chess is similar to maths because they are both constructed from a system of axioms. There are lot's of cool stuff about this topic, hope you learned sth new from this.
As a mathematician and recently trying to be a chess player, this video is something nice to watch. At a first glance I thought the edition could have had more work, but thinking of a 2 million subs proffesional channel. Actually, as a small channel, it's the opposite, it's a very nice job! Greetings from Argentina!
My perspective on this is that the similarity probably goes deeper than axioms. In fact, the way chess and math use axiom is completely different on some levels. Stockfish 14 might evaluate a position as "lost" for black because it sees mate in 24, but to human, this evaluation holds no water, because it would be impossible for a human to see that sequence. A 1000 rated player might love a mid-game position but a grand master sees that this is obviously lost. Additionally, axioms in math generally develop from ideas that are discovered by mathematicians. Calculus did not arrive from the formulation of the axioms of analysis but it was the other way around, whereas ideas - openings, gambits, mating patterns - always derive from the initial rules of the game. It's like the rules of chess are a microcosm of the mathematician's lived experience. one-move blunders and puzzles are like axioms, and real games are theories. Math research on the other hand, based on this theory, is probably very unlike chess. What's the best move? Just run it through the computer. I suspect that for every academic field, strategic game, or activity that involves learning, this comparison can be made, with varying degrees of success. Chess is a lot like Ochem and BioChem, which all hugely rely on visual-spatial reasoning and pattern recognition, as well as "axioms" such as electron pushing or molecular orbital theory. Advanced reactions in organic chem might involve a dozen reagents, intermediates, and reaction conditions, and this is barring physical/chemical considerations. Even in English, you need to cover huge amounts of text and somehow synthesize it into your own topic based on the entirety of your personal experiences. I imagine sometimes writing might be like playing chess or solving a math problem. It's probably the learning experience itself that makes the similarity. Learning in humans is inherently "axiomatic". We observe a huge amount of data from reality, and the brain's recognition of patterns that arise from this experience constitute learning. There is so much more to talk about here. In addition to being neuroscience, this is a philosophical topic, and probably someone has touched upon this before, although it's not as mainstream like Karl Marx or Nietzsche or even authors like the existentialist Albert Camus. Maybe philosophers of the mind like Daniel Dennett have covered this. I know Catholics refer to Christ as Logos, or the Word, from God and of God, which is God, and so Christ in his divinity is the source of all logic, reason, pattern, and even reality in the universe. There's a lot more, but I think this idea that there is a single universal logic that all human experience shares is something getting at the truth.
why is that a fear, you cannot memorize an entire game and expect it to happen, top GMs, do prepare but only a few moves, (5-8) not 40 or 80 their are 10^120 possible chess games, and thats just an estimation their might be more, memorizing the best moves of all those games is impossible
Haha, I actually already have a course, you can find it on this playlist: ua-cam.com/play/PLhHHnBbrRHBdWGgrq3taQfvYRkaOLFw7u.html Unfortunately it's about maths, logic specifically... But! logic is as soft-core as maths can get, and there's even some application to linguistics *wink *wink. I'd say the first three lectures don't involve the math portion of logic (except maybe the first one), and from that point on it's all abstraction. And really, that's because symbols in math are just an abstraction of ordinary language to begin with.
A little nitpicky perhaps but I don't believe you defined a mathematical axiom properly in the video. You explain an axiom to be a "rule" but then the clip you play after that with Terrance Tao and his lecture regarding prime gaps at UCLA didn't display that concept at all, that clip depicted a THEOREM, not an axiom. Namely, the theorem that all primes have a prime gap that is an even number (excluding 2 and 3). It's important not to be misleading with your presentation in that sense. A more correct alternative definition that I might propose is that a mathematical axiom is something that we assume to be true, and then operate under that assumption. Whereas a theorem is something that we prove to be true and would not believe unless we had a proof for it. For example, the fact that the shortest distance between two points is a straight line is an axiom, we can't prove that rigorously, but we assume it to be true and from that we have built all of Euclidean Geometry. The clip you presented however displayed a theorem, the idea that every prime gap larger than 3 is even is a provable fact that we only operate on now because we have demonstrated it to be true with a proof (the proof of which i can present as a reply if anybody is curious). Just thought I should point that out, seemed a little misleading the way it was displayed in the video.
