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I agree that there are mathematicians with this viewpoint. However, I argue that this viewpoint is obsolete and should no longer be acceptable. Sure, it's grea
by dwheeler 6y ago
I agree that there are mathematicians with this viewpoint.
However, I argue that this viewpoint is obsolete and should no longer be acceptable. Sure, it's great if a proof can be clearly understood completely by human. But humans are frighteningly limited creatures. Humans struggle to understand some things, and make mistakes all the time. Euclid's Elements was one of the most popular books of all time, and no one noticed an omission of an axiom for over two thousand years. Mathematicians are smart people, but they are merely people. They make mistakes all the time. Even published papers have had many mistakes found in them.
If the goal is to make up stories and communicate them, then sure, there's no need for computer verification. But that sounds like a fiction writer. I don't think that describes mathematics adequately. Science and engineering all depend on mathematics, and for that to work well, mathematics has to be rigorously correct.
If the goal is for absolute certainty that certain claims are true given certain assumptions, then we need to move beyond the traditional manual methods of verification. Mathematics has gotten too complex for that to work anymore with a reasonable level of confidence. It will be challenging and take time, but so are many other important endeavors.
Is mathematics about truth, or about something else? In many ways this discussion is basically an argument about what is mathematics. You can see where I land on that question. I think truth should be the goal.