### An open mind from love towards mathematics

#### 7 November 2016

**“A mathematician is a machine for changing coffee into mathematical theorems” – this quotation is often imputed to Paul Erdős. Putting aside the fact that he is not the author, this sentence perfectly describes this eminent 20th century figure.**

**Childhood and education**

Paul was born on 26 March 1913 into a Hungarian family. Both his father and his mother were math teachers.

Paul demonstrated above-average mathematical skills from when he was a child. For example, at the age of four he could change a person’s age expressed in years to a value expressed in seconds. At the age of 21, Erdős received a PhD degree at the University of Budapest. Shortly after, he migrated to the USA. In 1938, he became a scholar at Princeton University, however due to many problems caused by his eccentric nature, he was finally forced to leave the institute in 1941.

**An open mind and group work**

After the Second World War, the most creative period of Paul Erdős’s life began. He published a number of works in combinatorics, graph theory and number theory, collaborating with many mathematicians. Erdős was on a constant journey. He had no wife and no kids, his belongings fitted into a couple of suitcases and so he travelled the world, often visiting his mathematician friends. In their doorways he spoke his famous words: “I have an open mind”, which meant he was ready for joint work on a new issue. The visits lasted as long as the gentlemen were able to inspire one another and to create new mathematical theorems. According to Erdős, exercising mathematics was a social activity and it should be done in groups, which was contrary to the independent work so popular at that time. He knew well the preferences of each mathematician, so he was able to suggest to others problems that were interesting to them, which gave him general respect. He was also famous for establishing financial prizes for solving various mathematical problems he could not solve by himself.

**The Erdős number**

Erdős was one of the most prolific mathematicians, with the number of publications comparable only to that of Euler. Paul wrote over 1,500 scientific works and he certainly had the greatest number of co-authors: 511.

Therefore, his friends coined the term the “Erdős number” – attributable to any mathematician, meaning the distance from Erdős counted with co-authored publications. This means that Erdős is the only one to have an Erdős number equal to 0 (for being himself), whereas all his co-authors have an Erdős number equal to 1 and their co-authors have an Erdős number equal to 2 and so on. This number was attributed to about 200,000 mathematicians.

It is estimated that about 90% of all scientifically active mathematicians worldwide have Erdős number lower than 8.

Erdős attached great importance to “open-mindedness”. In his opinion, it was not enough to be in the right place at the right time, you also need to have an open mind at the right moment. Erdős himself was known for drinking loads of coffee and taking other stimulants. All this to be able to keep the mind sharp for even 20 hours a day.

**Proof for Erdős**

The eccentricities of Erdős showed among others also in his particular lexicon. He called children epsilons; as in mathematics this Greek letter stands for a small but significant value. When he said someone had died, he meant the person was not into mathematics anymore, and about the people that had actually died he said they had passed away. Also his attitude towards faith in God was peculiar. He was an atheist, yet he believed in the existence of the Book – a collection of the most beautiful mathematical proofs. They were written by God who keeps them in secret and only from time to time lets someone look into it. During his entire life, whenever he encountered a really clever mathematical proof, he would shout “This proof comes from the Book!” When he died, two mathematicians decided to collate all the most beautiful proofs and the “proofs from the Book” were actually written down, with a dedication to Erdős.

**An open mind from love towards mathematics**

Erdős devoted his entire life to mathematics. He died on 20 September 1996 during a mathematical conference in Warsaw, hours after he had solved another problem in geometry. On his gravestone, it was written: Végre nem butulok tovább (Hungarian: I’ve finally stopped getting dumber).