Today I spent an hour on trigonometry exercises and another half hour reading The Mathematical Tourist by Ivars Peterson, which I’m considering as my next light reading book. It’s an explanation for the lay reader of some of the developments in mathematics current in the mid 1980s. Its first section is about the proof of the four-color theorem in 1976, which was controversial because it was one of the first proofs to be partly generated by computer. Proofs of this kind are less controversial now; the proof of the ternary Goldbach conjecture that I mentioned a few weeks ago is another example. A little outside reading suggests there is still some dissent, though, regarding whether proofs that cannot be fully verified by a human being should be considered valid.
One of the people who proved the 4 color theorem defended the proof by saying that there are thousands of proofs in mathematics that anyone can understand, so there ought to be at least one proof that no one can understand.
Ha! When the computers start proving things on their own there may truly be proofs no one can understand. (Or have we already reached that time?)
tee-hee
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