I'd love to see recommendations for textbooks that satisfy these criteria for various topics, whether those recommendations are newly aggregated here in a comment or from an existing list elsewhere. I'm aware of several enormous lists of textbooks, but I don't know of any that index favorites from this perspective. I'm particularly interested in {proof, geometry, complexity, chemistry, information, thermodynamics, RL} theory.
I agree. Maybe it's time to repost The Best Textbooks on Every Subject again? Many of the topics I want to self-study I haven't found recommendations for in that thread. Or maybe we should create a public database of textbook recommendations instead of maintaining an old forum post.
Someone's idea today was to make a Best of X tag for posts that are specifically recommending a product while having tried at least two other products in that reference class (of which textbooks are one existing example), and then people are encouraged to make top-level posts in this genre, which are easier to search.
I get very little value from proofs in math textbooks, and consider them usually unnecessary (unless they teach a new proof method).
I think the problem is that proofs are typically optimized for "give most convincing possible evidence that the claim is really true to a skeptical reader who wants to check every possible weak point". This is not what most readers (especially new readers) want on a first pass, which is "give maximum possible into why this claim is true for to a reader who is happy to trust the author if the details don't give extra intuition." At a glance, infinite Napkin seems to be optimizing much more for the latter.
A property common to many of my favorite textbooks: the author points out what is important to track (especially in ways not already part of the "standard wisdom").
For example (grabbing the textbook nearest to me), The Geometry of Physics by Theodore Frankel is full of statements like:
Since and are diffeomorphic, it might seem that there is no particular reason for introducing the more abstract , but this is not so. There are certain geometrical objects that live naturally on , not .
or
There is a general rule of thumb concerning forms versus pseudoforms; a form measures an intensity whereas a pseudoform measures a quantity. [...] Our conclusions, however, about intensities and quantities must be reversed when dealing with a pseudo-quantity, i.e., a quantity whose sign reverses when the orientation of space is reversed.
Additional good textbook quality: Prove to me in the first chapter the power of the topic your textbook is written on. I do not want the first 5 chapters to be a bunch of definitions, because then I have no clue whether the rest is worth reading. Either get me inspired to learn your subject, or tell me the myriad things I will be able to do that I otherwise couldn’t and what they’re good for.
This is understandably absent from most textbooks as most don’t read textbooks for fun or profit, but as a requirement imposed on them by their professor, and the professor neither needs to be inspired or reminded of the applications of their subject.
First posted this as a comment on the open thread, where I was encouraged to repackage it as a top-level post. Feel free to shift your votes to this one.
Heuristics for choosing/writing good textbooks (see also here):