The Princeton Companion to Mathematics [pdf] | Hacker News Reader

The Princeton Companion to Mathematics [pdf]

sites.math.rutgers.edu

92 pointsk2enemy25 comments

This book is brilliant. An overview of all of mathematics, insofar as that's possible. High quality articles. For instance Terence Tao wrote the entry on Compactness and Compactification (topology/analysis) among others. I've had the print volume for a few years now, highly recommended.

> An overview of all of mathematics

It covers only pure mathematics. From the Preface:

"... it was suggested that a more accurate title would be "The Princeton Companion to Pure Mathematics": the only reason for rejecting this title was that it does not sound as good as the actual title."

Worth noting for the interested reader that's disappointed upon reading your comment that there's also a Princeton Companion to Applied Mathematics (ISBN-13: 978-0691150390, ISBN-10: 0691150397).

Sadly there is something here, but it is not that: https://sites.math.rutgers.edu/~zeilberg/akherim/PAM.pdf

As an aside, from time to time I try to cut the filename out of these kinds of urls and I'm delightedly nostalgic whenever I can browse the server, as it was so common some years ago; these were the kind of "secret powers" that attracted a lot of kids to learning about computers...

Could anyone with expertise comment on its accuracy and overall quality? I already have Gowers' book, which I love.

I also bought the print volume right when it came out. Not gonna lie, it’s my monitor stand now ;)

Thank you. Doron Zeilberger is an original; do not miss a chance to hear him speak.

I can access though my university, but I'm limited to 100 pages per download, requiring 11 logins. Here, I just needed Acrobat to crop for an iPad, and to remove the four instances of "This page intentionally left blank".

He is perhaps the worst speaker I have ever witnessed.

Thanks you. Nice to see a condensed history of Mathematics in it.

First non-fiction book that I read cover to cover was a little book in college library called "the history of numbers" (If I remember it correctly). Somehow I really love when a chapter starts with historical overview of the subject. The seemingly "obvious" ideas have taken so many centuries to become "obvious" to everyone. I find it both scary -- how slow the truth propagates -- and humbling as well.

You (or others) may like Struik’s A Concise History of Mathematics [1]. It’s also quite easy to read cover-to-cover. My other favorite, Stillwell’s Mathematics and Its History, is excellent as well.

In my opinion, Stillwell’s book is better to read as a way to motivate a particular topic, whereas Struik’s book really tries to illustrate the arc of mathematics through history—of course, Struik’s approach has its limits.

History can motivate otherwise inscrutable or dry mathematics in a way that would probably interest many students. Why isn’t the history of math a serious part of secondary school? I don’t think US students remember that much of whatever we do teach there anyway.

[1]: https://www.google.com/books/edition/A_Concise_History_of_Ma... or https://archive.org/details/concisehistoryof0000dirk

That sounds like a great idea. It might help reduce the Dunning-Krueger effect which says that people who don't know what they don't know are overly confident about the knowledge they (think they) possess.

Teaching the history of math would tell the students what they don't know and would no doubt motivate many to learn more.

I had a short course on History of Philosophy in high-school which I liked but which was kind of fuzzy because that's the way philosophy is. It was hard to discern any progress or direction in the study of philosophy over the centuries.

Whereas with math, there is no fuzziness about it, except in Fuzzy Logic of course.

> Why isn’t the history of math a serious part of secondary school?

Because 4 years already isn't enough time.

> I find it both scary -- how slow the truth propagates -- and humbling as well

Very true, similar to what happened to geometric algebra.

This is the book that got me into mathematics as a high schooler

Is there a book like this that is for physics? For biology?

For physics have you seen _Motion Mountain_?

https://www.motionmountain.net/

There’s The Road to Reality by Roger Penrose.

What's the legal status of this?

I'm fairly confidently betting "illegal" since the Princeton University Press's own page about the book offers an ebook version for sale at a nontrivial price, which I doubt they would be doing if they were also offering a free PDF download.

(My saying this is not intended to imply anything about the ethics of reading this copy online, or downloading it, or printing it out, or of Doron Zeilberger's decision to make it available. Or for that matter about the ethics of selling it commercially and not making it officially available for free. Whatever the rights and wrongs, some people will care whether it's legal or not, and I'm pretty sure it's not.)

Indeed. Please consider paying for it. Mathematicians aren't rolling in cash.

> Doron Zeilberger's decision to make it available

We don't know if it was a decision or a permissions error.

I'm guessing (hoping) permissions error since there is PII in the same directory.

Out of interest, what does "PII" stand for? I can't seem to locate it in the directory or on google.

"Personally identifying information".

Why is this flagged?

Because it’s still being sold for 70$ in ebook form.

https://press.princeton.edu/books/ebook/9781400830398/the-pr...

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