The key here isn’t fitness—it’s just a feeling of being free, of forgetting for a moment that we are bound by gravity and logic and convention, of letting the magic happen. For me, perhaps it’s that my ideas just need to be jostled into the right place. Jogging jogs them. But there are mathematicians who try to alter their brain chemistry a little more directly. The Hungarian mathematician Paul Erdős was notoriously prolific, someone to whom the magic tricks seemed to come enviably easily. So, what was his secret? His friend Alfréd Rényi, a fellow-Hungarian, once said, “a mathematician is a machine for turning coffee into theorems.” And both men were caffeine enthusiasts. But Erdős was a person of extremes, and he also fuelled his ideas through a don’t-try-this-at-home technique: he used stimulants such as Ritalin and Benzedrine for much of his career. At one point, a friend, worried about Erdős’s health, challenged him to go off the drugs for a month, and Erdős agreed, but when the experiment was over he said that, on the whole, mathematics had been set back by his weeks of relative indolence.
Whereas Erdős sought hyper-focussed vigilance, other eminent mathematicians have found a hazy drowsiness to be the most fertile state of mind. Poincaré described lying in bed in a half-dream state as the ideal condition for coming up with new ideas. The philosopher and mathematician René Descartes famously loved to lounge in bed in the morning and think (I suppose to give evidence that he was). It was on one such morning—as the story goes—while dreamily watching the path of a fly flitting around on the ceiling, that he came up with the xy plane of Cartesian coordinates.