio2059]

Wow !! This is new

[@alfredhitchcock45]

My crossover is from Chess to Math. I noticed that the same love for logical reasoning and pattern recognition could be translated in Math.

[@AhmedMahmoud-tv9vw]

8:34 That segment was on point, especially for me! sometimes I forget that maths is a skill that I need to put effort into (like memorizing, practicing, etc.), and focus on the "fun" part where I understand the great picture or change my way of thinking about a particular problem.

[@sanelprtenjaca9776]

Small details = basic principles. Also, chess is much about memory. Mathematics is more about pure logic. But they have many things in common. If you take any two intellectual disciplines you would find many simillarites tough.

[@jacoboribilik3253]

I disagree. Chess is pure logic, memorisation simply spares you time in making all the calculation over the board but you first need to understand the position. It's like integrating via u-substitution: you don't prove the result (however easy it may be) every time you apply the technique, you simply limit yourself to applying it.

[@funkycatglasses01]

Loved the advice about puzzles 🧩

[@Alannnn14]

I had a very positive experience when i was trying to get better at chess. I felt that it made me feel better and do better at other areas of my life like time management and studying.

[@DrTrefor]

That’s cool to see those spillover benefits

[@nerdintellect956]

this channel is so under rated

[@GoldenSniper303]

Hi Trefor! Former student Carter here from Calc 1 in Fall 2018 at UC. I'm glad to see that you picked up chess. I started playing obsessively about a year and a half ago. Lots of professional chess players ended up with careers in mathematics. I suppose the opposite may be true as well. I reached a similar conclusion to you about the importance and significance of understanding ideas as opposed to memorizing ideas a few months ago when I was helping one of my friends get better. He was trying to always play/memorize the "best engine move" and not trying to understand ideas or concepts in specific positions. He lacked the ability to recognize very early mistakes in chess games from his opponents. Once I realized that I have a tenancy try to brute force studying and that's usually not the best approach to learning. I'm trying to improve my habits in a similar way that you mentioned in this video.

[@DrTrefor]

Hey Carter, great to hear from you again! I always love when my older students find my channel again:D And I think you are totally right, it is kind of interesting how often people are willing to put in an insane amount of work to do "brute force studying" despite it not necessarily being the most effective.

[@erikawimmer7908]

Thats exactly what im saying! Im now 14 and I play chess since i am 8. Im not perticulary good at it because even tho i play it for a long time now i didnt do so in a real team for a long time and i also lost a little bit of the regularity of playing it due to covid. However since i also love math this connection was obvioud to me really fast and most good chess players wood probobaly also be good mathematicians. Glad you discovered the game!

[@DrTrefor]

Very cool, thanks for sharing!

[@erikawimmer7908]

@@DrTrefor you're welcome ;)

[@parameshwarhazra2725]

This nice man encouraged me to study core math fields though being a Physics student.

[@rahul2000]

sir how can u make everything so simple to understand, u r an inspiration

[@socrates4730]

That was a great speech👍

[@demogorgon2125]

Yup, pretty interesting indeed!!!🤩🤩 Thanks a lot Dr. Trefor

[@DrTrefor]

Very!

[@demogorgon2125]

@@DrTrefor Subscribed to your channel.😄

[@babybeel8787]

How clever! Very insightful thank you :)) , both chess and maths are beautiful , that's for sure...

[@DrTrefor]

I definitely think so!

[@saiajaygelli2380]

🔥🔥🔥🔥 Interesting 🤩

[@IamVaskar]

I am an engineering student and recently I started learning sketching and drawings and I found a lot of similar learning techiniqes there too! with the same mind we are able to learn so many different fields its like discovering the hidden corners of the mind😄

[@DrTrefor]

That's awesome!

[@sachinthaniabeynayake41]

one of great teacher that I have seen in my life🔥❤️

[@alejrandom6592]

11:33 totally true, anyone can learn! It's about consistency and good sources, no natural talent needed :) and today thanks to youtube we have awesome teachers to learn from like you ;)

[@shyamdas6231]

Welcome to the world of infinite possibilities. Chess is love.

[@steliostoulis1875]

10^120 < infinity

[@shyamdas6231]

@@steliostoulis1875 10 to the power 120 is based on the assumption that the game is 40 moves long. If you allow for the full length , which can be 100 moves long, the total possible number of games is stunningly more. In any case, what I meant was that the game of chess had lots of possibilities.

[@anandnadar3080]

As an International Chess Master, I absolutely agree with this! Love your videos!

[@DrTrefor]

Very cool, thank you for sharing!

[@botanr101]

very good - things that apply to learning math also apply to learning chess and learning poker and learning languages. LEarning from people better than you accelerates the learning curve but your brain doesn't make connections without actually doing and if you don't look at what you're doing wrong you're going to be more likely to make the same mistakes. Love that this goes over the different types of study - cause you can easily go too much in one direction end up studying and never playing or playing and never studying.

