I have just stumbled on a fascinating book, Duel at Dawn by Amir Alexander at Harvard University. It throws an interesting light on a question I asked in several earlier posts: is there a relationship between Asperger’s syndrome or autism and mathematical genius?
Alexander’s thesis is that the nature of mathematical thought changed about two centuries ago. Before that, mathematicians beginning with the Renaissance believed that they were describing the way the universe worked. Mathematicians like Newton, for instance, saw mathematics as a description of the underlying structures and rhythms of the real world. By describing the reality of the objective world, mathematicians literally were seen as the companion explorers of the sea-going ships discovering new worlds.
About two centuries ago, however, a dramatic shift took place . A whole new group of mathematicians cut mathematics free from the constraints of describing the objective world. Mathematics, for them, exists in itself, by its own rules and logic. It is not necessarily connected to our objective world at all.
These new mathematicians are often seen as tortured geniuses, living in an abstract world of mathematical perfection but most often unable to live in the real world the rest of us inhabit. Some are clearly seen to be mentally ill. John Nash, whose story is told in the film A Beautiful Mind, suffered from paranoid schizophrenia. Galois died at the age of 20 in a duel, Kurt Gödel starved himself to death out of fear of being poisoned. The list is long and extends into our own day.
It is these modern mathematicians who live in a world of numbers which exists independently of the objective world most of us inhabit that has fascinated me. They relate to a world which is not inhabited by other living, thinking, feeling beings. Their world is absolutely logical, absolutely predictable, completely cleansed of the potentially inexplicable. As a result, despite their towering genius, they are often unbelievably poor in negotiating the real world with real people in it.
In other words, it seems to me, they are frequently autistic. One half of their brain seems to function at levels few of us can fathom, while on the other hand, they seem unable to comprehend inter-personal realities often grasped by even normal two-year-olds.
What Alexander’s book seem to suggest however, is that not all mathematical geniuses are intrinsically unable to adapt to life in the world as we know it. Quite possibly it is the other way around, that the highest regions of modern mathematics have been fashioned by a certain kind of mathematical genius – the kind of genius who is separated from concrete reality and inhabits an abstract world of numbers that is as real to him ( occasionally it is a her) as the world of people and cars and tables are to the rest of us.
If this is so, then mathematics will continue to evolve and change. It will not always find its locus totally isolated within itself.
So fascinating as Alexander’s thesis is, I still don’t know if Plato was autistic.
But can you see why I’m asking?