Erdős Numbers

If you are a professional mathematician then you might be lucky enough to possess what is known as an ‘Erdős number’.  Erdős numbers are only meant to be a bit of fun, but many mathematicians are surprisingly proud to have one and are very interested in finding out what theirs is.

Erdős numbers are named after Paul Erdős who was the world’s most prolific mathematician, writing over 1500 papers in his lifetime.  Erdős was an eccentric Hungarian mathematician who lived and breathed mathematics, living out of a suitcase and travelling between mathematical conferences and friends’ houses, rather than settling down in any one place. Erdős didn’t like to do mathematics alone, but instead liked to collaborate with other mathematicians, writing joint papers with over 500 other people.

Erdős collaborated so much with other people that it gave his friends the idea of creating what is called the Erdős number.  If you are someone who wrote a paper directly with Erdős then you possess an Erdős number of 1.

Imagine someone has an Erdős number of 1.  Let’s call this person Mathematician A.  If Mathematician B then writes a joint paper with Mathematician A, then they will get an Erdős number of 2.  If Mathematician C then writes a paper with Mathematican B, then Mathematician C will have an Erdős number of 3 and so on.  Erdős himself was the only person to be assigned an Erdős number of 0.

Erdős collaboration graph

You might suppose that many mathematicians would have large Erdős numbers, especially since Paul Erdős died in 1996, meaning that no new people can have an Erdős number of 1.  In fact many mathematicians have a low Erdős number and the median Erdős number is thought to be around 5.  This reflects the popular idea of six degrees of separation, where people suggest that everybody is connected by a chain of less than six acquaintances.

The general public often view mathematicians as people who work alone, creating theorems in isolation.  While there have been a few cases of famous mathematicians working in relative isolation, it is in fact much more normal for mathematicians to work with other people, collaborating on their research.  The Erdős numbers reflect this fact – showing that mathematics is a highly social subject where lots of people work together.

If you want to find out more about the life of Paul Erdős (pronounced “Air-Dish”), you might enjoy reading a biography called ‘The Man Who Loved Only Numbers: Story of Paul Erdős and the Search for Mathematical Truth’ by Paul Hoffman.

If you have a passion for mathematics, then maybe one day you will have an Erdős number of your own.  To obtain one, you will need to co-author a mathematical research paper with somebody who already has an Erdős number.  To do this, you will usually need to be a professional mathematician or mathematical research student.


Article by Hazel Lewis