The original version From this story appeared in Quanta Magazine.
David Bessis was drawn to mathematics for the same reason many people turn away from it: he didn’t understand how it worked. Unlike other creative processes, such as making music, which can be heard, or painting pictures, which can be seen, mathematics is largely an internal process, hidden from view. “It felt a bit magical. I was intrigued,” he said.
His curiosity eventually led him to earn a doctorate in mathematics from Diderot University in Paris in the late 1990s. He spent the next ten years studying geometric group theory before abandoning mathematical research and founding a machine learning startup in 2010.
Through it all, he never stopped wondering what doing mathematics really means. Bessis was not content to simply solve problems. He wanted to further question – and help other people understand – how mathematicians think and practice their craft.
In 2022 he published his answer: a book titled Mathematica: a secret world of intuition and curiositywhich he hopes will “explain what happens in the brain of someone who is doing math,” he said. But above all, he added, “this is a book about the inner experience of human beings.” It was translated from the original French into English earlier this year.
In MathematicsBessis provocatively states that, whether you realize it or not, you are constantly doing mathematics and that you are capable of expanding your mathematical abilities far beyond what you think possible. Eminent mathematicians such as Bill Thurston and Alexander Grothendieck did not owe their mathematical ability to inherent genius, Bessis argues. Rather, they became such powerful mathematicians because they were willing to constantly question and refine their intuitions. They developed new ideas and then used logic and language to test and improve them.
According to Bessis, however, the way mathematics is taught in school emphasizes the logical part of this process, while the most important element is intuition. Mathematics should be thought of as a dialogue between the two: between reason and instinct, between language and abstraction. It is also a kind of physical practice, like yoga or martial arts, something that can be improved through training. It requires tapping into a childlike state and embracing your imagination, including the mistakes that come with it.