[@alans8771]

The thumbnail of this video gave me PTSD from last semester , spending long sleepless nights trying to wrap my head around calculus2 topics on a daily basis. Toughest math class I’ve ever had lol

[@DrTrefor]

Haha oh no!

[@Nik-qh7cq]

What a crossover!!!

[@NickKravitz]

I have my masters in both mathematics and chess. Prior to the Internet, when books were the primary method of learning both math and chess, around 80% of chess literature sold focused on opening theory, where the primary skill required is memorization. However, chess students would improve their game more by focusing on middle game tactics and endgame technique. Great talk.

[@alfredhitchcock45]

You can’t memorize chess. I’ve proven that with the same opening i’ve used a million times with different opponents but with different reactions. It’s impossible to memorize all their possible reactions.

[@Nik-qh7cq]

It was in this position that we had a new kind of video.

[@DrTrefor]

haha, vintage agadmator line:D

[@jacoboribilik3253]

the most remarkable similarity between chess and mathematics imo is the simplification of complicated positions (problems) (using previously cooked up simple techniques) into simpler ones to which we already know the solution. This happens a lot in endgames: if you can trade a couple of pieces off the board and you visualise a simple schematic ending at the end of the tunnel then you should go for it. The great French mathematician Henri Poincare once stated: a good mathematician is a good chess player and vice versa.

[@a7md944]

Thanks Dr. for this channel. I wish if you would consider applying propabability example on chess.

[@DrTrefor]

I have actually thought about sharing some slightly more mathematical treatments of chess. Mostly it doesn't take high level math knowledge, but there are some interesting things to analyze.

[@abhijeetgore310]

Both are my favourite topics😀

[@y154707]

I think the most important thing you mentioned in the video is the growth midset concept. It doesn't matter if you started with math and then you pick up chess, or other way around: the mind-pattern that has developed in you is useful for other disciplines as well, provided it stays flexible and adaptable. You can also use the same mind-patterns to recognize a beautiful piece music, identify a plumbing issue in your bathroom or study the vast literature of the Vedic school of Yoga. The information and expresions are different - "in" and "out" -, but the internal, adimentional mind processes are the same for all examples.

[@DrTrefor]

I totally agree!

[@NatureLibrary]

Love from India 🇮🇳

[@mathadventuress]

You’re my hero

[@arsalanwareslessons1834]

Nice video...

[@physira7551]

Make more "random" videos like this They are very helpfull Thank you

[@sparkleofknowledge1102]

So interesting

[@BboyKeny]

The Growth Mindset is important for every activity in life. For example, last week me and my gf were grinding the paint of wood and repaint the whole apartment. It was both our first time doing any of this. We watched an expert on KZbin explain and show it. Made a list of supplies and went to work. Our first main objective/question was "What we are doing, does that look like what the expert was doing?" Second objective was exploratory, trying out different ways to do it and discover why it works or doesn't work. The third was optimization, reflect on the day and think of ways to improve the next day. For our first time painting a whole apartment, it looks awesome. (Except for the wood needing an extra layer of glossy paint. We were made to be scared of drippers, so we didn't use nearly enough paint.) This mindset makes you acknowledge you need to learn and don't have the "gift of God" to simply just be an expert in anything the first time you try. It also acknowledges that if you don't succeed the first time, it's because you need to learn and reflect on what went wrong. It's not because "You simply can't do it and never will be able to". Growth mindset makes any failure into the most valuable experience since Failure = Growth.

[@continnum_radhe-radhe]

🔥🔥🔥

[@zoulzopan]

Great video.

[@DrTrefor]

Thank you!!

[@zoulzopan]

@@DrTrefor what rating are you in chess.com?

[@manishsapkal2641]

I am a math student and I found the memorization point very much relatable to me. I am very bad at memorization and always think that I can do any problem with just mere understanding but in exam I don't remember formulae or principle required to solve certain problem and Perform badly in test. My teacher always wonder how I get such less Marks despite having such good understanding of concepts😕

[@naveenvijay08]

Sir plz make videos for 'Matrix Eigen value problems' 🙏🙏🙏

[@mvkarthik6756]

i am 300th person to like your video :)

[@DrTrefor]

That’s a good number!

