Mathematical equivalent of Feynman's Lectures on Physics?

I'm slowly reading through Feynman's Lectures on Physics and I find myself wondering, is there an analogous book (or books) for math?

Solution 1:

The Princeton Companion seems to me to be an attempt to achieve a similar mixture of depth, accuracy, content, motivation, and context. However, because math is a different kind of subject, this is a very different kind of book.

Solution 2:

I tend to agree with Adam-the sheer scale and difficulty level of most mathematics beyond the level of basic calculus would make a book like this almost impossible to write. I think the closest anyone's ever come to writing the kind of book you're suggesting is Kolomogrov, Alexandrov and Laverentev's Mathematics:Its Content, Methods And Meaning. This 3 volume overview-originally in Russian-attempts to give an overview of all mathematical fields for students without much background-only some high school algebra,geometry and calculus is needed. Admittedly,though-in the Soviet Union in the 1960's, most of these students had stronger backgrounds then most of today's undergraduates in America! It's currently available in Dover paperback-I think you'll find it worth a serious look.

Solution 3:

As for me, Vladimir Arnold's writing style is sometimes similar to Feynman's style. For instance, Arnold's Ordinary Differential Equations may be appealing to those, who appreciate Feynman's lectures. I can also recommend the following books:

• V. I. Arnold, Mathematical Methods of Classical Mechanics (Graduate Texts in Mathematics)
• V. I. Arnold, Lectures on Partial Differential Equations
• V. I. Arnold, A. Avez, Ergodic Problems of Classical Mechanics (Advanced Book Classics)

Solution 4:

Tristan Needham's Visual Complex Analysis has sometimes been compared to Feynman's Lectures.

"...it is comparable with Feynman's lectures in Physics. At every point it asks 'why' and finds a beautiful visual answer. ...I believe that this book can make every student understand and enjoy complex analysis. If its methods could be applied in teaching more generally, mathematics would become a flourishing subject" -- NEWSLETTER OF THE EUROPEAN MATHEMATICAL SOCIETY

It's much more specific in scope then Feynman. But it remains the best written math text book I've read.