Mathematics

What Hacker News says

1. alok-gJul 2026
   Very very cool! Somehow most names are unfamiliar.

   I have very much enjoyed the OP (Mathematics: Its Content, Methods and Meaning). Any particular books that you would recommend?

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2. rramadassFeb 2026
   If one wants to study Mathematics (or any Science for that matter) sincerely, one has to put in conscious self-effort/time/be-persistent and have the attitude of "knowledge for the sake of knowledge". The goal should be personal development/understanding and not competition/ego-boosting/fame/money/etc. (these are only relevant for the job market) which will not sustain motivation over the long-term. The emphasis should be on one's self-effort and not on the merits/demerits of the Professor/Teacher/Books i.e. "The Master can only show the way, but it is the Student who must walk the path".

   Also Mathematics should be approached from multiple perspectives including (but not limited to) Imagination, Conceptual, Graphical, Symbolic, Applications, Modeling, Sets/Relations/Definition/Theorem/Proof.

   As i mentioned, for studying Mathematics you need both 1) Overview/General books which help in building interdisciplinary intuition/insight and 2) Textbooks which teach methods/tools and put them to use in solving real-world problems. You will find plenty of recommendations for textbooks both on HN and elsewhere on the web (especially college/university websites).

   One excellent must-have book that straddles both is; Mathematics: Its Content, Methods and Meaning by Aleksandrov/Kolmogorov/Lavrent'ev. It covers almost all domains of mathematics until the early 20th century in an introductory succinct form up to undergraduate level. You can then look for individual textbooks for each of the domains given there. See the ToC at - https://store.doverpublications.com/products/9780486157870

   W.r.t. books on Proofs, my first suggestion would be to not focus too much on the formal mechanics of it but try to understand the reasoning/logic behind it in a informal way i.e. the "proof idea" problem-solving process.

   The first book to read here is George Polya's classic; How To Solve It. It gives a problem-solving process with heuristics and thumbrules which is the prerequisite to mathematical formalization - https://en.wikipedia.org/wiki/How_to_Solve_It

   With the problem-solving process in hand, you can now get a gentle introduction to Logic/Discrete Maths leading to Proofs. One very accessible book with broad coverage and a bent towards CS is Nimal Nissanke's Introductory Logic and Sets for Computer Scientists. The author wrote it as the needed background mathematics for formal methods and hence contains everything (including doing Proofs) within one pair of covers - https://www.amazon.com/Introductory-Computer-Scientists-Inte...

   I highly recommend getting all of the above before looking for more. Given your background (as i understood it) i think this would be the best and easiest path.

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3. nabla9Nov 2025
   > Russian books doing this.

   Mathematics: Its Content, Methods and Meaning by A.D. Aleksandrov, A.N. Kolomogorov, M.A. Lavrent’ev,.. https://www.goodreads.com/book/show/405880.Mathematics

   It's still a masterpiece. Originally published in 1962 in 3 volumes. The English translation has all in one.

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4. rramadassOct 2025
   There is no one book which can give you the overall sweep of Mathematics. However, you might find the following (though not textbooks per se) useful.

   1) The Princeton Companion to Mathematics by Timothy Gowers et al. and The Princeton Companion to Applied Mathematics by Nicholas Higham et al. - The closest you have to a Modern Encyclopedia of Mathematics. You get unmatched breadth after which you can move on to dedicated books as needed. Well worth the money.

   2) Mathematics: Its Content, Methods and Meaning by Aleksandrov, Kolmogorov et al. - Absolutely brilliant overview of Basic Mathematics. Published by Dover and hence very affordable.

   3) Elements of Mathematics: From Euclid to Gödel by John Stillwell - Written as sort of an update to the great Felix Klein's Elementary Mathematics from an Advanced Standpoint books. The Topics are particularly well chosen given modern advances; they include Arithmetic, Computation, Algebra, Geometry, Calculus, Combinatorics, Probability, Logic.

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5. __rito__Mar 2025
   When it comes to mathematical concepts- to understand everything broadly, connected to its context, and to understant "what's the point?", nothing tops this book- Mathematics: Its Content, Methods and Meaning (3 Volumes in One) by Aleksandrov, Kolmogorov, and Lavrentev [0].

   [0]: https://www.amazon.com/Mathematics-Content-Methods-Meaning-V...

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6. nextosJul 2024
   Garrity's All the Math You Missed book, mentioned elsewhere in the comments, draws a nice map of subjects, along with little introductions and book recommendations. The map is good for continuous mathematics, but IMHO fails to consider logic and type theory, which is a bit odd given the separate chapter for category theory. It also does not do proper justice to computation and clumps everything together under the label "algorithms".

   Good alternatives are The Princeton Companion to Mathematics by Gowers and Mathematics: Its content, Methods and Meaning by Alekxandrov, Kolmogorov, et al. Those present much more detailed maps so YMMV.

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