REHMEYER: Well, one version is where two parallel lines might in fact meet, and another version is where there are lots of different parallel lines through one point. SIEGEL: Where two parallel lines might in fact meet at some point. And in particular, what mathematicians had found that they were responding to was that they had discovered non-Euclidean geometries, which are kind of whole different universes of geometry that are mathematically consistent but utterly non-intuitive and not at all what we experienced in the everyday world.

SIEGEL: Even if the math they were describing involved things that we didn't see in everyday life and that seemed to. So, Russell and Whitehead set out to show that math really boiled down to logic and to define at the very most basic level what mathematics was, and to show then that all of math was logical consequences from some very, very simple principles. Mathematicians had found some surprising results that led them to realize they needed to be a whole lot more careful than they had been previously. REHMEYER: They were really trying to rescue math from a deep crisis of foundations. SIEGEL: And first, describe for us what Bertrand Russell and Alfred North Whitehead were trying to show in this book that in 1910. JULIE REHMEYER (Science Writer, and 'Wired' Magazine): Thank you, delighted to be here. And she joins us now from Berkeley, California. She writes about math for Science News and for Wired. I am deeply in over my head in these mathematical and philosophical waters, but Im hoping that Julie Rehmeyer can swim through them a bit. It was volume one of Bertrand Russell and Alfred North Whitehead's 'Principia Mathematica.' Two more volumes of the work would follow. One hundred years ago this month, Cambridge University Press in England published a book that lost money, that according to one of its two co-authors was probably read in full by only six people, but that influenced the thinking of people who influenced the thinking of other people, who influenced the thinking of still others, and so on and so forth.

Principia of mathematics