Everyone Can Think Mathematically—Yes, Even You

The first version of this story appeared in Quanta Magazine.

David Bessis was drawn to math for the same reason many people are fired: He didn’t understand how it worked. Unlike other creative processes, such as making music, which can be heard, or painting pictures, which cannot be seen, mathematics is largely an internal process, hidden from view. “It felt magical. I was surprised,” he said.

His curiosity eventually led him to pursue a doctorate in mathematics at Paris Diderot University in the late 1990s. He spent the next decade studying geometric group theory before leaving to research mathematics and co-founded a learning startup in 2010.

Through it all, he never stopped asking what it means to do math. Bessis was not content to simply solve problems. He wanted to continue to investigate—and help other people understand—how mathematicians think about and practice their work.

In 2022, he published his answer — a book with the title Mathematica: The Secret World of Insight and Curiosityhe hopes it will “explain what goes on inside the brain of a person doing math,” he said. But more than that, he added, “this book is about people’s inner experiences.” It was translated from the original French into English earlier this year.

In StatisticsBessis makes the provocative claim that whether you realize it or not, you’re doing math all the time—and that you can expand your math skills beyond what you think you can. Prominent mathematicians such as Bill Thurston and Alexander Grothendieck did not owe their mathematical prowess to innate intelligence, Bessis argues. Instead, they became powerful mathematicians because they were willing to constantly question and refine their ideas. They create new ideas and use logic and language to test and develop them.

According to Bessis, however, the way mathematics is taught in school emphasizes the cognitive part of the process, where the most important aspect is understanding. Mathematics should be thought of as a dialogue between the two: between reason and instinct, between language and abstraction. It’s also a physical practice of sorts, like yoga or martial arts—something that can be developed through training. It requires entering the child’s state and accepting the human imagination, including the mistakes that come with it.