I've mentioned two short mathematical/historical books that recently joined my bookshelf: Euler: The Master of Us All by William Dunham and The Way I Remember It by Walter Rudin. I recommend them both, with the following cautionary comments about the intended audiences.
Dunham's book begins with a brief biography of Euler, but most of the book is dedicated to exposing Euler's life work and characteristic style through his propositions and the proofs that he presented for them. The historical context -- as well as the mathematical context -- is an integral part of the text, and is not separated from the mathematical development. The book is self-contained, and almost all of it should be accessible to one who has taken elementary single-variable calculus and remembers a reasonable fraction of it. It is a good book to have if you enjoy playing with mathematical problems that do not involve too much intricate machinery.
In contrast, a large fraction -- more than half -- of Rudin's book
is dedicated to a non-mathematical autobiography. This part is
worthwhile on its own; all that is needed for enjoyment is an
appreciation of good writing and a modicum of interest in history or
biography. The latter chapters of the book are devoted to Rudin's
mathematical work, and while they are written for
and not just for analysts, I can't imagine reading them without
the background of an introductory graduate real analysis sequence.
For those interested in the biography but not the mathematics, I
recommend skimming through the latter part of the book for Rudin's
descriptions of interactions with his peers -- but skip the
mathematical content unless you're either brave or have a
math-phobic foe who you wish to terrify. For those who do
have a graduate analysis course in their background, I recommend
both halves of the book; it contains no proofs, but only theorem
statements and high-level descriptions of the landscape, and so can
be read faster than Rudin's monographs and texts.
- Currently drinking: Coffee