Math book recommendations?
June 24, 2014 2:09 PM   Subscribe

Years ago I read John Derbyshire's Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics and loved it. Now I'm studying formal theory/real analysis and I'm finding it really it interesting, but would like to be able to spend my downtime reading about the background of math and also explains some of the concepts. Thanks!
posted by MisantropicPainforest to Education (13 answers total) 35 users marked this as a favorite
Fermat's Enigma. Here's the summary:

xn + yn = zn, where n represents 3, 4, 5, solution

"I have discovered a truly marvelous demonstration of this proposition which this margin is too narrow to contain."

With these words, the seventeenth-century French mathematician Pierre de Fermat threw down the gauntlet to future generations. What came to be known as Fermat's Last Theorem looked simple; proving it, however, became the Holy Grail of mathematics, baffling its finest minds for more than 350 years. In Fermat's Enigma--based on the author's award-winning documentary film, which aired on PBS's "Nova"--Simon Singh tells the astonishingly entertaining story of the pursuit of that grail, and the lives that were devoted to, sacrificed for, and saved by it. Here is a mesmerizing tale of heartbreak and mastery that will forever change your feelings about mathematics.

I actually cried when I read it.
posted by dawkins_7 at 2:13 PM on June 24, 2014 [2 favorites]

Godel, Escher, Bach is kind of the canonical recommendation for this question, especially if you haven't had any computation theory yet.
posted by telegraph at 2:22 PM on June 24, 2014 [1 favorite]

Everything and More is a flawed (gets tangled at the end, despite simplifying the math) but really fun book in this genre. I particularly love set theory and DFW non-fiction, so I may be biased here.

I also really enjoyed Chaos when I was taking a chaotic dynamical systems class.
posted by snaw at 2:29 PM on June 24, 2014

I'm fond of The Art of the Infinite and Chances Are by Bob and Ellen Kaplan and Ellen and Michael Kaplan, respectively. I am biased towards them as I was an early member of the Boston Math Circle, but I did enjoy reading those. They are written for the layperson, but unless you have done work in a bunch of fields, you will still find something new (I had never done any projective geometry, which is encountered in The Art of the Infinite).

Seconding Fermat's Enigma. Or any other book by Simon Singh for that matter.
posted by Hactar at 2:31 PM on June 24, 2014 [1 favorite]

Journey through Genius: The Great Theorems of Mathematics is one of my favorite books of all time. It goes through the most interesting and beautiful theorems (and their proofs) from pre-Euclidean math to more recent mathematicians like Cantor. It also goes in-depth into the people that formed the backdrop for all of these advances, like the dramatic story of Tartaglia and his solution to the cubic equation. My college actually uses this book as the textbook for our History of Math class, but it's interesting enough that I've read it multiple times on my own and always manage to learn something new.
posted by PlasticSupernova at 2:33 PM on June 24, 2014 [3 favorites]

Zero: The Biography of a Dangerous Idea by Charles Seife. Goes through the history of the concept of 0 from the Babylonians coming up with the concept, the Greeks banning it, all the way through Descartes & Einstein.
posted by barchan at 2:40 PM on June 24, 2014 [2 favorites]

I liked Simon Singh's Code, about cryptography and number theory.

Godel Escher Bach is an easy rec (about logic and AI among other things).

Neal Stephenson's Anathem has a bit to say about the philosophy of math. Since you are studying analysis, you might look at his Baroque trilogy, which tells some stories about the founders of the subject (but light on math, and takes place before analysis was formalized).

Peter Smith has a book about Gödel's theorems that includes many different angles of approach (have not read but supposed to be good).
posted by grobstein at 2:54 PM on June 24, 2014

I have enjoyed several books in the Great Discoveries series.
Rebecca Goldstein's book on Godel was an excellent follow-up to the aforementioned GEB, and David Foster Wallace's book on Georg Cantor is quite good.
I would also nth Fermat's Enigma, my favorite in this genre.
posted by OHenryPacey at 3:27 PM on June 24, 2014

I don't have titles for you, but here are some research topics.

Newton and Leibniz. Who invented calculus?

Alan Turing and enigma (NAZI cryptography machine)

Geoffrey Cantor and the invention of set theory.

The strange, sad story of Srinivasa Ramanujan.
posted by SemiSalt at 4:04 PM on June 24, 2014

Just came in to second the recommendation of Zero by Charles Seife. The writing is exceptionally engaging for a math book, so it feels like a light read despite the topic and depth.
posted by dayintoday at 4:22 PM on June 24, 2014

Gamma: Exploring Euler's Constant by Julian Havil.
posted by schrodycat at 7:04 PM on June 24, 2014 [1 favorite]

Derbyshire's other math book: "Unknown Quantity" is also good.

I liked Ian Stewart's "From Here to Infinity"

"A Beautiful Mind", "The Man Who Loved Only Numbers", and "King of Infinite Space: Donald Coxeter, the Man Who Saved Geometry" are all fun biographies of mathematicians.

While checking titles for this answer I found "The Man Who Loved Only Numbers" online in pdf format.

"A History of Mathematics" . According to some reviews, the first edition had exercises (which might or might not appeal to you). If I remember correctly, the history in this book kind of cuts off about 50 years ago but it still contains lots of good stuff.
posted by metadave at 6:44 AM on June 25, 2014

Simon Singh's The Code Book and The Simpsons and Their Mathematical Secrets are entertaining sources of context both mathematical and historical. The Code Book in particular has a simplified explanation of the workings of the Enigma Machine that nevertheless gets pretty deep into the conceptual weeds.
posted by Flexagon at 8:46 AM on June 25, 2014

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