It is a well-known fact that our universe has three dimensions of space. Imagine for a moment that it had only two, like E.A. Abbott's Flatland, or A.K. Dewdney's Planiverse. What shape might it have? Well, it might be flat, like an infinite sheet of paper on an infinite tabletop; or it might curve round... Read More

Peter Watson's long book covers the entire history of humanity, in the tradition of H.G. Wells's Outline of History (1920) and Hendrick van Loon's The Story of Mankind (1922). His approach, as the book's title tells us, is to present the whole immense story as one of intellectual development, driven by changes in the way... Read More

Out in the remotest regions of mathematics, far from the bustling and long-populated center, out where this great thriving empire adjoins the windswept badlands of philosophy, is the topic called Foundations. Here mathematicians use the techniques of their discipline to inquire into the nature of that discipline itself, into the very fundamentals of math: number,... Read More

In forming the way we think about our human nature, the three great names of the modern age have of course been Darwin, Marx, and Freud. Each placed the main action of the human drama on a different stage. Darwin set it on the greatest stage of all, that of Nature herself. For Marx it... Read More

The God of the Gaps had a hard time of it in the 20th century. By 1900 thoughtful people had long since reconciled themselves to the fact that the Sun is not the chariot of a god, but a ball of incandescent gas whose apparent motions follow natural laws. They knew that lightning and thunder... Read More

Mathematicians are uncomfortably aware that theirs is a "cold" subject. Though full of wonders and delights, it has little appeal to the tender side of human nature, little connection with the clayey appetites and longings of our everyday lives. There is a story about the great German mathematician David Hilbert. Noticing that one of his... Read More

In May of 1997 an historic event occurred: the world chess champion, Garry Kasparov, lost a 6-game match to a computer, having never previously lost a professional match to anybody. The computer was a custom machine, designed and programmed by a team at IBM Research in Armonk, New York. It went by the name Deep... Read More

It is difficult to think of any literary enterprise more challenging than the presentation of advanced mathematical topics to a general audience. It is not just that math is hard; there is, as Keith Devlin noted in a previous book, The Math Gene, (and as Bertrand Russell remarked in the introduction to Principia Mathematica), something... Read More