What Are the Best Books on the Human Side of Mathematics?

[brainy kevin]

Mathematical "Culture" Books

I've been reading about math lately, and I'd be interested in learning a little bit more of the "human" side of mathematics. Could you please recommend some books on these topics? I don't mind more than one book per topic, or a book that would cover multiple topics.

Something of the sort "Famous mathematicians and what they did."
I have two requirements for that.
1. It talks more about their results, theorems, and whatever that their personal lives. I wouldn't mind some facts about their lives, I'm just more interested in their results.
2. It's organized by subject or chronologically, not alphabetically.

Something of the sort "History of Mathematics."
If a book about mathematicians would cover this too, that would be great. Also, I'm much more interested in modern developments in math, like when calculus was completely formalized, the development of topology, the incompleteness theorems, et cetera. I'm just uninterested in studying the hundreds of years it took for arithmetic to be developed, variables to be used, and whatever. Again, I don't want anything organized alphabetically.

Something of the sort "Philosophies of Mathematics"
Discussing formalism, Bourbakism, intuitionism, and so on. I prefer a comprehensive treatment rather than a "for dummies" style. Again, not alphabetically.

Thanks!

 

[Amanheis]

It might not be exactly what you are looking for, but I highly recommend this one:
Fermat's Last Theorem by Simon Singh.
http://www.amazon.com/dp/1841157910/?tag=pfamazon01-20

It covers not only the 300 year old history of said theorem, but also how Andrew Wiles tackled the problem with modern maths and it contains a short history about math as early as the Pythagoreans, if I remember correctly. I could imagine you would like this one.

 

[brainy kevin]

Thanks for the suggestion, but I was already aware of the fact that book existed. I appreciate it though. That reminds me, I've read Flatland, so nobody needs to recommend that. Edit: Is the series "History of Philosophy" by Copleston good?

 

[mal4mac]

Mathematics: A Very Short Introduction Timothy Gowers Oxford University Press 2002

He's a Fields medallist and top Cambridge professor.

Central to his book is looking at "philosophical barriers" that some students put in front of themselves that stops them being happy with notions like infinity, the square root of minus one, the twenty sixth dimension, and curved space. As he says: “It is possible to become comfortable with these ideas without immersing oneself in technicalities.”

The secret is to think abstractly, then many philosophical difficulties disappear.

Incredibly powerful stuff. Required reading for beginning mathematicians and physicists who want to use mathematics with getting lost in a philosophical fug. Not bad for experts as well!

"History of Philosophy" by Copleston is long and only a small part relates to mathematics. Gowers gives the same recommendations I would for longer books on the history/philosophy of mathematics, so I won't bother mentioning them as you should read Gowers first :-)

 

[swaroopa]

I'm also much interested in modern development in maths. Thank you, who people are shared their answers and books and suggestions under this post.

Regards,

http://www.culture.co.in"

 

[Goldbeetle]

I strongly suggest "What is mathematics" by Courant.

 

[jbunniii]

I like Stillwell's https://www.amazon.com/dp/0387969810/?tag=pfamazon01-20. It is arranged chronologically, and focuses more on the mathematics than the history/biographies of mathematicians. And while it does start with arithmetic/Euclid, but it does get to more modern material quickly. Excerpt from an Amazon review:

"Another flaw of many standard history textbooks is that they spend too much time on trivial things like elementary arithmetic, because they think it is good for aspiring teachers and, I think, because it is fashionable to deal with non-western civilisations. It gives an unsound picture of mathematics if Gauss receives as much attention as abacuses, and it makes these books useless for understanding any of the really interesting mathematics, say after 1800. Here Stillwell saves us again. The chapter on calculus is done by page 170, which is about a third of the book. A comparable point in the more mainstream book of Katz, for instance, is page 596 of my edition, which is more than two thirds into that book."

Another book you may find interesting (I certainly do), which spans all three of your topics and then some, is https://www.amazon.com/dp/0691118809/?tag=pfamazon01-20. Parts of this book are arranged alphabetically (the reference sections, mostly) while others are arranged by subject. The section on "Mathematicians" is chronological, and includes brief biographies with more focus on mathematical results than personal lives. The main parts of the book have a quite modern focus and the sections I've read are exceptionally well-written. This is why I've listed this book even though it doesn't fully meet your "no alphabetical contents" criterion.

 

[micromass]

Another book you may find interesting (I certainly do), which spans all three of your topics and then some, is https://www.amazon.com/dp/0691118809/?tag=pfamazon01-20. Parts of this book are arranged alphabetically (the reference sections, mostly) while others are arranged by subject. The section on "Mathematicians" is chronological, and includes brief biographies with more focus on mathematical results than personal lives. The main parts of the book have a quite modern focus and the sections I've read are exceptionally well-written. This is why I've listed this book even though it doesn't fully meet your "no alphabetical contents" criterion.

I also highly recommend the princeton companion! It's not only good for leisurely reading, but it often gives intuition and historic remarks on mathematical results. It's really a must for every mathematics student!

 

[brocks]

I notice that the Princeton Companion is edited by Timothy Gowers, who was very favorably mentioned by another poster for a different book.

 

[jbunniii]

In addition to serving as editor, Gowers also wrote a good chunk of the text. Terence Tao is another substantial contributor. Both are Fields Medalists, and excellent expositors. The whole book is beautifully written and produced. It's a great value even at the $100 list price.