Books: Some oblique angles on life

Do you have to be mad to be a mathematical genius? No, argues Ian Stewart - just enchanted by the magic of numbers; The Man Who Loved Only Numbers by Paul Hoffman Fourth Estate, pounds 12.99, 256pp; A Beautiful Mind by Sylvia Nasar Faber & Faber, pounds 17.99, 448pp

How old is the epsilon? Is it a boss or a slave?" If you hadn't encountered Paul Erdos before, it was an odd and rather disquieting question, but his friends and acquaintances, accustomed to his private language, had no difficulty in translating. He was asking about a child: was it a girl or a boy?

Erdos, the most prolific mathematician of modern times, loved children. His term for them was a mathematician's joke: in analysis, epsilon denotes an arbitrarily small quantity. The boss/slave terminology was a kind of private joke in which Erdos poked gentle fun at a world he understood but whose values were seldom aligned with his own. He referred to God as "SF', "supreme fascist", but reserved his greatest reverence for "The Book", an imaginary volume in which God had written down the best proofs of the best theorems.

John Nash was another brilliant mathematician and a rough contemporary of Erdos. At the age of 66, he was awarded the Nobel prize - not a bad trick when there is no Nobel for mathematics. But for much of his career, Nash suffered from paranoid schizophrenia.

So is mathematical ability akin to madness? Theodore Kaczynski, the Unabomber, is often cited as some kind of proof, mostly by people who feel uncomfortable at their own inability to handle mathematics and want reassurance that anyone who can do better is crazy. I think the answer is "no". After all, the Unabomber had to have had some profession, be it dentist or wall-of- death motorcyclist. But now biographies of both these remarkable mathematicians are available, and they provide some interesting first-hand evidence.

Erdos first: Paul Hoffman - former editor of Discover magazine, and publisher of Encyclopaedia Britannica - has written a wonderful, playful, insightful life of this century's most unusual mathematician. Erdos published 1,475 papers, "many of them monumental and all of them substantial". He engaged in more collaborations than any other mathematician ever, 485 to be exact. If you are a mathematician, your "Erdos number" is the length of the smallest chain of joint papers that links you to Erdos.

In March 1913, while Erdos's mother was in hospital giving birth to him, his two young sisters both died of septic scarlet fever. Young Paul was kept at home a lot, on the assumption that this would protect him against contagious diseases. Self-absorbed and self-sufficient, he was a strange, though sometimes charming, child. Possibly his unusual childhood was the cause of his later unworldliness: he never owned a house or rented an apartment.

Instead, he travelled the globe, staying with colleagues and friends. Most of the money he earned he gave away to deserving causes. The friends remember him with a mixture of exasperation and affection, but it is the affection that shines through.

Erdos's most famous feat was a proof by elementary methods of the "prime number theorem", which gives a good approximation to the number of primes less than a given value. His greatest love, however, was Ramsey theory, which stems from a curious discovery made by Frank Ramsey, an atheist whose brother Michael became Archbishop of Canterbury.

How many people must there be at a party in order that either three of them all know each other or three of them are mutual strangers? Six. If we ask the same question for foursomes, there must be at least 18 people at the party. For fivesomes, the best anyone knows is that the answer lies between 43 and 49; for sixsomes, between 102 and 165. Questions like this have useful applications outside party chit-chat, but it is striking how difficult they are. Erdos loved problems like that.

Nash is the subject of Sylvia Nasar's A Beautiful Mind, less playful than Hoffman's book but more meticulous and equally gripping. Like Erdos, Nash was a strange child, but it is the differences in their lives that are most revealing.

Nash published little, but what he did publish was absolutely spectacular. He was extraordinarily competitive, confidently anticipating the award of the Fields Medal, the mathematician's equivalent of a Nobel, desperately hurt when he was passed over. He missed by a hair's breadth, not that he could have known that. The committee may well have had it in mind to consider him again four years later, but by then Nash was suffering from delusions about messages from extraterrestrials.

While it is not against the rules to award a subject's most prestigious medal to a schizophrenic, it is a rare occurrence. All the more amazing, then, that in 1994 Nash (by then fully recovered) received the Nobel prize in economics for his work on game theory. Here Sylvia Nasar has done a fascinating job of reconstructing the Nobel deliberations: the infighting, the academic politics. By the slenderest of margins, we discover, justice was done.

