Paul Erdős: The Prolific and Eccentric Mathematician

Paul Erdős was born on March 26, 1913, in Budapest, Hungary. His parents, Anna and Lajos Erdős, were both high school mathematics teachers. Tragically, Erdős’ two sisters died of scarlet fever the day he was born, which profoundly affected his family. His father was captured as a prisoner of war during World War I, leaving Erdős to be raised primarily by his mother and a German governess.

Erdős showed an early aptitude for mathematics. By the age of three, he could multiply three-digit numbers in his head, and by four, he had discovered negative numbers. His mother, fearing he might contract a fatal childhood disease, kept him home from school until he was ten. During this time, Erdős immersed himself in his parents’ mathematics books, developing a deep love for numbers.

In 1930, at the age of 17, Erdős entered the Péter Pázmány University in Budapest, where he completed his undergraduate studies and earned a Ph.D. in mathematics in just four years. His early work included a simple proof of Bertrand’s postulate, which states that there is always at least one prime number between any integer ( n ) and ( 2n )2.

Erdős’s career was marked by his unique approach to mathematics. He was a “freelance” mathematician, traveling the world and collaborating with other mathematicians on a wide range of problems. His work spanned numerous fields, including number theory, combinatorics, graph theory, and probability theory.

One of Erdős’s most significant contributions was to Ramsey theory, which studies the conditions under which order must appear in large structures. He also made substantial contributions to discrete mathematics, solving many previously unsolved problems. Erdős published around 1,500 mathematical papers during his lifetime, a record that remains unsurpassed.

Erdős was known for his collaborative spirit, working with more than 500 co-authors throughout his career. This led to the creation of the “Erdős number,” a measure of the “collaborative distance” between a mathematician and Erdős based on co-authorship. For example, if a mathematician co-authored a paper with Erdős, their Erdős number is 1; if they co-authored a paper with someone who co-authored with Erdős, their Erdős number is 2, and so on.

Erdős was as famous for his eccentric lifestyle as for his mathematical prowess. He lived out of a suitcase, traveling from one university or conference to another, often staying with colleagues and friends. He had no permanent home and few possessions, dedicating his life entirely to mathematics.

Erdős had a unique way of speaking, referring to children as “epsilons” (a small quantity in mathematics) and to God as the “Supreme Fascist” (SF), who he believed kept a book of the most elegant mathematical proofs. He was known for his generosity, often giving away prize money and supporting young mathematicians.

Paul Erdős passed away on September 20, 1996, in Warsaw, Poland, while attending a mathematics conference. His death marked the end of an era in mathematics, but his legacy lives on through his extensive body of work and the many mathematicians he inspired and collaborated with.

Erdős’s contributions to mathematics are celebrated worldwide, and his collaborative spirit continues to influence the field. The Erdős number remains a testament to his belief in the social nature of mathematical discovery.

Paul Erdős’s life was a testament to his passion for mathematics and his belief in the power of collaboration. His prolific output, unique personality, and dedication to solving mathematical problems have left an indelible mark on the field. Erdős’s story is one of brilliance, eccentricity, and an unwavering commitment to the pursuit of knowledge.