Many people might think that math is such a logical field that it would have little in common with something as creative as music. But the way that mathematicians and musicians think is actually a lot alike, says Jeffrey Rosenthal, professor of statistics at the University of Toronto.
“Mathematics involves a certain sort of logical structure, so you certainly have to have a logical mind to see how things fit together. You can’t just go making things up,” explains Rosenthal.
“But on the other hand, what not everyone realizes is that to do research in mathematics also involves a form of creativity. It’s what I call creativity within structure. In fact, I also play some music, and a lot of math people play music, and it’s been pointed out that music also kind of has a structure: you can’t just play whatever you want, but it also has some creativity involved. So there’s creativity within the logical structure.”
Unlike the exercises most people remember from elementary school or high school, there is no textbook solution in mathematical research. There are still rules, but there are no prescribed steps to follow. So while there’s a lot of logic involved, there is also a lot of creativity involved in making something original, says Rosenthal.
At its core, mathematics is all about connections and relationships, and Rosenthal thinks about the problems he’s working on whenever he has the chance.
“A lot of it is thinking, because it’s all these mathematical, logical relationships, and they kind of have to fit together up here,” says Rosenthal, giving a gentle tap to his temple. “If they fit together up here I can get them onto the computer, so sometimes I’ll just be lying in bed and thinking, and I’ll try to make connections, too. So it can happen really anywhere, but quite a lot of it involves working with other people, too.”
Rosenthal has also worked with collaborators in medicine, law, psychology, and more. These fields may seem very diverse, but any area where data or randomness are involved, mathematics can help predict outcomes, describe how things work, or solve complex problems.
“There’s a real freedom to, in addition to doing my technical core work, to do work which has applications to other areas,” says Rosenthal. “When I was doing the really pure math, I didn’t always feel that, because you’re working on something so specialized that it only interested a few people. But you get a little more broadly into randomness and statistics and data, it has so many different connections and applications, so that’s been great, too.”