Thread

1. ForgotMyUUID · 1789802300 · focus · HN ↗

   I’m reminded of that famous debate between Poincaré and Hilbert at the International Congress of Mathematicians in Paris in 1900. It was then that everyone decided to follow Hilbert’s path, and proof came to be valued more than intuition. I think modern math at school and at applied university kind of lost this intuitive part.

   I try to teach my students that mathematics is, first and foremost, a very precise language of communication. It’s sometimes amusing to ask those who don’t like math to do without it entirely, just to see how much harder it becomes to describe the things around them.

   Second thing I tell them, formulas are the essence of mechanisms in their purest form. And in this form, they’re much easier to grasp and mentally manipulate. It always amused me, after taking a mechanics course, to imagine that for any formula, you could visualize a mechanism or process that implements it.

   And third thing, I suppose, the ability to verify one’s own statements as proof. Although, of course, mathematicians would probably tear me apart here for my heresy:sorry, I’m not a mathematician, but an engineer. You can make mistakes by using incorrect assumptions, but at some point, analysis itself will show you that you were mistaken. There’s a wonderful book, How to Prove It by Daniel Velleman, which provides an introduction to proof for the uninitiated like me. I really enjoyed it.

   1. bananaflag · 1789810853 · focus · HN ↗

      As a math prof, I care(d) much more about proof than intuition, not because proof is more important, but exactly because intuition is (I'm a bit Chesterton-ish here haha). You cannot do proof without intuition hence, if you emphasize proof, intuition will take care of itself. Whereas if you emphasize intuition, students won't have any idea of what a rigorous proof should be.

      1. Aerroon · 1789830515 · focus · HN ↗

         >You cannot do proof without intuition hence, if you emphasize proof, intuition will take care of itself.

         This isn't always the case. Our algebra (or analysis) course focused a lot on proofs for the exam. The result was that a lot of people learned the proofs by heart.

         1. senderista · 1789839246 · focus · HN ↗

            Same here, but I didn't memorize the proofs, I tried to internalize their logic, so I could reconstruct them on demand by just thinking systematically. It did work for me pretty well on my real analysis final exam IIRC (27 years later).

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