There have been mad mathematicians, then, but the question is to what extent madness, or at least eccentricity, is essential for mathematical creativity. And here we must avoid being selective. Hardly any of the other mathematicians in these books are crazy. John von Neumann, inventor of game theory, was an accomplished political operator; Lloyd Shapley, who worked at the RAND corporation, was a war hero.

Usually creative people, in arts and business as well as in science and mathematics, need not be crazy - but they do need to be driven. And if the human mind is driven too hard, it may bend, even snap. That may be what happened to Nash, though there is evidence that his condition was in part genetic.

Erdos, on the other hand, was simply too sane for his own good. He had no interest in money, and proved by example that he had no need for it. He spent 19 hours a day working on his beloved mathematics - and that was all he had ever wanted to do.

PROMOTED VIDEO
Have you tried new the Independent Digital Edition apps?
Arts and Entertainment

ebooksAn evocation of the conflict through the eyes of those who lived through it
Arts and Entertainment

ebooks
Independent
Travel Shop
the manor
Up to 70% off luxury travel
on city breaks Find out more
santorini
Up to 70% off luxury travel
on chic beach resorts Find out more
sardina foodie
Up to 70% off luxury travel
on country retreats Find out more
Latest stories from i100
Have you tried new the Independent Digital Edition apps?

ES Rentals

    Independent Dating
    and  

    By clicking 'Search' you
    are agreeing to our
    Terms of Use.

    Dress the Gaza situation up all you like, but the truth hurts

    Robert Fisk on Gaza conflict

    Dress the situation up all you like, but the truth hurts
    Save the tiger: Tiger, tiger burning less brightly as numbers plummet

    Tiger, tiger burning less brightly

    When William Blake wrote his famous poem there were probably more than 100,000 tigers in the wild. These days they probably number around 3,200
    5 News's Andy Bell retraces his grandfather's steps on the First World War battlefields

    In grandfather's footsteps

    5 News's political editor Andy Bell only knows his grandfather from the compelling diary he kept during WWI. But when he returned to the killing fields where Edwin Vaughan suffered so much, his ancestor came to life
    Lifestyle guru Martha Stewart reveals she has flying robot ... to take photos of her farm

    Martha Stewart has flying robot

    The lifestyle guru used the drone to get a bird's eye view her 153-acre farm in Bedford, New York
    Former Labour minister Meg Hillier has demanded 'pootling lanes' for women cyclists

    Do women cyclists need 'pootling lanes'?

    Simon Usborne (who's more of a hurtler) explains why winning the space race is key to happy riding
    A tale of two presidents: George W Bush downs his paintbrush to pen father’s life story

    A tale of two presidents

    George W Bush downs his paintbrush to pen father’s life story
    Restaurateur Mitch Tonks has given the Great Western Pullman dining car a makeover

    The dining car makes a comeback

    Restaurateur Mitch Tonks has given the Great Western Pullman dining car a makeover
    Gallery rage: How are institutions tackling the discomfort of overcrowding this summer?

    Gallery rage

    How are institutions tackling the discomfort of overcrowding this summer?
    Louis van Gaal has £500,000 video surveillance system installed to monitor Manchester United players

    Eye on the prize

    Louis van Gaal has £500,000 video surveillance system installed to monitor Manchester United players
    Women's rugby: Tamara Taylor adds fuel to the ire in quest to land World Cup

    Women's rugby

    Tamara Taylor adds fuel to the ire in quest to land World Cup
    Save the tiger: The day America’s love of backyard tigers led to a horrific bloodbath

    The day America’s love of backyard tigers led to a horrific bloodbath

    With only six per cent of the US population of these amazing big cats held in zoos, the Zanesville incident in 2011 was inevitable
    Samuel Beckett's biographer reveals secrets of the writer's time as a French Resistance spy

    How Samuel Beckett became a French Resistance spy

    As this year's Samuel Beckett festival opens in Enniskillen, James Knowlson, recalls how the Irish writer risked his life for liberty and narrowly escaped capture by the Gestapo
    We will remember them: relatives still honour those who fought in the Great War

    We will remember them

    Relatives still honour those who fought in the Great War
    Star Wars Episode VII is being shot on film - and now Kodak is launching a last-ditch bid to keep celluloid alive

    Kodak's last-ditch bid to keep celluloid alive

    Director J J Abrams and a few digital refuseniks shoot movies on film. Simon Usborne wonders what the fuss is about
    Once stilted and melodramatic, Hollywood is giving acting in video games a makeover

    Acting in video games gets a makeover

    David Crookes meets two of the genre's most popular voices