Books I Recommend

To me, the book is decent for background listening during chores or driving (it is a free audiobook if your library has an associated Hoopla account), but almost all stories boil down to either "I was such a horny guy", or "I used different math tools which allowed me to solve the physics problem", which gets old after a while.

I definitely sympathize with your position. But I think a few things are worth pointing out.

Firstly, it's useful to remember that the purpose of a mathematics book is to teach mathematics, and conversely the purpose of studying one is to learn mathematics, not to solve its exercises. That is, the exercises are not a goal in themselves — they are an additional gift offered by the author in addition to the mathematical content. (Many famous mathematical books don't even have exercises... writing a book is already a lot of effort, coming up with good exercises is additional work, and including solutions is a bit more on top of that.) Moreover, even if a book has exercises, they are never enough, and it is the reader's job to make up many more of their own. (I think readers' giving so much weight to exercises that happen to be written in the book come from school/college mathematics education and testing.)

[1]: https://academia.stackexchange.com/questions/56739/why-dont-...

[2]: https://math.stackexchange.com/questions/57889/hardy-wrights... ("A random sample of 10 maths books I have handy shows that 4 doesn't have exercises.")

[3]: https://www.ocf.berkeley.edu/~abhishek/chicmath.htm (search for "no exercises")

To put it in programming terms: the exercises are the tests, the way to verify that your understanding of the mathematics has no bugs in it. If you're trying to verify that your solutions to exercises are correct, you're in a position akin to writing tests for your tests: it can be useful, but it's a second-order concern. Just as tests should be as “dumb” and “obvious” as possible, if there's any doubt at all that you've solved an exercise correctly, that itself is an indication that your understanding of the mathematics isn't complete, and you need to go back and engage with the material (think deeply, write your own exercises/tests, etc) until it becomes obvious. Of course this takes a lot more effort than plowing through exercises and verifying one's solutions.

Programmers have another advantage over other mathematics students: you can test your understanding of the mathematics by writing actual programs. For example, if you're reading an elementary number theory book and learn about the Chinese Remainder Theorem, you can write an actual program/function for finding solutions to a system of modular congruences. As computers require a level of precision greater than human readers, this will force your understanding to become really sharp, as you have to deal with all the corner cases as well. (No doubt there are areas of mathematics for which this is hard to do, but most of the undergraduate curriculum can fit, and if you find something that's hard then maybe making it “programmable” can be your unique contribution.)

All that said, it's definitely comforting to have solutions to exercises: there's a boost in motivation from being told that your answer is correct and you can progress to the next section, and though there's a cost here (if you needed to be told your solution is correct then maybe you should actually spend more time understanding the mathematics instead of going to the next section — but then again maybe not everyone really wants to understand the mathematics that well), I think that's probably the main thing that's missed when books don't have solutions. As a self-learner, motivation is most of the challenge, and solutions can definitely help there.

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Personally, if I look back at books I went through a good fraction of as a self-learner (and loved), there's an even mix:

• Concrete Mathematics and Generatingfunctionology have complete solutions.

• Burton's Elementary Number Theory has “Hints”, and “Answers” to selected exercises (i.e. those where the answer was a number, not a proof — these are not much work for an author to include).

• The Art of Computer Programming (obviously I've read only a tiny bit of it) has problem ratings and sometimes very terse solutions / outlines of solutions.

• Uspensky and Heaslet's Elementary Number Theory (which I read before Burton) and Analytic Combinatorics have no solutions at all.

I don't think solutions to exercises have made a substantial difference in my engagement with these books, but who knows.

Whenever I read a book thread on HN I end up adding most of the books to my reading list on goodreads. But a year later, I don't remember why I've added the book and all I have to go on is the Goodreads rating and goodreads comments.

These aren't that bad, but if the book has been on a HN book thread, I would much rather see a one sentence comment from HN that reads: "I loved this book, you should read it right now." Instead of any other comments from normal Goodreads users.

How else is it possible to even begin parsing a thread like this? https://news.ycombinator.com/item?id=17980964

Btw, small bug with an empty history (iOS): https://ibb.co/C2hT5Jq

    > So, why would we want to write mathematics any differently?

I haven't looked at the book in question, but generally, you don't just "know if" your solution is correct, you prove it, or at least consider examples that can demonstrate if your solution works in some conceivable cases. That's how "unit tests" work in mathematics.

If the book has armed you with enough knowledge to work though a problem to the end, it has done it's job. The real test will come as you build on that knowledge later on in the book or in real-life applications.

Moreover, it's not like this stuff is obscure knowledge. You can find help online or by looking at other books or connecting with others.