We’re always lumping them together, scientists and mathematicians. They’re “STEM” professionals: bespectacled, smart, pleasantly soft-spoken until you conflate Star Trek and Star Wars, after which their wrath is visited upon you.
But the fact is that, aside from being the butt of cheap jokes, mathematicians and scientists don’t share all that much in common.
And you can tell that from the way they look at each other’s fields.
When it comes to research, scientists view mathematics the way a handyman views a toolkit. To a scientist, math is a way of solving problems, as practical as a step-ladder or a roll of duct tape.
Want to describe an object falling to earth? Draw up a quadratic equation!
Want to investigate a rate of change? Take a derivative!
Want to model an electromagnetic attraction? Bring out the vector fields!
When people extol the “real-world” benefits of mathematics, they’re talking about moments like this, when a scientist employs quantitative techniques to analyze the world around us.
Meanwhile, mathematics draws on science the way an artist draws on a muse. Science reveals a real-world phenomenon—and the mathematician asks, how can we make this abstract? How can we generalize?
Take the idea of spatial dimension. Most of your ordinary objects—microwaves, teapots, housecats—are three-dimensional. That means they can be measured in three directions—length, width, and height.
Thus, any point in our three-dimensional world can be summarized with three numbers—call them, x, y, and z.
But the mathematician pushes further. What if we had four numbers? Or five? Or n? What would words like “volume” and “distance” come to mean? Can we imagine a six-dimensional sphere, and if so, what in blazes is it? Which of our 3D intuitions will carry over into higher dimensions, and which will break down?
For mathematicians, physical reality—that is, scientific reality—is nothing more or less than a source of inspiration. And like any inspired artist, mathematicians feel free to extrapolate and invent, to ask “What if?” and “How else?” and “Couldn’t we pretend…?” It doesn’t matter whether any of this higher-dimensional stuff really exists—it’s still a marvelous stroll to take your brain on.
Mathematics and science, then, aren’t like two members of the same species. They’re like two entirely different animals, sharing a lovely symbiosis. Math is like a parasite-eating bird, perched on the rhino of scientific reality.
Math gets nourished. Science solves a problem. Everybody wins.
The bird and rhino don’t share much in common, but they make a heck of a team.