The Princeton Companion to Mathematics
Timothy Gowers
26 people recommended it in 10 threads, 2009–2025.
3 of those were in the last year.
2 commenters pushed back on it — worth reading the threads.
What people on Hacker News said
The authors were evidently chosen also for their communication skills since the articles come across as quite discoursive and really convey the beauty of modern maths.
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.
Princeton companion regular and applied version 100% is the one book I wished I got in HS. Shows how big the world is which is very useful at that age.
The Princeton Companion is something your child will return to throughout their math career. It will be an anchor book that will remind them of your support for them when they were still a budding mathematician.
In that regards, The Princeton Companion to Mathematics is fantastic because it maps out how the different fields of mathematics are interrelated.
I personally find it useful as a survey on the field, but I wouldn't recommend it as a teaching guide in and of itself for people who happen to be as dumb as me.
It looks like a pretty complete guide to all of modern mathematics and sounded like it was easy enough for a beginner to get through while still being able to teach math experts some new things.
Something else I’ve found extremely useful in getting into maths topics is the Princeton Companion to Mathematics - it doesn’t have exercises but gives excellent overview essays of a wide range of maths topics
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