Ur right, I never intended the lecture video to relate to the topic, I just wanted some maths guy teaching in the background as I explained a few things, but yes it was misleading. I am aware of the rigorous definition, but decided to use the word “rule” as I thought it would make it easier to draw the connection to chess and their respective rules. Your comment is very helpful for those that are curious, thanks for taking the time to write it out.
@@aaronwelson Ah okay yes and sorry to nitpick just thought I should mention it in case, thanks for taking the time to reply! Loved your video btw, severely overperforming channel for you subscriber base, I've subbed!
Oh, wow. I always thought the opposite. I mean at least chess has a goal, what math want to acheive is not clear, understanding the world for example. -1×-1 is always 1 in math applying the axioms, but if you do the same in chess, let's say you move here you give this you take this and it's equal a queen for example or 3 pawns, that cannot be always the same because you have, what if the other player plays here and here and not take here. The result wont be the same.
Basically, maths consist of rules and these rules go on to shape the theory of mathematics. Chess is similar, it consists of rules, and these rules shape the theory of chess. This is the extent of their similarity What you say is also true, chess is super complicated because it branches out so quickly, there are many options to consider and this makes it difficult to translate the rules into theory. However, in an endgame, where there are less pieces and therefore less moves to consider, the theory becomes more precise.
@@aaronwelson yeah, true. I've always had this connect to be honest, chess to the 3N + 1 problem. The rules are take a number if odd multiply by 3 and add one, if the result is even devide by 2 if odd do the same and the numbers appear to be random yet from a fixed rule, similar to middlegame in chess, you don't know what to expect, but all at the end converge to a simple loop 4 2 1 4 2 1, but can anyone prove it or solve it, probably no, lol. Thanks I'm enlightened.
while math definetly has similiarity with chess, it is still a similiarity that exist also in other games as well. while concept exist in both math and chess, its seems that it actually more different than they are similiar. math theory are discovered through research but they are somewhat already exist in nature. chess theory isnt exactly a theory. when people study chess and looking for the best move, or study openings they arent creating formulas except just working with the formulas. and these formulas probably has anything to do with much system and concept in math.dchess theory are just memorization of the certain moves. all chess theories and openings and traps etc are just fundamentalyl memorization. the truth is if one can memorize every moves in every game of chess, chess can be solved.but given the rules of the game it is still to this are bordelrline impossibleto solve. not to nitpick much, but in my opiniion chess is not more similiar to math as it is with any subject. math pretty muche exist in every thing in this worlds so one can always make a point of how something is similiar to math.
"chess was just inventing they couldnt have known how to find the objectively best move WHICH exists" .. thats not true.. there can be several potential best moves and several winning strategies both according to theory n logic and ones that can be found abstractly like when computers play chess lol come on now let's not insult the intelligence of the first chess players
Yooooo I literally thought I was watching some 3 million subs channel.. I'm really surprised. You caught my attention for the whole video.
Thanks, I appreciate the kind words
Duh i was shocked to see ur comment
I thought the same
@@aaronwelson BRO HOE COME YOU DONT HAVE MILIONS OF SUBS. NOT FAIR MAN. you got my attention the WHOLE vid. Thx!
As a mathematician and recently trying to be a chess player, this video is something nice to watch. At a first glance I thought the edition could have had more work, but thinking of a 2 million subs proffesional channel. Actually, as a small channel, it's the opposite, it's a very nice job! Greetings from Argentina!
Great video. Provided key insight on the basic principles of mathematics. Definitely helpful.
