On this day in 1048, the great mathematician and poet Omar Khayyam was born. It is a point of some annoyance to me that most people think that mathematics is not a creative field but rather just one where complex rules are applied to problems. But if that were the case, math would be easy. You would just memorize the rules and apply them. But it isn’t like that at all. In fact, in college I noticed that math classes were very much like music classes: some people just got it and other didn’t. (This is an indictment of both math and music instructors!)
There is a very famous story about a very young Carl Friedrich Gauss, which is probably apocryphal, but it hardly matters. Because mathematics education was as bad then as it is now, his teacher had the class add up all the numbers from 1 to 100. I suspect this was more a way to keep the children busy for a while than anything else. But Gauss immediately answered 5,050. His solution was brilliant but also quite easy. He didn’t do what most of us would do: 1+2=3; 3+3=6; 6+4=10… Instead, he noted that 1+100=101 and 2+99=101 and so on. Thus the answer is 50×101=5,050.
So the essence of mathematics is seeing the universe in a different way than others see it. Work is adding together a hundred numbers; play is finding clever ways to not add up a hundred numbers. Work is grinding out yet another story just like the hundreds of stories that went before; fun is finding a new way to tell a story. I think mathematics is the most creative human endeavor because it is normally done without context. It is not much different from the writing of The Marriage of Figaro, except that the audience that can appreciate it is sadly so much smaller.
Khayyam focused on geometry. In a sense, he invented non-Euclidean geometry. Euclid created five postulates from which all of what we think of as normal geometry can be derived. That’s a remarkable thing. But the essence of non-Euclidean geometry has to do with the fifth postulate. It posits a line and a point and says that there is only one line that passes through the point that doesn’t intersect with the first line. For centuries, mathematicians tried to show that you could derive this result from the other postulates, but you simply can’t. However, since it is a postulate, you could say that there are no lines to that do that—or an infinite number of lines that do that. The universe that such assumptions imply are not the universe as we generally find it. But that’s one of the things that makes math such an amazing thing: it’s pure thinking.
He was also a great poet and astronomer and philosopher. And not surprisingly, he was a mystic as I think all mathematicians are. There is something about the nature of mathematics that strikes me as the closest that we ever get to what one might call God. And the ineffable nature of mathematics itself leads one to a simple appreciation of existence itself.
Happy birthday Omar Khayyam!