Comment by hiAndrewQuinn
2 years ago
Category theory is a pretty good one. But I think a lot of people would get a surprising amount of value from reading Halmos's slim _Naive Set Theory_, to see just how much work we can create using sets alone.
2 years ago
Category theory is a pretty good one. But I think a lot of people would get a surprising amount of value from reading Halmos's slim _Naive Set Theory_, to see just how much work we can create using sets alone.
“A pretty good one.” Right. The amount of generalization and insight is incomparable.
Let me qualify my claim. I'm thinking of the average HN reader, who is a software professional who may never have touched proof based math before - not you or I who got a perfect score on the abstract algebra final after skipping linear.
_Naive Set Theory_ was a much faster and more accessible read than even _Seven Sketches in Compositionality_ for me, and correspondingly I read it much earlier in my mathematical life. Seeing the natural numbers defined in Chapter 17 or so out of the building blocks of sets alone, more as an afterthought / convenience, was indeed what got me interested in taking a math minor in the first place. And it took, what, two weeks of self study for me to get to that point? Fantastic ROI.
And yet, there are times to use the other theories:
Eg, type theory has more succinct proofs of unique inverses.