The Princeton Companion to Mathematics [pdf]

https://sites.math.rutgers.edu/~zeilberg/akherim/PCM.pdf

by k2enemy • 3 years ago

92 25 3 years ago

sites.math.rutgers.edu

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.

wolverine8763• 3 years ago

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."

JonathanMerklin• 3 years ago

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).

oefrha2• 3 years ago

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

bmitc• 3 years ago

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

WillAdams• 3 years ago

For physics have you seen _Motion Mountain_?

https://www.motionmountain.net/

oefrha2• 3 years ago

There’s The Road to Reality by Roger Penrose.

imranq• 3 years ago

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

Syzygies• 3 years ago

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".

bigbacaloa• 3 years ago

He is perhaps the worst speaker I have ever witnessed.

dilawar• 3 years ago

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.

antioedipus• 3 years ago

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

TylerE2• 3 years ago

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

Because 4 years already isn't enough time.

galaxyLogic• 3 years ago

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.

plumeria• 3 years ago

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

Very true, similar to what happened to geometric algebra.

gjm112• 3 years ago

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.)

TylerE2• 3 years ago

wolverine8763• 3 years ago

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.

sixstringtheory• 3 years ago

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

local_issues• 3 years ago

Why is this flagged?

graypegg• 3 years ago

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

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

The Princeton Companion to Mathematics [pdf]

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