Science history: Paul Erdös goes in search of coffee

A mathematician for whom maths was life.

By Jeff Glorfeld

Paul Erdös in Adelaide, Australia, in1985 with then 10-year-old Terence Tao, now one of the world’s leading mathematicians and winner of the Fields Medal in 2006.

Billy and Grace Tao / Wikimedia Commons

“A mathematician is a machine for turning coffee into theorems,” was a favourite saying of Paul Erdös, one of the most prolific mathematicians the world has ever known.

The quote comes from a 1998 biography The Man Who Loved Only Numbers: The Story of Paul Erdös and the Search for Mathematical Truth, by Paul Hoffman.

Erdös, born on 26 March 1913 in Budapest, Hungary, published more than 1500 papers, often collaborating with other mathematicians whose work interested him.

This outpouring was as obsessive as it was brilliant. Erdös “had no wife or children, no job, no hobbies, not even a home, to tie him down”, Hoffman says.

“In a never-ending search for good mathematical problems and fresh mathematical talent, Erdös crisscrossed four continents at a frenzied pace, moving from one university or research centre to the next.

“His modus operandi was to show up on the doorstep of a fellow mathematician, declare, ‘My brain is open’, work with his host for a day or two, until he was bored or his host was run down, and then move on to another home.”

One result of this peripatetic life was the creation of what’s known as an Erdös number, which is a sort of six degrees of separation exclusive to mathematicians.

Here’s how it works, according to the Erdös Numbers Project, an initiative from Oakland University, in Michigan Erdös’ Erdös number is 0. Erdös’ co-authors have the Erdös number of 1. People other than Erdös who have written a joint paper with someone with an Erdös number 1 but not with Erdös have Erdös number 2, and so on. If there is no chain of co-authorships connecting someone with Erdös, that person’s Erdös number is said to be infinite.

(Do you have an Erdös number? Find out here.)

But apart from his sheer productivity, and the range of solutions to mathematical problems he worked out, Erdös also “founded the field of discrete mathematics, which is the foundation of computer science”, says an article published by the University of St Andrews, Scotland.

An online study module offered by the University of Chicago says discrete mathematics is concerned with the study of objects that can be represented within bounds or limits (or countably). “It includes topics that can be used to answer many tangible questions that arise in everyday life”.

For example:

Logic: Is a given argument logically sound, or does it contain a fallacy?

Number theory: If a leap year happens every four years and US senators are elected every six years, how frequently is a Senate election held in a leap year?

Counting: How many different outfits can you make from the clothes in your closet?

Probability: What are your chances of winning the lottery?

Recurrences: How much will you pay over the lifetime of a mortgage if interest is compounded monthly?

Graph theory: What is the fastest way to get from your home to your workplace?

Moving from these examples, the course expounds how discrete mathematics “provides an essential foundation for virtually every area of computer science, and its applications are correspondingly vast”.

It says the problem-solving techniques “honed in discrete mathematics are necessary for writing complicated software”, making it possible to “generalise from a single instance of a problem to an entire class of problems, and to identify and abstract patterns from data”.

For this we can thank Paul Erdös, who died in Warsaw, Poland, on 20 September 1996, suffering a fatal heart attack while working on an equation during a conference.

An obituary published by The Times newspaper in the UK says he “fuelled his efforts almost entirely by coffee, caffeine tablets and Benzedrine. Somehow his body seemed to thrive on this punishing routine.”

Jeff Glorfeld is a former senior editor of The Age newspaper in Australia, and is now a freelance journalist based in California, US.
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