Science Editorial 11
March 25,2011

On the dangers of being a research mathematician

“Archimedes ... was ..., as fate would have it, intent upon working out some problem by a diagram, and having fixed his mind alike and his eyes upon the subject of his speculation, he never noticed the incursion of the Romans, nor that the city was taken. In this transport of study and contemplation, a soldier, unexpectedly coming up to him, commanded him to follow to Marcellus; which he declining to do before he had worked out his problem to a demonstration, the soldier, enraged, drew his sword and ran him through.”
-Plutarch on Archimedes

This story famously illustrates the perils associated with high-level research in mathematics. In his autobiographical writings Einstein admits that he found it impossible to relax at a party, even if he happened to be the guest of honor. He could sit alone for extended periods, deep in his private thoughts anc calculations, unable to relate to anything going on around him. Fortunate it was that the presence of others on these occasions gave him some protection against Roman soldiers!

Such obsessional mental labors can be disabling. There are people who have becomes so muscle-bound through their pre-occupation with mathematics, that the capacity to function at doing anything else has effectively atrophied: whether operating machines, driving a car, using a camera, holding a conversation, learning other subjects, playing musical instruments, dressing properly, cooking or paying attention to what one is eating (cf anecdotes about Isaac Newton at the dinner table), that is to say, the entire range of skills required for normal human living.Paul Erdös is the classic example. (Note that this did not inhibit him in the least from a lifestyle built around constant travel!)

These handicaps can become life threatening when crossing the street, driving a car, walking on ice-covered pavements, drifting into stupid arguments, remembering appointments, warding off danger, and similar crises.

Based on these observations I have developed the following provocative thesis: it isn’t because mathematicians are any smarter than other people, that the fields of mathematics took so many centuries to evolve (For example: although the conceptual basis and essential constructions for the calculus were developed by Archimedes in the 3rd century B.C.E., it did not emerge as a practical universal tool until the 17th century C.E.) but because in times and places in human history, the psychological disabilities associated with being a research mathematician rendered the profession too dangerous.

People who tried to do mathematics in the past risked being killed in war, dying from accidents, wandering off and getting lost, falling off cliffs, and so forth. The dearth of mathematicians before the rise of civilization is thus explained: people who fell into the category of research mathematicians frequently ended up being eaten by wild animals (or cannibals)!

Ground down to dust is the cliché that a mathematician, unlike a physicist or biologist, only needs a pencil and a few pieces of paper to do his research: a sand-pile will do. This is incorrect: if mathematical discoveries were so cheaply underwritten, everybody would be making them. Doing mathematics requires access to the most complex and expensive piece of equipment on earth: the organized power, as narrowly focused as a burning glass, of the human brain, absorbed in difficult activities of visualization and calculation to the virtual exclusion of everything else, over the full 24 hours of each day. No cyclotron can compete with this.

Yet this also carries great risks, risks far greater than one can allow in a world with tigers roaming outside the cave, or decimating plagues , or multiple invasions, or herds of wild elephants trampling the crops.

It is not merely a question of “having enough leisure time”, ( yet another time-worn cliché) ; it is a matter of having the kind of leisure that permits certain people to allow themselves to become so distracted from the perils of life that they can replace normal vigilance by an ingrown mindset based on obstinate ratiocination.

How dangerous is the life of a professional research mathematician! Has anyone written about that? To everyone who knows this community, or who has done such work themselves, it’s an obvious fact of life. It may help explain, for example, why so much research is accomplished by persons in their 20’s: after a decade or so of intensive research, the accumulated risks make it impossible to continue.

No-one needs to have their attention directed to the great dangers in professions such as fireman, policeman, coal miner, medical investigator of infectious diseases, or stunt man, or auto car racer. That the risks run by mathematicians are equally great is much less understood. The so-called ‘absent-minded professor’ may actually be the victim of a occupational hazard, one that can, and sometimes does, prove lethal.

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