1,2,4,8...What comes next? Nothing. If we're talking numbers, the obvious next term is 16. But if we're talking a particular kind of algebra, there is no next term. And it turns out that this is highly significant. The ultimate number ― the humble 8 ― lies at the heart of a mathematical system known as the octonions, and this system appears to be the key that will allow physicists to fit quantum theory and gravity together. Strange as it may seem, the number 8 may provide us with a "theory of everything". The tale of the octonions begins in the mid-16th century. Until that time, mathematicians had thought that numbers were God-given, a done deal. No one could contemplate inventing a new number. But around 1550 the Italian algebraists Girolamo Cardano and Raphael Bombelli did just that, by writing down the square root of -1. It took about 400 years to sort out what the thing meant, but only 300 to convince mathematicians that it was too useful to be ignored.
展开▼
