Mathematics: Its Content, Methods and Meaning

Post by alok-g » Wed, Jul 01, 2026, 10:51 PM UTC

rramadass wrote: post #29

alok-g wrote: post #27

Earlier quoted context omitted.

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?

Not the person you asked the question of; I thought everybody knew of this site especially Indians since it was started and is lovingly maintained by an Indian :-) A lot of hard work has gone into it with not just scanning of the books but also typesetting some of them in latex for better rendering and reading. The website author deserves all the credit/acclaim he can get. All of the books are hosted on internet arch…

Post by helterskelter » Thu, Jul 02, 2026, 3:52 PM UTC

soulofmischief wrote: post #36

helterskelter wrote: post #6

I've been relearning trigonometry lately by myself for navigation and astronomy; not for work, just curiosity I guess. One book I've really enjoyed is Heavenly Mathematics by Van Bremmelen. It's a spherical trig textbook, but it's written by a math historian who describes how trigonometry was gradually developed over human history and he discusses its early proofs, methods and applications. I have to confess that the…

This is the approach I take to learning just about everything: Ask the five W's: Who, what, when, where, why? It compounds, as you learn more history, you're able to connect more and more dots, and learning new information becomes easier on average.

Post by nathan_compton » Sat, Jul 04, 2026, 1:56 PM UTC

rramadass wrote: post #35

hamburgererror wrote: post #34

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Thanks for the references, I'll have a look. I can tell you what I don't want: books that throw theorems one after the other without any context, like Baby Rudin [1] for instance. I tried once to read Terence Tao's Analysis I [2], it's really good but my main problem was that I wasn't able to know if my proofs are correct when I do an exercise. So maybe the solution is to get a teacher. [1]: https://en.wikipedia.org/…

AI is a godsend here. One can use the Socratic (aka Maieutic) method with AI to both explain and verify one's understanding. For some references see https://news.ycombinator.com/item?id=48342887 I have used Google's "AI Overview" and "AI Mode" profitably to have it explain new concepts to me in simple terms and also have had it verify my own understanding of something. The reason i prefer it is because it is a search…

Post by rramadass » Sun, Jul 05, 2026, 4:46 AM UTC

nathan_compton wrote: post #45

rramadass wrote: post #35

Earlier quoted context omitted.

AI is a godsend here. One can use the Socratic (aka Maieutic) method with AI to both explain and verify one's understanding. For some references see https://news.ycombinator.com/item?id=48342887 I have used Google's "AI Overview" and "AI Mode" profitably to have it explain new concepts to me in simple terms and also have had it verify my own understanding of something. The reason i prefer it is because it is a search…

I've got a PhD in Physics (undergraduate in Math, fair amount of self study) and I have to caution against taking what the AI's say seriously.