My perspective on this is that the similarity probably goes deeper than axioms. In fact, the way chess and math use axiom is completely different on some levels. Stockfish 14 might evaluate a position as "lost" for black because it sees mate in 24, but to human, this evaluation holds no water, because it would be impossible for a human to see that sequence. A 1000 rated player might love a mid-game position but a grand master sees that this is obviously lost.
Additionally, axioms in math generally develop from ideas that are discovered by mathematicians. Calculus did not arrive from the formulation of the axioms of analysis but it was the other way around, whereas ideas - openings, gambits, mating patterns - always derive from the initial rules of the game. It's like the rules of chess are a microcosm of the mathematician's lived experience. one-move blunders and puzzles are like axioms, and real games are theories. Math research on the other hand, based on this theory, is probably very unlike chess. What's the best move? Just run it through the computer.
I suspect that for every academic field, strategic game, or activity that involves learning, this comparison can be made, with varying degrees of success. Chess is a lot like Ochem and BioChem, which all hugely rely on visual-spatial reasoning and pattern recognition, as well as "axioms" such as electron pushing or molecular orbital theory. Advanced reactions in organic chem might involve a dozen reagents, intermediates, and reaction conditions, and this is barring physical/chemical considerations. Even in English, you need to cover huge amounts of text and somehow synthesize it into your own topic based on the entirety of your personal experiences. I imagine sometimes writing might be like playing chess or solving a math problem.
It's probably the learning experience itself that makes the similarity. Learning in humans is inherently "axiomatic". We observe a huge amount of data from reality, and the brain's recognition of patterns that arise from this experience constitute learning.
There is so much more to talk about here. In addition to being neuroscience, this is a philosophical topic, and probably someone has touched upon this before, although it's not as mainstream like Karl Marx or Nietzsche or even authors like the existentialist Albert Camus. Maybe philosophers of the mind like Daniel Dennett have covered this. I know Catholics refer to Christ as Logos, or the Word, from God and of God, which is God, and so Christ in his divinity is the source of all logic, reason, pattern, and even reality in the universe. There's a lot more, but I think this idea that there is a single universal logic that all human experience shares is something getting at the truth.
Severely underrated
Thanks
My fear is that chess is starting to become more of a memorisation game rather than creativity which inevitably is.
thats only when you get too good
why is that a fear, you cannot memorize an entire game and expect it to happen,
top GMs, do prepare but only a few moves, (5-8) not 40 or 80
their are 10^120 possible chess games, and thats just an estimation their might be more,
memorizing the best moves of all those games is impossible
you can always change varieties in the game
I will totally sign up for your course. Can you give, like, a lecture series on something and go super in-depth?
Haha, I actually already have a course, you can find it on this playlist: ua-cam.com/play/PLhHHnBbrRHBdWGgrq3taQfvYRkaOLFw7u.html
Unfortunately it's about maths, logic specifically... But! logic is as soft-core as maths can get, and there's even some application to linguistics *wink *wink.
I'd say the first three lectures don't involve the math portion of logic (except maybe the first one), and from that point on it's all abstraction. And really, that's because symbols in math are just an abstraction of ordinary language to begin with.
I was expecting more:( what am I missing? Some practical points. Basically I listened to an elaborated statement....
what a small channel, but a very nicely edited video , remember me when you get famous!
(note:i am your 80th subscriber.)
Thanks for the support
pretty good explanation
Homeboy really put all his statpoints into calligraphy and none into drawing
Cool content
great video
A little nitpicky perhaps but I don't believe you defined a mathematical axiom properly in the video. You explain an axiom to be a "rule" but then the clip you play after that with Terrance Tao and his lecture regarding prime gaps at UCLA didn't display that concept at all, that clip depicted a THEOREM, not an axiom. Namely, the theorem that all primes have a prime gap that is an even number (excluding 2 and 3). It's important not to be misleading with your presentation in that sense. A more correct alternative definition that I might propose is that a mathematical axiom is something that we assume to be true, and then operate under that assumption. Whereas a theorem is something that we prove to be true and would not believe unless we had a proof for it. For example, the fact that the shortest distance between two points is a straight line is an axiom, we can't prove that rigorously, but we assume it to be true and from that we have built all of Euclidean Geometry. The clip you presented however displayed a theorem, the idea that every prime gap larger than 3 is even is a provable fact that we only operate on now because we have demonstrated it to be true with a proof (the proof of which i can present as a reply if anybody is curious). Just thought I should point that out, seemed a little misleading the way it was displayed in the video.
