Thomas Lin - The Prime Number Conspiracy: The Biggest Ideas in Math from Quanta

James Gleick

I t is sometimes said that writing about music is like dancing about architecturea category mistake. If so, where does that leave writing about mathematics? The writer has only words, and the mathematician inhabits a different place entirely.

Like music, mathematics draws on deep wells of creativity and inspiration, and it can be dark down there. Even the best mathematicians have trouble explaining their own uncanny mental lives. This creates a challenge for the poor journalist. Long ago, I asked Benoit Mandelbrot, the founder of fractal geometry, to describe the source of his intuition about these fantastic shapes and the peculiar methods he had invented. (By intuition, mathematicians dont mean clairvoyance but rather a sense of what is correct.) He explained it as merely an exercise of the will: Intuition is not something that is given. Ive trained my intuition to accept as obvious shapes which were initially rejected as absurd, and I find everyone else can do the same. In one of the fine profiles and interviews youll find in this book, Siobhan Roberts presses the great Michael Atiyah, now 89 years old, to describe how inspiration arrives, and he at least tries: The idea floats in from heaven knows where. It floats around in the sky; you look at it and admire its colors. Its just there. And then at some stage, when you try to freeze it, put it into a solid frame, or make it face reality, then it vanishes; its gone.

Why should they have to explain, anyway? Let mere mortals do that for them.

As you will see repeatedly in these pages, inspiration strikes willy-nilly. Petr eba was at a bus stop in Cuernavaca, Mexico, watching drivers pay cash for slips of paper that recorded the departure times of the buses ahead. It made him think of quantum chaotic systems. Yitang Zhang was in a friends backyard in Colorado, waiting to leave for a concert, when the solution suddenly came to hima way forward to proving a landmark theorem of number theory. A retired German statistician was brushing his teeth when he saw the key to solving the decades-old Gaussian correlation inequality. (Natalie Wolchover describes this moment as Thomas Royens bathroom sink epiphany.) Like so many others, Royen struggles to find words to express the ineffable joy that comes with this kind of discovery. It is like a kind of grace, he told Wolchover. We can work for a long time on a problem and suddenly an angel[which] stands here poetically for the mysteries of our neuronsbrings a good idea.