Chess and mathematics

Do you think there is any correlation between mathematical ability and chess. Where does schizophrenia fit in. There are several people who are good at math or at chess but totally worthless when it comes to dealing with other human beings of average intelligence. John Nash is the math example and Bobby Fischer is the chess example.

Please chime in.

yeah i agree but what you said about mathematics being about daily life is a subtle point.There are mainly two schools of thought. One(the rubbish one) is sort of like that mathematics is about constructions of the brain and the mind and the second one , the dominant one, though people do not know the roots, is that mathematics, even high mathematics sort of describes the universe. I am personally a Platonist or a neo Platonist. Plato said that there is a higher world than this. And that world is the world of Ideas. He called it the Ideal world and the Ideal world was inhabited by an Ideal table an Ideal chair, an Ideal lake and so on and that our world partakes of the objects of the ideal world. Roger Penrose points out that things like fractals cannot exist if there was not a higher world. Since fractals are never ending dimensionally, there was to be a higher world of mathematics. We might even say that Alpha Zero's game of chess is close to the ideal world of chess.

When it comes to math skill there is a lot of fantasy floating around.

They are separate skills (I'm a former math teacher with serious background, have coached people for the oral part of french engineer schools exams, never really felt any difficulty when I was a student. I am also a terrible struggling chess player who gives free pieces every day in spite of having spent years on it).

I had a colleague, teaching commutative algebra and finite fields to undergraduate who were interested in cryptography. He told me he had an IM among his students. And the IM wasn't good at math...

I think chess can give you good working ethics in intellectual activities and initiate a kid to the pleasure of solving intricate problems. But that's all. To sum it up: if you want to improve at maths you have to study maths and if you want to be good at chess you have to study chess.

I love maths and chess becouse I like logic and thinking outside the box

yeah that's what draws a lot of people to mathematics and likewise chess. what you said about thinking outside the box is interesting. today i was trying to solve a phsyics problem in which there is a forcce of equal magnitude acting towards the vertices of a regular pentagon. The question was what is the total force exerted on the center. Anybody can see that since it is a regular pentagon, the sum is zero but the question was how to prove it. i finally managed to come up with a proof after about two hours. i am out of touch. The simplest way you can do this is by converting the vectors to complex numbers and then summing them. The sum forms a geometric series of five terms and then you just reduce it using a simple technique to get the answer which turns out to be zero.

Chess is more involved though. There is no rule to go by. Every position is different. This is why it cannot be labeled a science.

Mate It a super easy proof

Physics and maths are also labeled by rules

yeah exactly. that's what i said. there are rules in physics and mathematics and there is a methodology. in chess steinitz tried to formalize chess but it is still not as precise. it requires a great deal of original thought and creativity. kasparov is one of the primary exponents of the creative school of thought in chess. he lectured at stanford saying that chess is a great area for AI to investigate.

Reminds me of Kafka who was another legitimate nut.

Wow I almost forgot you guys exist. I always thought Platonists died out with the Aristotle beliefs of the elements.

ZFC proves fractals exist (even ZF without choice does. The Cantor set can be described using only elementary facts about real numbers). But most mathematical objects aren't "physical".

hey superchessmachine blocked me for no reasons

One of my physics teachers was an Aristotelian and he used to tell us that negative numbers do not exist nor do complex numbers nor does the number zero exist.

how would you prove it. don't say stuff like its obviously true. you have to prove it without resorting to a calculator, just using algebra.

If I recall correctly, GM John Nunn is superb in both chess and math.

I don't know much about set theory but fractals look different at different zoom levels. they aren't physical objects but you can't predict what a fractal like say the Mandelbrot set will look like at a certain zoom level without actually feeding it into a computer or otherwise computing it. This brings us to the conclusion that it must exist somewhere though not in a physical sense.

hey pdve

yeah john nunn is excellent in both areas. i believe he is a graduate of oxford or cambridge.

#16

The idea that negative numbers don't exist (but ordinary positive numbers do) is all garbage philosophy and bullshit.

If you don't believe in negative numbers, you still can define relative numbers without any circular argument in the following way.

Let N the set of natural numbers; +,x denotes the usual operations. 
A "relative number " is a subset X of N^2 (the set of pairs of numbers) having the following property:
there exist a pair (a,b) in X such that for every pair (c,d), (c,d) belongs to X if and only if a+d=b+c.

if X,Y are relative numbers in the above sense we define X+' Y as the set of all pairs (p+q,r+s) where (p,r) is in X and (q,s) is in Y. We also define X *' Y as the set of all pairs (p*q+r*q, p*r+q*s).
If n is an element of N we define f(n) as the set of pairs (k+n,k) where k is any natural integer.
Finally we say that the relative integer X is strictly smaller than the relative integer Y and we write X <' Y if for some (a,b) in X and (c,d) in Y, a+d < b+c (it turns out that when it is the case then for every(a',b') in X and (c',d') in Y,we also have a'+d' < b'+c'). 

If you're motivated you can check that

1°) if X and Y are relative integers, so are X +' Y and X *' Y.

2°) The set of relative integers with the operations +',x' defined as above is a ring with f(0) being neutral for the sum+' and f(1) neutral for the product x' (i.e usual algebraic properties hold)

3°) for every p q natural integers, f(p+q)= f(p)+' f(q) and f(p x q)= f(p) x' f(q)

4°) for every p, q natural integers, if f(p)= f(q) then in fact p = q ( 3° and 4°  allow to view N as a subset of the set of relative integers with the same operations)

5°) <' is a total strict order and for every natural integers k l, k < l if and only if f(k) < f(l)

6°) for every X relative number, if by  -'X we denote the set of all pairs (q,p) where (p,q) is in X, then -'X is also a relative integer and X + (-' X) = (- X')+ X = f(0). -'X is the only relative number to have this property.

7°) for every relative number Y, f(0) <' Y or Y= f(0) or Y <' f(0). Y <' f(0) if and only  f(0) <' -'Y;  and  -'Y <' f(0) if and only if f(0) <' Y.

8°) if A,B are relative numbers A <' f(0) and B<' f(0), then f(0) <' A x' B (NB: so in that construction, the infamous fact that "the product of two negative numbers is a positive number" can be deduced).

The set of relative integers is usually abbreviated  by the letter Z.

i was never trying to say that success in one field translates to success in the other. fischer for example was never interested in his studies. or if john nash played chess he could probably be world champion. it's also a matter of interest and perseverance.