If all you had at your mathematical disposal was the idea of real numbers, you could still get very far. From Galileo to Newton to Coulomb to Maxwell, the entirety of classical physics is built on the ...

Mathematicians were disturbed, centuries ago, to find that calculating the properties of certain curves demanded the seemingly impossible: numbers that, when multiplied by themselves, turn negative.

Last winter, at a meeting in the Finnish wilderness high above the Arctic Circle, a group of mathematicians gathered to contemplate the fate of a mathematical universe. It was minus 20 degrees Celsius ...