Recommendations for books that provide a good survey of the history of mathematics, and are meant to be read by mathematicians/mathematics students?

Question

Preferably:

1. The book should not be fixated upon the "standard/popular" accounts of the Greeks (which usually begin with Pythagoras, move on to Euclid and Aristotle, and end with Hypatia).
2. The book should be more concerned with achievements over the past 500 years.
3. The book should be aimed at an audience of mathematicians or mathematics students.

Answer 1

Stillwell's Mathematics and Its History is an excellent book that fits your description perfectly. See my review.