Ask HN: Which books do you consider real gems in your field of work/study?

Inspired by Marty Cagan is the best book on product management I've ever read, despite its corny name.

Some favorite math books

Intro to Smooth Manifolds, Lee -- sweeping intro to geometry with minimal prereqs, great at balancing the nitty gritty details with conveying intuition

A Course In Arithmetic, Serre -- classically terse and elegant intro to algebraic and analytic number theory. Goes from quadratic forms to Dirichlet's theorem to modular forms in a mere 100 pgs!

Princeton Lectures in Analysis, Stein & Shakarchi -- 4 books covering much of classical/modern analysis, they really shine in their discussion of applications

The large scale structure of space-time, Hawking & Ellis -- The most mathematically satisfying treatment of general relativity I've found. High points include proof of singularity theorems!

Spin Geometry, Lawson & Michelson -- Deep dive into the enigmatic "spin groups" and their applications in geometry. Also the only good (book) reference I could find on the index theorem

In psychology, I think Culture of Honor is absolutely stellar:

Culture of Honor: The Psychology of Violence in the South by Richard E. Nisbett & Dov Cohen

https://www.amazon.com/Culture-Honor-Psychology-Violence-Dir...

The authors weave together a basically airtight argument for their thesis, drawing on historical, sociological, and experimental evidence to describe and explain the phenomenon called "culture of honor". It's a short book and really worth reading to see how well an argument can be made.

Rightfully considered a classic in the field, and its third edition was highly anticipated for many years.

This book's niche is in building the intuitive understanding that is often lacking after the typically highly mathematical treatment seen in 200-level circuit theory courses. It's a great transition from "ok, I can manipulate the equations for a circuit with one or two transistors" to being able to design complete, practical electronic devices. The book is also heavily used as a cookbook and reference by practicing electronics engineers as it contains a lot of expert wisdom particularly in the area of high-precision analog circuits (the authors' background is in physics lab instrumentation design).

Just note that the mentioned book, colloquially known as Papa Rudin, is definitely not an introduction to analysis, which is usually said to be "Principles of Mathematical Analysis", i.e. Baby Rudin. Even then, Baby Rudin is terrible as an introduction in my opinion, though it is quite good as a reference.

> I'm not doubting it's great because I do hear it lauded, but it's hard to imagine.

Everyone has their own taste, even with math textbooks; there are plenty of acclaimed textbooks I hate (looking at you CRLS).

> I've been ever-so-slowly self teaching higher maths.

I happen to be in a Discord server for people self-studying math. It's a pretty cool place; if you are interested you can contact u/CheapViolin on Reddit.