Paul Erdős Biography [1, 2, 3]

“My brain is open” – Paul Erdős

Paul Erdős was born on March 26, 1913 in Budapest, Hungary to a Jewish family whose name was originally Engländer. Though the times of antisemitism was behind them, the Hapsburgs did not want to be reminded of their Jewish neighbors. Thus, Paul’s father picked a common Hungarian name that means “from the woods”. It’s approximate pronunciation is air-dish. His parents Lajos and Anna had two daughters who died just days before Paul was born. This would make his mother extremely protective of Paul. He would get his introduction to mathematics from his parents who were both mathematics teachers; a profession that was held in high regard in Hungary which boasted an outstanding educational system.

It turned out that Paul was a childhood prodigy who had an affinity for numbers. He would learn to count when his mother left for teaching. One day when Paul was just four years old a visitor, who after Paul had calculated the number of seconds he had lived, decided to give Paul a tricky question. He asked, “What is 150 minus 200?” Paul went quiet for a moment as his mind went of into unknown territory. Then he smiled and yelled excitedly, “150 below zero!” This was no small feat. He just independently discovered negative numbers! He would later down play his calculating abilities, but he would always remark with pride “his discovery” at the age of four.

When he was seventeen, he met his lifelong friend Andrew Vázsonyi at the request of Andrew’s father. Andrew had developed an interest in mathematics and wanted to meet the already famous Paul Erdős. Paul, on upon meeting Andrew, said, “Give me a four digit number.” Andrew, who was started, responded, “2,532.” Paul instantly said, “ The square of it is 6,411,024..” Then he asked Andrew how many proofs of the Pythagorean theorem did he know and Andrew noted only one. Paul mentioned he knew of 37 proofs. Andrew, would recall more than sixty years later that Paul was not boasting. He was merely feeling out the mathematical context that the two can best investigate. After the feeling out process, Paul felt he and Andrew were ready to go over Georg Cantor’s proof of infinities within infinities. Paul would do this throughout his life, giving his time to young mathematicians, helping and inspiring them with his knowledge and kind demeanor.

His love of numbers would be his life and would lead him to becoming a mathematician. Despite the restrictions on Jews entering universities in Hungary, Erdős was allowed to enter in 1930. He studied for his doctorate at the University Pázmány Péter in Budapest. Awarded a doctorate in 1934, he took up a post-doctoral fellowship at Manchester, essentially being forced to leave Hungary because he was Jewish. During his tenure of the fellowship, Paul traveled widely in the UK. He would continue to face discrimination, but that would not stop him. In March 1938 Hitler took control of Austria and Erdős had to cancel his spring visit to Budapest. He did visit during the summer vacation but the Czech crisis on September 3, 1938 made him decide to return hurriedly to England. Within weeks Paul was on his way to the USA where he took up a fellowship at Princeton. He would visit a friend in Madison, interview with Los Almos, take a part time appointment at Purdue University, and a temporary post at the University of Notre Dame. During this time he would travel extensively to the UK and Holland. During the early 1950s senator Joseph R McCarthy whipped up strong feelings against communism in the United States. Erdős began to come under suspicion from authorities. When asked by US immigration, as he returned after a conference in Amsterdam in 1954, about communism and Marx, he gave unacceptable answers and so deported. Paul was not allowed back to the United States but no reason was given.

During the early 1960s he made numerous requests to be allowed to return to the United States and a visa was finally granted in November 1963. By this time, however, Erdős had become a traveler moving from one university to another, and from the home of one mathematician to another. However, he did have a home of sorts with his friend Ronald Graham. Erdős and Graham met at a number theory conference in 1963 and soon began a mathematical collaboration. It was Graham who provided a room in his house where Paul could live when he wanted, he also stored Paul’s papers there and, in many ways, acted as a secretary to Paul. Paul would live out of a suit case for the rest of life. Traveling from conference to conference, to mathematician to mathematician. When he would visit, he would knock on the doors and greet the host with “My brain is open.” Indeed it was, as he would become second to Euler as the most prolific mathematician ever. He wrote or collaborated on more than 1,500 papers with over 450 different collaborators. He approached mathematics as a social activity and he enjoyed the company of others. He often said, “Another roof, another proof.” He was a brilliant, eccentric, simple, and beloved man. Loved and devoted by everyone he crossed paths with. The mathematical community started as a tribute to there friend and colleague the Erdős number, where Erdős himself has a number of 0, those who collaborated directly with him on a paper have an Erdős number of 1, and those who collaborated with Erdős collaborators have an Erdős number of 2, ad infinitum. He worked in fields of mathematics that proved pivotal to computer science, and discrete math. He became a leading number theorist, though he was know for being a problem solver. He died on Sept 20, 1996 in Warsaw, Poland while attending another conference!


[1] Bruce Schechter. My Brain is Open: the mathematical journeys of Paul Erdős. Simon & Schehter, 1998.

[2] Paul Hoffman. The Man Who Loved Only Numbers: the story of Paul Erdős and the search for mathematical truth. Hyperion, 1998.

[3] JJ O’Connor and EF Robertson. Paul Erdős. Available at

Watch the documentary, by George Paul Csicsery, N is a number: a portrait of Paul Erdős here.