[aschismatic]

Exactly! Proofs are why I love mathematics so much. There's nothing quite like the great "ah-ha!" moment when you find that one leap of logic that topples the rest of the dominoes in a proof. Of course, I understand that some people are better at teaching proofs by involving students in the discovery. Maybe the parent commenter was taught proofs in that same rote manner. I've had professors that have done that, and it's like someone sucked all the fun and learning out of the subject.

From the preface of Computation: Finite and Infinite Machines by Marvin L Minsky:

> The reader is therefore enjoined not to turn too easily to the solutions; not unless a needed idea has not come for a day or so. Every such concession has a price—loss of the experience obtained by solving a new kind of problem. Besides, even if reading the solutions were enough to acquire the ability to solve such problems (which it is not), one rarely finds a set of ideas which are at once so elegant and so accessible to workers who have not had to climb over a large set of mathematical prerequisites. Hence it is an unusually good field for practice in training oneself to formalize ideas and evaluate and compare different formalization techniques.

[Fr0styMatt88]

For proofs, could you recommend any good resources for a beginner? Is there a 'beginner proof' that's great to start with?

I figured out I actually like maths waaaay after I'd left uni. From that time at uni I have a vague memory of proofs being something like a whiteboard full of equations that I got lost somewhere in.

I have a vague feeling that what I'm thinking of is 'formal proofs', but I'm not sure.

[gumby]

Euclid. He tried to prove theorems of basic plane geometry (hence "euclidean geometry). Since we all have an intuitive understanding of (at least the basics of) plane geometry you can look at the work and not have to also learn the domain.

People recommending the classics can come off as pretentious so I will add that I am serious: a modern book of Euclid's methods should be quite accessible.

As a followon bonus: Minsky's and Papert's 1967 book "Perceptrons" (the one that said you can't do XOR with a single-layer network, though you can with a multilayer one) that lead to 25 years of lack of interest in neural networks is entirely about using neural networks on Euclid. So you can go from one to the other!

[aschismatic]

The first upper-division course I took in college concerned itself solely with learning the art of mathematical proofs. I had an excellent professor, so I can't really say how much this book helps with the learning process when used by itself, but we were assigned An Introduction to Mathematical Reasoning: Numbers, Sets and Functions, by Peter J. Eccles. Might be a good place to start!

[ghufran_syed]

I really like "Mathematical proofs - A transition to advanced mathematics" by Polimeni, Chartrand and Zhang If you're looking for a free option, "Book of proof" by Hammack also looks good, but I have less experience with it ( https://www.people.vcu.edu/~rhammack/BookOfProof/ )