Everyone is capable of mathematical thinking, yes, even you

The original version from this story appeared Quanta Magazine.

David Basis was drawn to mathematics for the same reason that many are driven. he didn’t understand how it worked. Unlike other creative processes, such as making music that can be heard or painting that can be seen, mathematics is largely an internal process that is hidden from view “It seemed a little magical. I was intrigued,” he said.

His curiosity eventually led him to earn a PhD in mathematics at Diderot University in Paris in the late 1990s.He spent the next decade studying geometric group theory before leaving research mathematics to found a machine learning startup in 2010.

Through it all, he never stopped questioning what it really means to do mathematics. He wanted to further question and help other people understand how mathematicians think and practice their craft.

In 2022, he published his response, a book titled Mathematics. A secret world of intuition and curiositywhich he hopes will “explain what goes on in the brain of someone doing math.” But more, he added, “this is a book about people’s inner experience.” It was translated from the original French into English earlier this year.

In MathematicsBasis provocatively argues that whether you realize it or not, you’re doing math all the time, and that you’re capable of extending your mathematical abilities far beyond what you think possible Thurston and Alexander Grothendieck did not owe their mathematical prowess to inner genius, Bessis argues. Rather, they became such powerful mathematicians because they were willing to constantly question themselves and refine their intuition.They developed new ideas and then used logic and language to test and improve upon them.

According to Basis, however, the way mathematics is taught in school emphasizes the logic-based part of this process, when the most important element is intuition. Mathematics should be seen as a dialogue between reason and instinct, language and abstraction, for example Yoga or martial arts, something that can be improved through training. It requires tapping into the childish state and accepting one’s imagination, including the mistakes that come with it.