# Brilliant minds out to lunch

## Under the Microscope/Prof William Reville: The idea that scientists are eccentric is a stereotype but, like most stereotypes…

Under the Microscope/Prof William Reville: The idea that scientists are eccentric is a stereotype but, like most stereotypes, it contains a grain of truth.

The most popular image in this regard is the absent- minded professor. In my experience, in their personal manner, most scientists are like any other group I have come across. However, a small minority are genuine eccentrics.

First of all, a story about an absent-minded Cambridge professor of mathematics who posted an "OUT" notice on his office door and went off to give a lecture. He forgot to bring his notes and returned to his office but, on seeing the "OUT" notice, turned away sadly.

Another example of eccentricity was the Hungarian mathematician, Paul Erdös (pronounced air-dish). His story is told by Bruce Schechter in the book, My Brain is Open (Simon & Schuster, 1998). Erdös was born in Budapest in 1913, the son of two Jewish secondary school mathematics teachers. He quickly showed a prodigal talent for maths and at the age of three he would entertain visitors by multiplying three-digit numbers in his head. He began to publish original maths as a teenager.

Erdös's first big interest in maths was prime numbers. A prime number is an integer that can be divided only by one and itself. When Erdös was 10, his father showed him Euclid's proof that the number of primes is infinite. Entranced by the elegance of the proof, Paul decided to devote his life to maths.

Questions about prime numbers are easily framed, but not easily answered. The question, "Is there a prime number between every number and twice that number?", was not solved until 1850 when the Russian, Pafnuty Lvovitch Chebyshev, proved that the answer is yes. Chebyshev's proof is difficult, long and laborious. Erdös loved elegant, or beautiful, proofs. He imagined that god kept a book in which he wrote all the most beautiful mathematical proofs. When Erdös derived or saw an elegant proof he would exclaim: "That's one for the book." At 17, he developed a short and beautiful new proof of Chebyshev's theorem. The wider mathematical world began to notice the young star.

Erdös was awarded his PhD at 21 and left Hungary to study in Manchester. He returned home on holidays but could not do so after Hitler's Anschlüss in 1938. He went to the US and spent time at the Institute for Advanced Studies, Princeton, and later at Notre Dame University. Because of his voluminous correspondence with mathematicians worldwide, he came under suspicion in McCarthy-era America. After attending a conference in Amsterdam in 1954 he wasn't allowed to re-enter the US.

Apart from his four years in Manchester and his sojourn in the US, Erdös effectively spent the rest of his life as a homeless person until his death in 1996. In a never-ending search for quality mathematical problems and new mathematical talent, he roamed over four continents moving from one university or research centre to the next. He had no home, wife, children, job or hobbies to tie him down. He would appear on the doorstep of a fellow mathematician, carrying a small shabby suitcase and a plastic bag stuffed with papers, and declare: "My mind is open." He would work with his host for some days and then move on.

Erdös's mannerisms and habits were very strange. He was fidgety and would frequently jump to his feet and wave his arms, or race towards a wall and stop suddenly, an inch from collision. His shabby suitcase held only enough clothes for a few days and his socks and underwear had to be washed several times a week - by his hosts. Tasks such as paying bills or preparing food were beyond him. He washed his hands 50 times a day and flooded bathroom floors. Erdös made up a private vocabulary and used it in public without any explanation: god was "the supreme Fascist", a child was an "epsilon" (mathematical notation for a small quantity), women were "bosses", men were "slaves", and so on.

Erdös worked all his life in the areas of maths he first explored in his youth, including number theory and graph theory. One of his big contributions to mathematics was an "elementary" proof of the prime number theorem. It is about the distribution of prime numbers and describes how they thin out as the numbers get larger.

Erdös is the most prolific mathematician ever and the final total of his publications is expected to top 1,500. He wrote papers in collaboration with over 485 co-authors.

His fellow mathematicians were happy to tolerate the eccentricities of Erdös, not only because of his brilliant mind but also because of his warmth and companionship. He would always help a colleague when he could. He once loaned a young man \$1,000 to help him attend Harvard and told him he could repay the debt when he was able to. Years later, when the young man was working, he offered to repay the money. Erdös told him: "Do with the \$1,000 what I did."

Erdös apparently had no sex life; maths was his all-consuming passion. The following joke is told about him. On one of his frequent journeys across the US, Erdös decided to take the train and found himself seated next to a stunningly beautiful young woman.

The two struck up a conversation and one thing led to another. By the time the train was pulling into Penn Station they had written a joint paper. William Reville is associate professor of biochemistry and director of microscopy at University College Cork