How is Mathematics Like Making Music?

Both math and music work within logical structures, but leave lots of room for creativity, according to this statistics professor.

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Many people might think that math is such a logical field that it would have little in common with something creative like music. But the way 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.”

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Jeffrey Rosenthal is a professor of Statistics at the University of Toronto. Born in Scarborough, Ontario, Canada in 1967, he received his BSc in Mathematics, Physics, and Computer Science from the University of Toronto at the age of 20, his PhD in Mathematics from Harvard University at the age of 24, and tenure in the Department of Statistics at the University of Toronto at the age of 29.

For his research, Rosenthal was awarded the 2006 CRM-SSC Prize, and the 2007 COPSS Presidents’ Award, the most prestigious honour bestowed by the Committee of Presidents of Statistical Societies. For his teaching, he received a Harvard University Teaching Award in 1991, and a University of Toronto Outstanding Teaching Award in 1998. He was elected to Fellowship of the Institute of Mathematical Statistics in 2005, and to the Royal Society of Canada in 2012, and was awarded the SSC Gold Medal in 2013, and a President’s Impact Award in 2019.

Rosenthal’s book for the general public, Struck by Lightning: The Curious World of Probabilities, was published in sixteen editions and ten languages, and was a bestseller in Canada. It led to numerous media and public appearances, to his work exposing the Ontario lottery retailer scandal, and to a President’s Impact Award. It was followed by a second book for the general public, Knock On Wood: Luck, Chance, and the Meaning of Everything.

Rosenthal has also published two textbooks about probability theory, and well over one hundred refereed research papers, many related to the field of Markov chain Monte Carlo randomised computer algorithms and to interdisciplinary applications of statistics. He has dabbled as a computer game programmer, musical performer, and improvisational comedy performer, and is fluent in French.

His web site is, and on Twitter he is @ProbabilityProf.

Despite being born on Friday the thirteenth, Rosenthal has been a very fortunate person.

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