Ur right, I never intended the lecture video to relate to the topic, I just wanted some maths guy teaching in the background as I explained a few things, but yes it was misleading. I am aware of the rigorous definition, but decided to use the word “rule” as I thought it would make it easier to draw the connection to chess and their respective rules. Your comment is very helpful for those that are curious, thanks for taking the time to write it out.
@@aaronwelson Ah okay yes and sorry to nitpick just thought I should mention it in case, thanks for taking the time to reply! Loved your video btw, severely overperforming channel for you subscriber base, I've subbed!
Good explanation
Amazing video
HAHAHAHA almost didnt catch that at 0:12
High quality
spaceship from wall.e
spaceship from wall.e
cherry bomb in a random maths video?!??? based .,.,,,
Very good Video, really inspiring! Would you be interested in playing a game of chess online with me?
Sure! Though I'm not exactly sure how to arrange that.. What's your rating?
Idk whats wrong with UA-cam but its deleting all of my comments...
So? Is there a way to play?
@@wissensbox lichess.org/Zgh0y35Y
ah so both require high iq people and both aren't for me
Bro definitely you should be an world champion of chess player than Carlson's or nakamura 😝
Sorry to burst ur bubble but that's not happening, not in a million years, I'm a measly 1600
Oh, wow. I always thought the opposite. I mean at least chess has a goal, what math want to acheive is not clear, understanding the world for example.
-1×-1 is always 1 in math applying the axioms, but if you do the same in chess, let's say you move here you give this you take this and it's equal a queen for example or 3 pawns, that cannot be always the same because you have, what if the other player plays here and here and not take here. The result wont be the same.
Basically, maths consist of rules and these rules go on to shape the theory of mathematics.
Chess is similar, it consists of rules, and these rules shape the theory of chess.
This is the extent of their similarity
What you say is also true, chess is super complicated because it branches out so quickly, there are many options to consider and this makes it difficult to translate the rules into theory. However, in an endgame, where there are less pieces and therefore less moves to consider, the theory becomes more precise.
@@aaronwelson yeah, true. I've always had this connect to be honest, chess to the 3N + 1 problem. The rules are take a number if odd multiply by 3 and add one, if the result is even devide by 2 if odd do the same and the numbers appear to be random yet from a fixed rule, similar to middlegame in chess, you don't know what to expect, but all at the end converge to a simple loop 4 2 1 4 2 1, but can anyone prove it or solve it, probably no, lol. Thanks I'm enlightened.
i prefer turtles
Now ik y i suk at both
while math definetly has similiarity with chess, it is still a similiarity that exist also in other games as well. while concept exist in both math and chess, its seems that it actually more different than they are similiar. math theory are discovered through research but they are somewhat already exist in nature. chess theory isnt exactly a theory. when people study chess and looking for the best move, or study openings they arent creating formulas except just working with the formulas. and these formulas probably has anything to do with much system and concept in math.dchess theory are just memorization of the certain moves. all chess theories and openings and traps etc are just fundamentalyl memorization. the truth is if one can memorize every moves in every game of chess, chess can be solved.but given the rules of the game it is still to this are bordelrline impossibleto solve. not to nitpick much, but in my opiniion chess is not more similiar to math as it is with any subject. math pretty muche exist in every thing in this worlds so one can always make a point of how something is similiar to math.
"chess was just inventing they couldnt have known how to find the objectively best move WHICH exists" .. thats not true.. there can be several potential best moves and several winning strategies both according to theory n logic and ones that can be found abstractly like when computers play chess lol come on now let's not insult the intelligence of the first chess players
chess is board game