Algebraic number theory
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…maybe Milne on etale cohmology: http://www.jmilne.org/math/CourseNotes/LEC210.pdf If you find that incomprehensible, start with Dummit and Foote's Abstract Algebra (read it cover to cover), Neukirch's Algebraic Number Theory, Atiyah and Macdonald's Commutative Algebra, and Fulton and Harris's Representation Theory. If you indeed want to read all that, you may as well enroll in a Ph.D. program in math....
on “Ask HN: Understanding inter-universal Teichmüller theory?” ↗…patterns (exempli gratia, Cox's "Primes of the Form x^2 + ny^2"). But it is also true that, when you are doing mathematics, such a book is not nearly as helpful as an impenetrable tome like Neukirch's Algebraic Number Theory. From my own experience (which, I'll admit, is not much to extrapolate from), the former was great for its "insight" and the latter just had too much unnecessary "information". Until I got stuck in…
on “Why do many math books have so much detail and so little enlightenment? (2010)” ↗