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Comment by bunderbunder | Hacker News Reader

As someone who mostly only applies math, that strikes me as a peculiarly academic take. Intuition is more important for me because it’s what enables me to know what methods are most applicable to whatever practical problem I’m trying to solve. The proof’s purpose is to verify my intuition. It’s just a means to an end. I only take the time to do my own when I can’t confirm what I need from a textbook or paper.

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> As someone who mostly only applies math, that strikes me as a peculiarly academic take.

Yeah I was talking strictly about preparing students to become pure mathematicians. No opinion here on other goals.

If what you teach is proofs, then wheat you will filter for are students who live proofs.

And if your job is to train people to become mathematicians, that is absolutely what you should be doing.

The idea the proofs are the heart and soul of mathematics is an unfortunate unforced error, and will lead to the death of the professions now that machines are better at making proofs.

The explanation of proofs I got in school was terrible. I had no idea that you could actually reduce everything to one of the applications of the axioms until I found metamath's proof explorer.

Of course, it's too much work for most normal purposes, and in school they accepted whatever random breakdown people used inconsistently and never explained why.

Actually understanding that it wasn't about convincing anyone so much as having a chain of reasoning going all the way back to the axioms was something of a revelation for me.

Fortunately proofs were still part of the curriculum when I was in school. Typically, geometry focused on proofs. When my kids took geometry, proofs took a back seat to problems. This also got us to the point where the college math curriculum has to include a class on how to do proofs.

or memorize a few

Love is more important than breathing. It is and it isn't.

What good is an end you can't reach, or worse, you can reach but it's wrong?

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