AcademicHamster

I like the sentiment, but I have to disagree. I believe there is something genetically different about Grothendieck that makes him possess superior intelligence. I don’t think you can cultivate a bunch of Grothendiecks in mass by teaching a bunch of children advanced mathematics at a younger age.

I wondered the same. I have no idea, other than to speculate. In this case, it might be out of habit (since this is usually how textbooks are written) or laziness. I can’t recommend any of these books for self-studies unless the person studying is fine with posting every exercise they do online for correctness checks or can hire a tutor.

Probably not. That’s why most of these books are useless for people that self-study. There isn’t an external feedback mechanism to check your work. I’d recommend hiring a tutor. You can post online too, but the answers to your questions may vary.

> Outside the CS bubble, being a PhD physicist has more prestige and status than being a PhD computer scientist.

I disagree with this take. Just as there is more “applied” physics and “theoretical” physics there is similarly “theoretical” computer science and more “applied” computer science. The former camp are similar to the theoretical physicist as many of them are mathematicians with a computer science bent. Even within the “applied” CS camp you have experts in number theory and algebra that apply their skills to cryptography, whereas in the “theoretical” camp you may find theorist using mathematics like homotopy type theory, category theory and the like in their research. Number theory, graph theory, combinatorics, abstract algebra, category theory and the like can get really hardcore in the pure math world. Similarly, theoretical physicist also have to know a lot of mathematics.

I think your optics of what a computer scientist is and does is a bit removed from reality and that PhDs in CS are highly respected (I didn’t even mention the folks working in AI or quantum computing or the other important areas of the field).

What are good beginner resources to learn Lean?