From e-commerce to flying in airplanes and spacecraft, mathematics enables almost every aspect of our lives in this post-industrial age. But exactly what are the areas of mathematics that make these things possible? And just what was it that made someone sit up and think, 'I must solve this!'

In the follow-up volume to the best-selling On the Shoulders of Giants: The Great Works of Physics and Astronomy, world-renowned author and physicist Stephen Hawking presents thirty-one landmarks of mathematical thought. From basic geometry through the theory of transfinite numbers, this comprehensive volume traces the work of 17 mathematicians over 2,500 years. Each chapter is laid out in an accessible format: A biography of each mathematician which discusses the significance of the

mathematical research, The full proof of the work, reproduced from the original publication.

In addition, three significant results are translated, for the first time, into English.

Revolutions in thought and how we perceive the world around us have always occurred with revolutions in mathematical thought.

Mathematics has been integral to the development of physical science. But it also stands as an independent discipline pursued for its own sake. The work of Karl Weierstrass, Georg Cantor, George Boole, Alan Turing, Kurt Godel, and others have all built on the work of their predecessors, stretching as far back as the Babylonians and the Greeks. And their work, in turn, feeds the new theories being developed by contemporary researchers.

Hawking posits that, if the wonders of the ancient world were physical (like the pyramids), then the wonders of our world are the works of the intellect. This volume gathers some of the brightest minds in one place and discusses the influences on and impact of their work. Book jacket.