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It is still better to have a clean 1-page proof. There is no direct value for proving a theorem. Mathematics is nice because it's useful for further mathematics
by lacker 12y ago
It is still better to have a clean 1-page proof. There is no direct value for proving a theorem. Mathematics is nice because it's useful for further mathematics, useful for real-world applications, and beautiful. A 10,000 page proof that only a computer can follow is none of these things.
- Retra 12y agoIt is the second thing. Anyway, the number of pages is arbitrary -- it is a function of your language and terminology. Not every proof can be simplified, so surely there exist useful proofs that require 10,000 pages minimum for a given finite set of terms. So you are very wrong. You are essentially asserting that the only mathematics worth doing is easy or already known in some compact form.
- jackmaney 12y ago> surely there exist useful proofs that require 10,000 pages minimum The classification of finite simple groups "consists of tens of thousands of pages in several hundred journal articles written by about 100 authors, published mostly between 1955 and 2004."[1] [1]: http://en.wikipedia.org/wiki/Classification_of_finite_simple_groups http://en.wikipedia.org/wiki/Classification_of_finite_simple...
- Retra 12y agoThat is a long proof, yes, but it doesn't support my point. One could easily imagine a formalization that could compress all that work into a single sentence. What you can't do is compress _all_ proofs to single-sentence proofs using a finite number of unique symbols.