original version Of this story appeared in quanta magazine,
David Basis was attracted to mathematics for the same reason that turns away many people: he didn't understand how it worked. Unlike other creative processes, such as making music, which can be heard, or making pictures, which can be seen, mathematics is for the most part an internal process, hidden from view. “It felt a little magical. I was curious,” he said.
His curiosity eventually led him to pursue a doctoral degree in mathematics 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.
Throughout all this, he never stopped to question what it really meant to do mathematics. Basis was not satisfied with merely solving problems. He wanted to further interrogate – and help other people understand – how mathematicians think about and practice their art.
In 2022, he published his answer – titled Mathematicians: A Secret World of Intuition and CuriosityWhich he hopes will “explain what's going on inside the brain of someone doing math,” he said. But more than that, he said, “It is a book about the inner experience of man.” It was translated from the original French into English earlier this year.
In MathematicaBasis makes the provocative claim that whether you realize it or not, you are constantly doing mathematics – and you are able to expand your mathematical abilities far beyond what you thought possible. Basis argues that the mathematical prowess of eminent mathematicians such as Bill Thurston and Alexander Grothendieck was not due to intrinsic talent. Rather, they became such powerful mathematicians because they were willing to continually question and refine their intuitions. They developed new ideas and then used logic and language to test and improve them.
However, according to Basis, the way mathematics is taught in school emphasizes the logic-based part of the process, when the more important element is intuition. Mathematics should be thought of as a dialogue between the two: between logic and instinct, between language and abstraction. It is also a type of physical practice, like yoga or martial arts – something that can be improved through training. This requires harnessing the childlike state and embracing one's imagination, including the mistakes that come with it.