Educate me on modern mathematics!
June 10, 2013 7:25 AM
My math knowledge ends just past Newton. What books provide a good, relatively general-audience introduction to the past 150-250 years of problems and developments in mathematics?
Ideally, I'm looking for something (1) that's accessible to a relatively knowledgeable layperson (comfortable with practical math through calculus/elementary analytic geometry, no real background in theoretical math at all), and (2) that blends serious explanations of the actual math with some "softer" historical background about interesting personalities, wider societal influences, etc. A bouquet of books that fall on one side or the other would be fine, too, though, as would some books that treat more specialized topics within that very broad umbrella (like just geometry or just arithmetic, just the early nineteenth century, whatever.) What should I be reading on the beach this summer?
Ideally, I'm looking for something (1) that's accessible to a relatively knowledgeable layperson (comfortable with practical math through calculus/elementary analytic geometry, no real background in theoretical math at all), and (2) that blends serious explanations of the actual math with some "softer" historical background about interesting personalities, wider societal influences, etc. A bouquet of books that fall on one side or the other would be fine, too, though, as would some books that treat more specialized topics within that very broad umbrella (like just geometry or just arithmetic, just the early nineteenth century, whatever.) What should I be reading on the beach this summer?
Sorry, to be more clear, my question was about math generally, but some of the responses regarded more modern mathematicians than Newton.
posted by dfriedman at 7:48 AM on June 10, 2013
posted by dfriedman at 7:48 AM on June 10, 2013
I recently read Gowers' book, and it was indeed great. It was very helpful to me (with about 2 semesters of calculus and one of discrete mathematics, which is more math than you need to read and understand it) in understanding what mathematicians are doing, and in getting the basics of some cool topics like non-Euclidean geometry.
Gowers' website has some similar material, if you want a taste. I think there are some chapters that were cut from the book.
posted by thelonius at 8:05 AM on June 10, 2013
Gowers' website has some similar material, if you want a taste. I think there are some chapters that were cut from the book.
posted by thelonius at 8:05 AM on June 10, 2013
I'd have thought you'd get more answers than this!
Another book I enjoyed was Rudy Rucker's Infinity and the Mind, which is an eclectic book with a lot of material about Cantor, transfinite numbers, Godel, and so on.
posted by thelonius at 2:53 PM on June 10, 2013
Another book I enjoyed was Rudy Rucker's Infinity and the Mind, which is an eclectic book with a lot of material about Cantor, transfinite numbers, Godel, and so on.
posted by thelonius at 2:53 PM on June 10, 2013
Here are some that might interest you.
The Math Book is a fun, easy to read compendium to get you in the mood. It provides short coverage of things like the ABC Conjecture and the NP completeness of Tetris.
The Honors Class is a very good book on math in the last century based on Hilbert's problems. Highly recommended.
Turning to more specific topics, there is John Derbyshire's (yes, that John Derbyshire) Prime Obsession, which discusses the Riemann Hypothesis with many great historical and biographical interjections.
Finally, a little book on the history of Poincare's Conjecture, leading to its proof by Perelman: Poincare's Prize. I quite enjoyed the biography of Poincare at the beginning. Also, I really did read this one on the beach!
posted by Bokmakierie at 4:00 PM on June 10, 2013
The Math Book is a fun, easy to read compendium to get you in the mood. It provides short coverage of things like the ABC Conjecture and the NP completeness of Tetris.
The Honors Class is a very good book on math in the last century based on Hilbert's problems. Highly recommended.
Turning to more specific topics, there is John Derbyshire's (yes, that John Derbyshire) Prime Obsession, which discusses the Riemann Hypothesis with many great historical and biographical interjections.
Finally, a little book on the history of Poincare's Conjecture, leading to its proof by Perelman: Poincare's Prize. I quite enjoyed the biography of Poincare at the beginning. Also, I really did read this one on the beach!
posted by Bokmakierie at 4:00 PM on June 10, 2013
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I haven't read Tim Gowers's Mathematics: a Very Short Introduction but I am 100% confident it's great.
posted by escabeche at 7:40 AM on June 10, 2013