Comment by sanxiyn

10 hours ago

This is basically On proof and progress in mathematics by Thurston restated. When Thurston wrote it in 1994, many people didn't understand what he is talking about.

https://arxiv.org/abs/math/9404236

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sanxiyn

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Tazerenix  7 hours ago

And already on page 2 Thurston cuts the the root of the issue, 30 years ago:

>On a more everyday level, it is common for people first starting to grapple with computers to make large-scale computations of things they might have done on a smaller scale by hand. They might print out a table of the first 10,000 primes, only to find that their printout isn’t something they really wanted after all. They discover by this kind of experience that what they really want is usually not some collection of “answers”—what they want is understanding.

The difference in reactions by the maths community should probably be spit up into those who have read and understood On Proof and Progress and actually thought deeply about why they do mathematics, and those who haven't.

  • lhd1  6 hours ago

    Are you suggesting that Tao, whose banner image on his blog is a quote from On Proof and Progress, has not read Thurston's essay?

    • Tazerenix  5 hours ago

      Tao is not the one who needs to worry, but it bears pointing out that Tao is probably one of the most famous archetypal "problem solving" mathematicians in history (though at that echelon all mathematicians are both problem solvers and theory builders, in the same way that Chess Super GMs are all universalists).

      Tao only changed the heading of his blog to that quote in the last month, which is part of my point. Somehow despite this framework for viewing the field of mathematics having been beautifully described by one of our greatest leaders over 30 years ago, Terence Tao who has spent the last 5 years thinking about this has only just come around to it. Perhaps it has something psychologically to do with his greatest skills being those most under attack (though of course I'm not actually implying anything about Tao, he is obviously an honest and good-natured contributor to the community).

      The people who need to read On Proof and Progress are the undergraduates and PhD students who have ended up down an academic pathway without looking up because they've always been good at proof and understanding mathematics, without ever pausing to ask why.