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Paul Erdős

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Paul Erdős was a Hungarian mathematician who became one of the most productive thinkers of the 20th century. He was a specialist in solving specific mathematical puzzles rather than building large, abstract theories. His work touched many different branches of mathematics. These included discrete mathematics, number theory, and graph theory. He also studied mathematical analysis, set theory, approximation theory, and probability theory.

ronald graham couple with erdos 1986
ronald graham couple with erdos 1986

Erdős focused on cracking previously unsolved problems. He was particularly known for his contributions to Ramsey theory, which investigates the specific conditions under which order must appear within a system.

Erdős's mathematical journey began in Budapest, Austria-Hungary, where he was born on March 26, 1913. His parents were both high school mathematics teachers. This environment helped his talent grow at a very young age. By age five, he could calculate how many seconds old a person was just by knowing their age. His early education was shaped by difficult family circumstances. His father was held as an Austro-Hungarian prisoner of war in Siberia from 1914 to 1920. During this time, his mother worked long hours to support the family.

Erdős Pál sírja
Erdős Pál sírja

Erdős taught himself to read using the math texts his parents left around the house.

As he entered adulthood, Erdős began to engage deeply with the mathematical community. At age 16, he became fascinated by infinite series and set theory. While studying at the University of Budapest, he met several future colleagues. In 1935, he and George Szekeres published a paper that generalized a problem proposed by Esther Klein. This became known as the "Happy ending problem" because it led to the marriage of Szekeres and Klein. By the age of 20, Erdős had already found a proof for Bertrand's postulate. He earned his doctorate in mathematics in 1934 under the advisor Lipót Fejér.

Erdős lived a life that was very different from most academic scholars. He was often described as an eccentric wandering scholar. Instead of staying at one university, he lived out of a suitcase and traveled constantly. He believed that mathematics was a fundamentally social activity. He spent his life moving between institutions to collaborate with others. He would visit universities and expect his hosts to provide food, lodging, and laundry services. This itinerant lifestyle allowed him to devote almost all his waking hours to writing papers.

Paul Erdos with Terence Tao
Paul Erdos with Terence Tao

He traveled to places like the United States, Israel, and Australia.

His productivity was truly massive and remains largely unsurpassed. Throughout his lifetime, Erdős published approximately 1,525 mathematical papers. To put this in perspective, the next highest article count in the Mathematical Reviews database is roughly 823. He was a prolific collaborator, working with more than 500 different mathematicians. This high level of teamwork led to the creation of the "Erdős number." This is a measurement of the shortest path between a mathematician and Erdős based on co-authorship. If you wrote a paper with someone who wrote a paper with Erdős, your Erdős number would be two.

Erdős faced many political and personal challenges during his travels. Because he was Jewish, leaving Hungary for the United States in 1938 was a matter of safety. Later, during the 1950s, he faced difficulties entering the United States due to the Red Scare. He was accused of being a Communist sympathizer because of his correspondence with a Chinese mathematician. The U.S. Immigration and Naturalization Service denied him a re-entry visa for several years. He finally regained his visa in November 1963. During the years he could not enter the U.S., he spent about ten years living and teaching in Israel.

Despite never winning the Fields Medal, Erdős received many prestigious honors. He was awarded the Wolf Prize in mathematics during the 1983/84 period. His work helped advance many fields, including extremal combinatorics and topology. He even provided the first example of a totally disconnected topological space that is not zero-dimensional, now called the Erdős space. He remained active in mathematics until the very end of his life. He died in 1996 while attending a mathematics conference in Warsaw.

Erdős Pál sírja
Erdős Pál sírja

His legacy lives on through the thousands of problems he posed and the many people he inspired.

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File:ronald graham couple with erdos 1986.jpg
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File:Paul Erdos with Terence Tao.jpg
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File:Erdős Pál sírja.jpg
Erdős Pál sírja.jpg
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