What motivates it, and what is its ultimate endgame? What does the world look like to someone steeped in the culture of mathematics? So when I discovered that Terence Tao, a living legend of contemporary math, was offering an online class on his approach to “mathematical thinking,” I had to check it out. But despite having been close to math for most of my life, I continue to be bewildered by mathematics research.

I often catch myself resorting to the vocabulary of research and analogies from physics to explain myself. Indeed, certain concepts-like the fact that opposite charges attract or that disorder or entropy tends to increase-are so universally ingrained in our experience that they creep into everyday language as metaphors. In physics, the questions we ask and the theories we come up with aim to explain the underlying reality better. And this feeling is only reinforced by popular books on math, which often take the tone of a pastor dispensing sermons to the faithful. As a graduate student in physics, I have seen the work that goes into conducting delicate experiments, but the daily grind of mathematical discovery is a ritual altogether foreign to me.

Perhaps part of the mystique comes from the fact that biographies of mathematicians often paint them as otherworldly savants-people who seem to pull nature’s deepest truths from thin air and transcribe them in prose so succinct and self-assured it must be read meditatively, one word at a time. Mathematics has long been presented as a sanctuary from confusion and doubt, a place to go in search of answers.

Bringing down the duke book review