Original version With this story appeared in Quanta Magazine.
David Bessis was fascinated by mathematics for the same reason that many people leave it: he didn’t understand how it worked. Unlike other inventive processes, such as making music that can be heard or painting pictures that can be seen, mathematics is largely an internal process, hidden from view. “It sounded a bit magical. I was intrigued,” he said.
Curiosity eventually led him to obtain a PhD in mathematics from the University of Paris Diderot in the late 1990s. He spent the next decade studying geometric group theory before abandoning mathematics research in 2010 and founding a machine learning start-up.
Throughout it all, he never stopped questioning what doing mathematics really meant. Bessis was not satisfied with simple problem solving. He wanted to further explore and help other people understand how mathematicians think about and practice their craft.
In 2022, he published his answer – a book titled Mathematica: The secret world of intuition and curiositywhich he hopes will “explain what’s going on in the brain of someone who does math,” he said. Moreover, he added, “it is a book about the inner experience of man.” It was translated from its original French into English earlier this year.
IN MathematicsBessis makes the provocative claim that, whether you realize it or not, you are constantly doing mathematics and that you are capable of extending your mathematical abilities far beyond what you thought was possible. Bessis argues that outstanding mathematicians such as Bill Thurston and Alexander Grothendieck did not owe their mathematical abilities to inner genius. Rather, they became 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.
However, according to Bessis, the way mathematics is taught at school emphasizes the logical part of the process, in which intuition is a more crucial element. Mathematics should be seen as a dialogue between them: 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 entering a child’s state and embracing one’s own imagination, including the mistakes that come with it.