[@barthonjiki9046]

wish i had you to calc 3 smh my professor made a practical and enjoyable math course seem very tough. Then again it was a 4-week summer session

[@jorriffhdhtrsegg]

Something in music theory that comes up a lot is the memorisation vs understanding. Relative to maths and chess its unbelievably simple, to be honest, yet the the style of teaching can be toward theory memorisation and a stupid complexity. Intuition comes more from an understanding, then can be applied to practice such as composition and improvisation. Yes, sometimes memorising pieces but its not achieved by head memory, its muscle memory and intuitive...which requires learning all the notes/scales but then forgetting what notes you are using and instead finding patterns of understanding for many musicians. (Or is a mathematician just someone who is best at times tables? Well...no, potentially they can be awful at them but achieve an abstract understanding So a lot of chess masters are either excellent at music or maths, right? But that's the pattern recognition i am familiar with. As Sun Ra said "learn everything about music theory then forget it all"...well its not forgetting but making it like automatic process, pattern recognition, moving it to intuition, familiarity etc. To calculate everything would be exhausting, but at some point learning to calculate(learn a piece, scale, theory) we did do hard prefrontal cortex stuff but then it moved somewhere else and almost became like a visual language, a physical memory.

[@achyuththouta6957]

Tbh I'm good at math but I really suck at chess. One thing that I really love about math is the fact that it rewards you for going in depth. That's why although I don't study math a lot, I get good grades just because I have interest and curiosity. That's all what math needs. For example if you know understand where a formula comes from, you can derive it on your own in case you forget it. I never remembered that the derivative of sin is cos and the derivative of cos is -sin. The negative sign makes it confusing. All I have to do is draw the sin graph and ask what the derivative would look like. It makes your work a lot easier and rewards you quite a bit. I think this is exactly why although some people study more than me, they don't get the same grades because they have no interest in the subject and don't know how to study it. But I've been playing chess for 8 years or so and I'm only rated 1200 on lichess. Although I like chess , one part of it that I don't like is that no one really cares about going in depth. For example, there's a common rule that you have to control squares in the centre of the board in the openings. I've asked a lot of high rated players ,why exactly they do that and they have zero clue as to why they play those moves. As chess has become more and more analysed, people have started to memorise a lot of things about the game that instantly give them an advantage over someone who didn't. Even if they don't know why they play the moves they play in the openings and certain positions, it works for them. There's very limited raw spontaneous creative play. Players like Mikhail Tal and Bobby Fischer had such beautiful games. The moves were so original. Most of it is lost today. Luckily enough, I'm ony rated 1200 , so at my level, the play is still spontaneous and raw but I can't spend hours and hours memorising things that I don't really understand.

[@alfredhitchcock45]

Chess can’t be memorized! You will really see the IQ of your opponent, how he thinks critically, what is the pattern of his thinking. Maybe you’re just frustrated about not advancing in Chess because in Math you can get by by just memorizing formulas and rules.

[@theguillaume73]

Hi from France. I am a decent chess player but at 49 I am going back to maths because I want to challenge my brain. I have studied organic chemistry as a student which is different.

[@user-wc7em8kf9d]

1nsp1r1ng as alway2 ! Thanks for teaching.

[@abhijeetgore310]

John Nunn is one of the greatest Grandmasters of chess and he also has Ph.D in mathematics. You should check his immortal games.

[@CancemCancem-he8fl]

man if you need any advise for resources on chess i would love to share my knowladge. I can reccomend you books to improve yourself.

[@gagemorgan7135]

Hearing the memorization part really helps me to get past some of my self doubts. Im tested in the top 99th percentile for memory recall buuutttt lower average processing speed. I beat myself up a lot because it sounds like i essentially have an NPC build. Which isnt helped by my autism diagnosis. Wait, I might just need a therapist...

[@anupamanand8545]

I really want to know your rating

[@mevnesldau8408]

if I am bad at chess, does it implies that I am also will be very bad at math or other science?

[@Nik-qh7cq]

Nice video, but Sicilian is very tricky if you are below 2000elo

[@EEFTARUNA]

Agadmator, gothamchess are the two best channels where you can improve and also entertained ("hanging pawn" is one of the greatest channels out there where you can learn about opening theory middle game and endgame )❤️. Try to play longer time control game instead of blitz Most importantly don't addicted to chess Keep making maths videos for us

[@DrTrefor]

haha chess definitely has affected my KZbin output lol:D

[@Nik-qh7cq]

HELLO everyone

[@EEFTARUNA]

@@DrTreforI know ,chess is the most addictive game out there , especially blitz and bullets

[@EEFTARUNA]

@@Nik-qh7cq sorry about that

[@tiegizzle1156]

I'm sorry for my negativity. Thanks Trevor for your great videos! Edit: I meant Trefor. My name is Trevor

[@DrTrefor]

Ha, another Trefor, even if you spell your name wrong lol! I'll give one more specific nuance though that I actually cut from the video as I wanted this first one a bit more general: Suppose you are trying to come up with a plan, either in chess of to prove something in math. If you are a bit stuck, a good way to get unstuck is to think "what do I WANT to be true?". For example, you might wish your bishop to be targetting the king in an ideal world, but unfortunately there is a mass of pawns blocking it. So then you can get the idea of using your own pawns to open up the centre and gain that sight-line for the bishop.

