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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. a-dub · 1789843830 · focus · HN ↗

      > There’s a wonderful book, How to Prove It by Daniel Velleman

      the name sounds familiar but i don't think i have read that one, i did enjoy "introduction to mathematical reasoning" by eccles.

      personally my relationship with mathematical proofs has been complicated. it took some work to understand basic proofs (dedekind cuts, ideas vs. instructions with mathematical notation), but all of the theory of computation proofs, which supposedly are difficult for many, were completely intuitively easy for me.

      i think mathematicians are facing a similar confusion as computer programmers. the medium used to require precise thinking and the simple act of reading, writing and composing it was a mechanism for thinking and learning. in the llm era, the question is: should there be a new mechanism and if so, what should it look like?

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