Proof of mathematical theorems

[kent davidge]

My question is simple. Can one prove any theorem in mathematics by having only a pen and a paper, or a super-computer for that matter?

Since math is essentially all about theorems, and we usually take them as true. I guess someone went in and proved them at some point in our history. But some of them are rather misteryous and I don't think their proof reduces to writing down equations and axioms.

 

[Stephen Tashi]

Are you the same @kent davidge , who's posted questions about general relativity? How is it that you don't understand the nature of mathematical proof?

 

[kent davidge]

Are you the same @kent davidge , who's posted questions about general relativity? How is it that you don't understand the nature of mathematical proof?

yes, but it is the other way. I should not stick my nose everywhere. I'm having my first classes of special relativity in the uni, but you know, general relativity and quantum mechanics are more interesting.

 

[fresh_42]

Can one prove any theorem in mathematics by having only a pen and a paper, or a super-computer for that matter?

You don't need computation capacities, as these are only rarely used, mostly to cover a finite number of exceptional cases. In general, you cannot proof any theorem (cp. Gödel), but you don't know in advance and most common theorems can be proven or disproven by a counterexample. Whether this takes minutes or centuries is another question. And you probably should have access to a good library and many journals!

 

[jbriggs444]

Can one prove any theorem in mathematics by having only a pen and a paper, or a super-computer for that matter?

By definition, a theorem is a well formed formula for which a proof exists.

Note that the notion of being "true" and the notion of being "provable" are different. Neither implies the other.

 

[Vanadium 50]

I would say "provable" implies "true".

 

[jbriggs444]

I would say "provable" implies "true".

In an inconsistent system, one can prove things that are not true. In a system where the axioms are not true, one can prove things that are not true.

 

[kent davidge]

By definition, a theorem is a well formed formula for which a proof exists.

yes, the problem is that someone can make a false claim that a given assertion is a theorem
so we are left with no option but to believe what authors are claiming to be theorems

 

[jbriggs444]

yes, the problem is that someone can make a false claim that a given assertion is a theorem
so we are left with no option but to believe what authors are claiming to be theorems

You could ask that a proof (or an outline thereof) be supplied as evidence for the claim that the assertion is a theorem.