Gifted mathematicians not like the rest of us

The American mathematician John Nash, whose life is portrayed in the movie A Beautiful Mind, was killed last weekend in a car crash. His devoted wife Alicia died with him.

It’s hard to contemplate this denouement without recalling the old saying: “Those whom the gods would destroy, they first make mad.” For Nash spent 35 years in the shackles of madness.

At the height of his powers, age 30 in 1959, he declined a prestigious university appointment because he was “busy forming a world government.” The schizophrenia that overtook him resulted in years of confinement. He endured massive doses of thorazine (involuntarily) and suffered through insulin shock therapy five days a week for weeks at a time.

Remarkably, in one of the more moving testaments to human endurance, he eventually put down his affliction by sheer force of will and resumed teaching at Princeton. He was awarded a Nobel Prize in 1994.

But what was remarkable is the extraordinary way his mind worked. Most of us think of math as a series of calculations. But in some unfathomable way, that’s not how he saw the world.

It was said of Mozart that he didn’t compose music, he simply wrote down what he heard in his head. Nash did much the same. He saw intuitively where the right path lay.

You can glimpse this inexplicable faculty in some of history’s most famous mathematicians.

John von Neumann, who helped found computer science, could divide two eight-digit numbers in his head. At age six.

Carl Friedrich Gauss corrected his father’s business accounts before he was three.

Shakuntala Devi was a child prodigy in her native India. Yet even by her late 60s, she was able to give, not the square root, but the 23rd root of a 201-digit number in less than a minute. At the time (1980), a mainframe computer with a specially written program was required to confirm her solution.

Of course, not all mathematicians have this talent. Andrew Wiles, the English mathematics professor who proved Fermat’s Last Theorem, needed seven years of heavy lifting. And even then his first attempt was wrong.

(There’s an endearing corollary to this story. When asked what Wiles had been doing all this time — much of it holed up in near secrecy — his department head replied he hadn’t seen the guy in years. We should all have such tolerant bosses.)

Does any of this matter? In one sense, maybe not. G.H. Hardy, another English mathematician, insisted: “No discovery of mine has made, or is likely to make … the least difference to the amenity of the world.”

Yet there is a divide here worth noting. Those who have this power over numbers are not just faster than the rest of us. They see the world in ways that are completely separate.

We think of our species as homogenous. What gradations there are, in physique or intellect, seem relatively minor.

Yet there is a special magic here that is not merely a few notches higher up the scale.

An invisible gulf separates this tiny sliver of our species. They are not like us, and we are not like them.

Did Nash gain admission to the “higher, perhaps celestial powers,” as Franz Kafka put it (I’m indebted to Nash’s biographer, Sylvia Nasar, for the reference).

Maybe. But if so, he surely paid for it. And the gods claimed Alicia — who deserves a special place in heaven — as the price of that admission.

John Nash was 86 and his wife 82 when they died.