[sverona]

Mathematics and Plausible Reasoning, in two volumes also by Polya, is the closest thing I've ever found to an explanation of how a working mathematician goes about her business. It has exercises, too. Great fun when I was in undergrad.

[3abiton]

Any recommendations of similar books?

[i_am_a_peasant]

How to Prove it is pretty nice

[vkazanov]

I have both the book discussed here, and How to prove it, and back in the day the Proof book was a revelation, unlike Polya's one, which was interesting but that's about it

How to prove it just made proofs click, and I wish I understood the material earlier, by high school the latest.

I am convinced that all the half intuitive half ("kind of like") mechanical ("just remember this") explanations we get in school and undergrad years are a huge waste of everyone's time.

[i_am_a_peasant]

There are other books in the literature that mainly focus on how to go about proving things rather than proving specific things.

Some titles that come up are:

Mathematical Proofs: A transition to Advanced Mathematics by Chartrand, Polimeni and Zhang.

Book of Proof: Richard Hammack

Jay Cumming’s Proofs

I remember I once had a book that advertised itself as a book on Discrete Mathematics but it turned out to be more in line with the titles above, was a gem, if I find it I'll let you know.

But it's nice to see I'm not the only guy who gets a kick out of this stuff.

I wouldn't bother with things from the foundations of mathematics area, like Russel or Frege and whoever else came from that era, back when people still wrote an 800 page treatise on what a "number" even is. A lot of the material coming from that period seems to have been thrown down the drain.

[sverona]

> I remember I once had a book that advertised itself as a book on Discrete Mathematics but it turned out to be more in line with the titles above, was a gem, if I find it I'll let you know.

Every discrete math book I've ever seen has a strong proof component; it's supposed to be an undergraduate's introduction to rigor. The classes taught out of those books may not actually be that rigorous, depending on whether the students are going to be expected to rigorously prove things later, or if it's just Leetcode combinatorics.

But for a guess, maybe Kenneth Rosen?

[i_am_a_peasant]

Ah yes, I think this was it, I see a note that I have the 7th edition and I wanted to get a hold of the 8th.

[retrocryptid]

+1