Found in 11 comments
by synthmeat
I’m going to go with a few assumptions here:

a) You don’t do this full time.

b) By “bottoms up” you just mean “with firm grasp on fundamentals”, not logic/set/category/type theory approach.

c) You are skilled with programming/software in general.

In a way, you’re ahead of math peers in that you don’t need to do a lot of problems by hand, and can develop intuition much faster through many software tools available. Even charting simple tables goes a long way.

Another thing you have going for yourself is - you can basically skip high school math and jump right in for the good stuff.

I’d recommend getting great and cheap russian recap of mathematics up to 60s [1] and a modern coverage of the field in relatively light essay form [2].

Just skimming these will broaden your mathematical horizons to the point where you’re going to start recognizing more and more real-life math problems in your daily life which will, in return, incite you to dig further into aspects and resources of what is absolutely huge and beautiful landscape of mathematics.



Original thread
by pavelrub
Nice! This book is modeled after the The Princeton Companion to Mathematics [1] which is simply awesome in every sense of the word, and extremely recommended for any person who is interested in mathematics.

I'm very glad to see more books being modeled after it, and I hope this trend will continue with things beyond math. My only hope is that those new books will match the quality of the original.

[1] -

Original thread
by webnrrd2k
I have a hard copy of the Princeton Companion to Mathematics and find it incredibly useful -- highly recommended.

Original thread
by pm90
Please please please have a copy of these books in your house:

Its certainly too advanced for a 6 year old (or even a 16 year old, TBH) but just having it around is really great, I think. I remember when I was younger, I would look up stuff in more advanced books even if I couldn't understand them right away. The feeling I had was always: "Someday, I will be able to understand this..." which made me learn more physics and math.

"How to Solve it" is especially great if you do/will teach her in the future.

Original thread
by cschmidt
The link was direct when I tried it. However, to answer your question, it is a chapter from The Princeton Companion to Mathematics. An amazing work covering much of mathematics.

Original thread
by zyfo
Tim Gowers is also the editor of the extraordinary mathematics companion Princeton Companion to Mathematics (
Original thread
by ffmmjj
by Maro
by kqr2
Book recommendation: Princeton Companion to Mathematics

It's a good way to skim a lot of different mathematical topics for further exploration.

Original thread
by dschobel
by harpastum
If you're really interested in learning a lot about mathematics, I would definitely recomment the Princeton Companion to Mathematics (see below for URL). It came out very recently, and while i'm only about 100 pages in (of well over 1000), it's down to earth writing and low prerequisites are very appealing to me.

or if you'd rather not use my affiliate link:

Original thread

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