Mathematical Thinking Isn’t What You Think It Is

The mathematician David Bessis claims that everyone is capable of, and can benefit greatly from, mathematical thinking. From Quanta Magazine.

David Bessis was drawn to mathematics for the same reason that many people are driven away: He didn’t understand how it worked. Unlike other creative processes, like making music, which can be heard, or painting pictures, which can be seen, math is for the most part an internal process, hidden from view. “It sounded a bit magical. I was intrigued,” he said. 

His curiosity eventually led him to pursue a doctoral degree in math at Paris Diderot University in the late 1990s. He spent the next decade studying geometric group theory before leaving research mathematics and founding a machine learning startup in 2010. 

Through it all, he never stopped questioning what it actually means to do math. Bessis wasn’t content to simply solve problems. He wanted to further interrogate — and help other people understand — how mathematicians think about and practice their craft. A book with a green and blue cover 

In 2022, he published his answer — a book titled Mathematica: A Secret World of Intuition and Curiosity, which he hopes will “explain what’s going on inside the brain of someone who’s doing math,” he said. But more than that, he added, “this is a book about the inner experience of humans.” It was translated from the original French into English earlier this year. 

In Mathematica, Bessis makes the provocative claim that whether you realize it or not, you’re constantly doing math — and that you’re capable of expanding your mathematical abilities far beyond what you think possible. Eminent mathematicians like Bill Thurston and Alexander Grothendieck didn’t owe their mathematical prowess to intrinsic 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 math is taught in school emphasizes the logic-based part of this process, when the more important element is intuition. Math 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 improved through training. It requires tapping into a childlike state and embracing one’s imagination, including the mistakes that come with it.

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