Here’s a philosophical question for you: was math invented or was it discovered?
Granite Geek David Brooks has been thinking about this question, and will lead leading a discussion after tomorrow night’s screening of "The Man Who Knew Infinity" at Red River Theatres in downtown Concord. He’s a reporter at The Concord Monitor and writer at granitegeek.org. All Things Considered host Peter Biello spoke with him about this quandary.
David, why has this question come to mind?
It’s come to mind because there is a new movie out called “The Man who Knew Infinity,” which is a “bio-pic” movie—a biography an Indian mathematician from the start of the twentieth century. His name is Ramanujan. He was an extraordinary mathematician in many ways, and was absolutely unique both for the math he did and for his life story. He started out as a poor clerk in south India when the British still controlled it, and managed to come to the attention of G. H. Hardy, one of the foremost mathematicians in the world. Hardy brought him to England, and tried to make him a twentieth century western mathematician.
You’re giving a post-movie discussion tomorrow night at Red River Theaters in Concord, but I did want to get to the meat of that question now; what do you think: was math invented or discovered?
All mathematicians act as if it was discovered. They act like mathematics is a thing that is out there and you have to hunt and find it. Ramanujan felt that way himself. He thought that a Hindu goddess actually gave him many of the answers. That was his form of the inspiration that you’ll find in many mathematicians; to him it took form in the goddess.
So they act as if it is out there, but if you think about mathematical concepts, and imagine that they exist somewhere out there, the question is: where do they exist and in what form? It’s one thing to say, “One plus one equals 2,” but when you get to things like imaginary numbers, it’s really hard to figure out how you can say they exist.
When we talk about “math,” are we talking about the characters we use to represent it on paper or are we talking about the abstract idea behind those characters?
The way we represent it on paper, to a certain extent, is trivial. It’s the abstract idea that’s interesting. The essence, the power, the beauty of mathematics is that it is abstraction. The ultimate abstraction. And I would argue that it is the greatest art form that’s been created by humans. It’s the thing that separates us from the beasts of the fields. Doing abstract, pure mathematics is a human activity that no non-humans do. Crows can count, for example, but there’s no evidence that there’s a quadratic equation lurking in the head of anything other than human beings.
How would knowing math was conclusively invented or conclusively discovered change how humanity understands itself and the world?
If NASA sent out a space craft and it went around the back of an asteroid and discovered all of the plutonic solids, which are what the Greeks thought were the absolute forms that circle and a sphere aspire to, lurking there on the back of an asteroid, that would change our concept of the universe. But I don’t think that’s going to happen. So in general, I think you can safely say this is an argument to chew over with a beer, or not a beer if you prefer, but it probably won’t change much. But it is really interesting to think about.