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> but the goal of proving a theorem is only rarely finding any proof No. The goal of proving a theorem is proving it any way possible. And "inelegant" proof is
by awkwarddaturtle 9y ago
> but the goal of proving a theorem is only rarely finding any proof
No. The goal of proving a theorem is proving it any way possible. And "inelegant" proof is just as much a proof as an "elegant" proof.
> and in the best case scenario a proof that actually forms a sensible new theoretical framework in which the theorem becomes almost trivial to prove.
What?
- gizmo686 9y ago>> and in the best case scenario a proof that actually forms a sensible new theoretical framework in which the theorem becomes almost trivial to prove. >What? The idea is that, in creating the proof a mathematician invents a new way of looking at the problem. When viewed in this new way, the problem itself sometimes becomes trivial. When this happens, the the framework that was developed could be used to attack new problems that had previously been unapproachable.
- daveFNbuck 9y agoIsn't tossing a bunch of computational resources at a problem a new way of viewing it that makes it trivial?
- snakeboy 9y agoBut it gives no framework for approaching other problems under any kind of new unified theory.
- daveFNbuck 9y agoInstead it gives a framework that will solve fairly arbitrary problems as you work on developing a unified theory. Techniques can be much more broadly useful than theories. When I was working on my PhD, I probably saved days or weeks of effort by writing a program to brute force an approximate solution to an equation I couldn't work out. After seeing that the solution wasn't what I wanted, I was able to spend the time I would otherwise have spent on figuring out the equation on something more useful.