[@matht8884]

Both I lern

[@srikanthtupurani6316]

Most surprising thing is chess is not popular in Japan. Fide rating of Japan in chess is very low. Even poor countries like burma where there are no facilities for chess training are better than Japan in chess. Japanese have done great things in mathematics.

[@davidp.7620]

I wouldn't call rook+pawn vs rook a "small detail". It's a fundamental endgame that all rook endgame theory relies on

[@LovesomeSpice]

Are you implying that if we can master chess it will improve our abilities in maths?

[@DrTrefor]

Ha, I’m not sure that is true. But it can’t hurt!!

[@LovesomeSpice]

@@DrTrefor I mean, it won’t hurt to try! I’ll let you know if I notice any improvements in my ability to complete maths questions efficiently. :)

[@srikanthtupurani6316]

I don't think math and chess are similar. In math we develop abstract concepts to solve tough problems. Problems like fermats last theorem required so many abstract concepts. We need a deeper understanding of the structure of the natural numbers when we deal with tough problems like fermats last theorem. We need to develop new concepts frameworks. It is a very creative process. When we try to solve problems like those in math olympiad we can solve them without having a deeper understanding of the structure of natural numbers.

[@aritra4028]

Sir when will u start game theory ?

[@DrTrefor]

2-3 weeks away, currently planned for 10 episodes:)

[@aritra4028]

@@DrTrefor ok sir thank u 😊😊

[@mercedesbenz647]

Whenever I play Chess I always think I am doing a math problem.

[@srikanthtupurani6316]

We have computers which play chess. But I don't think we can have machines which can come up with abstract concepts in math.

[@chasethescientistsaturre5009]

Chess has math there are 10^120 possible played games

[@imranq9241]

Chess just seems so arbitrary compared to math though. Like it's a bunch of rules some people made up and we follow them. Math however has more natural foundations and can describe all sorts of phenomena, although I guess Godel is always lurking

[@trongtue8384]

those who good with chess easy to learn math but the problem is that they usually dont like remember too much rule on math and they hate solve messy integral (they just like the corcept of math but lazy doing it) Or they born with bad mental math make them slow with number which can take their interest in math .

[@achyuththouta6957]

It's the other way around. Math has very limited memorisation. If you just memorise rules , you may get the grades you want in the exam but you won't be a good mathematician. I hardly memorise anything before math exams. All I do is understand where those " rules" come from. I actually have poor memory but I'm not bad at math. But I suck at chess because chess is a lot about memorising rules. For example, there's a rule that you have to control the centre of the board but a lot of people don't know why exactly they do that. They do it just because it's there in a book or someone told them

[@trongtue8384]

@@achyuththouta6957 that is 2 ways of learning, one is try to remmber everything as much as possible but dont understand them ,that style is come from school place we need to do exam but teacher dont have time to explain any rule for student, the second style is understand things but that take a lot of time and IQ to do that so they didnt teach that way in school. So normally we learn math from school follow the first style and that made people thing math is just a boring subject with memorize formula, and they dont know how to learn math the right way that can take thier love from math and made we bad about math

[@trongtue8384]

@@achyuththouta6957 and if school teach math follow the fist style, student from second style can become struggle with matb and have low score, can you love math but away have slow score and slow at school . So we have problem with defind what is good at math: good at school have high score or become a math person and have a love for math but have slow score .

[@trongtue8384]

@@achyuththouta6957 btw I bet you wont good at caculus with that decent meomory

[@imeprezime1285]

Chess has some irrational rules like: stalemate, castling move, 50 moves draw move etc. I don't like it. Better try to learn and improve at GO. That's the game for mathematicians. BTW, how many different positions on a chess board is possible? I want the exact number, not an estimate 👹

[@abdullahe3674]

Make a chess Playlist,series ;)

[@DrTrefor]

I might one day!! Have to get a bit better a chess still though:D

[@gardenmenuuu]

​@@DrTrefor that would be fantastic if you made videos on maths concepts of chess like the knight's tour,cominactorics on how many games of chess...

[@perfectrin207]

Are you light yagami?

[@abhijeetgore310]

U look like a indian superstar with ur beard

[@lennykoss8777]

💗🌈💗🌈💗

[@abdimoha9135]

Whoever is watching from bed 😁

[@billy-cg1qq]

You just spent your hole life with math, you see everything as math. Not a single similarity in my opinion to be honest 😂

[@suvankardas8916]

chess is far better than math to build a brain

[@achyuththouta6957]

I disagree quite a bit.

[@billy-cg1qq]

You just spent your hole life with math, you see everything as math. Not a single similarity in my opinion to be honest 😂

[@billy-cg1qq]

You just spent your hole life with math, you see everything as math. Not a single similarity in my opinion to be honest 😂