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. zmgsabst · 1789823298 · focus · HN ↗

         To agree:

         In my experience, proof is the gym reps that allows you to harness strong intuition elsewhere.

         In practice as an engineer, intuition is far more useful, eg, being able to “feel” when something is off in our reasoning — but proofs are where I train those same sensibilities on “harder” problems, (eg) details about how to model identity, equality, and equivalence in a formal model.

         1. lupire · 1789824436 · focus · HN ↗

            Engineering is a religion based on faith. Math is the god you follow :-)

            1. zmgsabst · 1789829895 · focus · HN ↗

               Not really: engineering is explicitly empirical compared to other fields — and mathematics serves as ontology for that experience.

               There’s not faith involved.

               1. oliculipolicula · 1789882173 · focus · HN ↗

                  There could be meta-faith, if you insert engineering into

                  Mathematics, physics, chemistry, astronomy, march in one front [lockstep]. Whichever lags behind is drawn after. Whichever hastens ahead helps on the others...

                  --Karl Schwarzschild

                  The problem or nonproblem before (elite) software engineers were pointed at rather bespoke conjectures, depending on one's specific denomination, was that the frontier mathematicians got too far ahead of the others to effectively drag them along (hence Tao's recent fundraising attempt using his one-off compressed-sensing work)

                  There is also the Experience<->Understanding "wave equation" if you will, codified by the popular engineers' joke about how mistakes/bugs mediate the two

                  Imho what academia+industry really need are GLM-wielding plumbers cheap but capable enough to find these abstraction leaks between silos. One taxes these plumbers so brutally that their clients can get by on basic tokens (morally speaking, so as not to drive demand in the farflung silos of billions bottles and babes)

                  There were interdisciplinarian buzzwords but these did not live outside the grant proposal, and probably won't survive better under the reign of Pangram

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