B Proof of mathematical theorems

  • Thread starter kent davidge
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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

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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?
 
798
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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

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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

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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

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I would say "provable" implies "true".
 

jbriggs444

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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.
 

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