What are mathematicians really like? What are the characteristics or traits of personality typical amongst them? Mathematicians are rarely the heroes of novels, so we have little to learn from literature. A few films have featured mathematicians, but most give little insight into the personalities of their subjects [TM226 or search for “thatsmaths” at irishtimes.com].

**Absentmindedness**

Sweeping statements about groups of people are risky but can be fun too and can provide insight. At the risk of cliché, we might start with absentmindedness. The earliest record of occupational absentmindedness concerns Archimedes, the greatest mathematician of antiquity. Upon making a momentous discovery, he leapt from his bath and ran naked thorough the streets of Syracuse.

William Rowan Hamilton’s intense preoccupation with the quaternions that he had discovered was obsessive. Maths historian E T Bell wrote that, over the last twenty years of his life, Hamilton worked almost exclusively on quaternions. Upon his death his office was found to be in great disarray. Bell wrote that “innumerable dinner plates were found buried in the mountainous piles of papers”, reflecting the domestic difficulties in which Hamilton lived.

Stories abound about mathematicians oblivious to their surroundings, missing lectures and appointments, or forgetting to eat their lunch. They have been known to drive to work, take the bus or train home and wonder next day where the car has gone. Are they really so chronically scatterbrained? Mathematician John Bowers of Leeds University claimed that he could rebut this thesis but that, unfortunately, he had mislaid his proof. QED.

**To solve a problem, think about it!**

Mathematical research involves sustained and focussed work. Asked how he discovered the law of universal gravitation, Newton reflected that he solved a problem “by thinking on it continually”. The months or years of concentrated and intensive work required to develop a proof can be exhausting. A somewhat scattered mind and eccentric behaviour may be an inevitable consequence. Such strain most likely contributed to the mental breakdown of Georg Cantor, inventor of set theory and of a hierarchy of infinities.

Untidiness is another common characteristic; glamour would not be the mathematician’s strong suit. Newton’s biographer Richard Westfall describes how, when this great scientist remembered to lunch, he would arrive at the dining hall dishevelled, unkempt and down at heel, with his hair uncombed. The stereotypical attire of mathematicians would be unimaginative and dowdy, with knitted jumpers, socks and sandals.

What about money? The analytical skills of mathematicians may enable them to make a fortune; but, once seduced by money, they generally lose interest in maths. Those who stay the course often have little interest in money. Grigori Perelman proved the Poincaré conjecture, a problem outstanding for a century. He declined to accept a Fields Medal, comparable in prestige to a Nobel Prize, for this brilliant research, stating simply “I’m not interested in money or fame”. Later, he turned down a Clay Millennium Prize of one million dollars.

In general, mathematicians are happily married, reasonably competent parents and good citizens. They are not noted for orgiastic behaviour, violence or excessive use of drugs. Have they any typical faults? E T Bell, writing about the Irish mathematician Robert Murphy, said that he “went the same disastrous way as Hamilton”. What could Bell have meant? He concluded: “I believe that not sex but alcohol is the snare that mathematicians have to look out for”. Discuss.