I recently spoke to a mathematician who said he only liked reading fiction.
“Fiction and math?” someone asked.
“No,” he said, “I count math as fiction.”
If you ask people, “Is mathematics fiction or nonfiction?” you get wildly different responses. Some people don’t even understand the question—of course it’s nonfiction! Yet many others, including those who do math for a living, are not so sure.
But there is an even more crucial point to address first.
What is math?
This is a surprisingly tricky question. Mathematics is really old. But modern math includes entire fields that have little to do with their ancient predecessors.
Many people think of numbers when they think of math. And around four thousand years ago, math could have rightly been called “the science of number.” The Babylonians developed a system of practical arithmetic. Egyptians used tables full of numerical information to build the pyramids. Other ancient societies, in the Arab world, China and India, developed number systems as well. What we would recognize as regular math– rules of addition and multiplication, as well as abstract formulas– began with the ancient Greeks.
”The science of number” doesn’t include geometry, however, which was also invented by the Greeks. How could “1” or “27” capture circles, triangles, or parallel lines? With the development of geometry, math transitioned from “the “science of number,” to “the science of number and shape.”
Fast forward to calculus, invented simultaneously by Gottfried Leibniz in Germany and Isaac Newton in Britain. Calculus is about motion and change: it’s the stuff of rockets, baseballs and waterfalls. The definition of math stretched to “the science of number, shape, and motion.”
So what do they all have in common?
Here is one suggestion:
Give a kindergartener four apples, and she may count “1, 2, 3, 4.” She might do the same thing with four crayons or four of her friends. Number is a pattern that people sense in the world. But it also exists independently in our minds. A person can think of the number 7 without picturing seven spoons or seven marbles. The same goes for seemingly real-world principles like population growth, rectangles, and acceleration. We can study them by just thinking about the patterns that they represent. In the words of award-winning mathematician Keith Devlin, mathematics is the science of patterns.
Thinking logically about patterns turns out to be extremely useful. Mechanics, in physics, depends entirely on the use of calculus. Encryption technology in computers was created with number theory. In a practical sense, the formulation of patterns allows us to make predictions. When we know a pattern, even of something as simple as the turn of seasons, we know what to expect in the future. The more precisely the pattern is formulated, the more precise the prediction. Mathematics is handy for this.
Sometimes, though, the reverse occurs: we think about patterns that don’t seem to apply to anything concrete at all. No one has ever seen a nine-dimensional space. But the pattern of a 9-D space is something people can study. Calculating, say, the distance between two points in 9-D is no more complex than calculating distance in 3-D.
So math is incredibly useful—even irreplaceable—in science and technology. Yet it seems that we can dream up math that has nothing to do with the real world. The actual “location” of math suddenly becomes unclear: whether it exists in the world or it exists in our minds.
Which brings us back to our original question: Is math fiction?
Let’s figure that out in the next post.