[FOM] FOM Digest, Vol 56, Issue 10
joeshipman at aol.com
Sun Aug 19 00:19:04 EDT 2007
Yes, unless there is another counterexample (Dirichlet's theorem is the
only unarguable counterexample so far, though I am currently
researching this to see how much of it can be made accessible).
Note that I did not propose that computer-aided proofs could be made
humanly readable within 100 years, just that anything the best human
mathematicians can do will be doable by undergraduates in 100 years.
The proof of the 4-color theorem is already accessible to
undergraduates now in the same sense it is accessible to any other
mathematician -- an undergraduate can easily understand the research
paper and verify the correctness of the program that checks the
unavoidable configurations for reducibility, and run the program. The
100-year interval is the time scale for boiling down human knowledge
Wiles's proof is being rapidly absorbed into an increasingly rich
theory, I fully expect it to be accessible to undergraduates by 2100.
Finite group theory is a good example of a field of mathematics with
lots of long messy unilluminating proofs, and I have no idea HOW the
proofs will eventually be simplified, but I discussed this with an
expert on the subject, John Conway, the other day, and he said he feels
sure that much much better proofs exist and that we have just not,
collectively, been smart enough to find them so far.
(My 100-year rule is an empirical observation, but it may take longer
in the case of the CSFG, since it is a very unusual example of a
theorem proved by a huge collective effort without anyone really
understanding it all, and it is amazing that it really could be fully
accomplished by "crawling around", as Conway put it.)
From: Insall, Matt <insall at umr.edu>
In the year 2100, will proofs of the four-color theorem, the
classification of finite simple groups, and Fermat's Last Theorem be
accessible to undergraduates, by your thesis?
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