Introduction to modern mathematics

This is real modern mathematics. Most of the stuff is in Part III, IV, V and VII. Part III includes 99 'mathematical concepts', i.e. compactness, differential forms, Hamiltonians, homotopy groups and so on. These are mostly short articles of about two pages. Part IV is a survey of 26 branches of modern mathematics, i.e. analytic number theory, algebraic topology, representation theory, PDE. These are longer articles reaching more than 10 pages. Part V is 35 'theorems and problems' that describes some of the more famous theorems and problems. Part VI is short biographies of 96 mathematicians. Part VII is the applications of math in 14 areas including chemistry, info theory, economics and statistics. The list of contributors is full of very famous mathematicians, i.e. Barry Mazur, Charles Feferman and Terry Tao. The style of these articles is mostly short in formalism and rich in intuition and motivation, making them ideal introductions to unfamiliar fields of mathematics. I found some of the articles extremely lucid and learned a great deal from them. The only problem is that this book is very heavy and is literally not light reading. Highly recommended.