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Paul Tur\u00e1n (Paul Tur\u00e1n), or in Hungarian, P\u00e1l Tur\u00e1n (Tur\u00e1n P\u00e1l), was born on August 18, 1910, in Budapest, Hungary, into a Jewish family that faced severe discrimination and anti-Semitism throughout his life. However, amid those hardships, Tur\u00e1n produced mathematical works that permanently transformed the fields of number theory and combinatorics.<\/p>\n
Turan displayed outstanding mathematical abilities since his high school years in Budapest. He enrolled at P\u00e1zm\u00e1ny P\u00e9ter University (now E\u00f6tv\u00f6s Lor\u00e1nd University) in September 1930, and in that same year, he met Paul Erd\u0151s, another great mathematician. They immediately discovered a shared interest in number theory, which became the beginning of a friendship and academic collaboration that lasted 46 years, producing as many as 28 joint research papers. Turan received a teaching certificate in 1933 and earned his doctorate under the supervision of Lip\u00f3t Fej\u00e9r in 1935.<\/p>\n
Being Jewish, Tur\u00e1n fell victim to the numerus clausus policy that limited the number of Jews in universities, which prevented him from finding a job at a university for many years. In 1940, he was arrested by the Nazis and sent to a forced labor camp in Transylvania, before being transferred to several other camps until 1944. Remarkably, during this brutal period, Tur\u00e1n was able to develop some of the best mathematical concepts of his life, using only small scraps of paper to record his ideas, and he published these works after the war ended. It is said that he was protected by a fascist soldier who had once been a mathematics student and admired his work.<\/p>\n
Tur\u00e1n's most famous work is Tur\u00e1n\u2019s theorem, which he developed during 1940-1941. This theorem answers the question of how many edges a graph with n vertices can have while still avoiding the presence of a complete subgraph of size r+1 within it. The solution to this problem is the Tur\u00e1n graph, which is the most balanced r-partite graph structure. This work is considered the origin of the field of extremal graph theory, which Erd\u0151s once described as one of the fastest-growing areas in combinatorics.<\/p>\n
In addition, Tur\u00e1n also had many other important works, such as the invention of the 'power sum method' in 1938 to study the zeros of the Riemann zeta function and the distribution of prime numbers, as well as significant work in probabilistic number theory and inequalities related to Legendre polynomials, known as 'Tur\u00e1n\u2019s inequalities'.<\/p>\n
After the end of World War II, Tur\u00e1n received the position of associate professor at the University of Budapest in 1945 and was promoted to full professor in 1949. He married Vera S\u00f3s, another mathematician, in 1952 and had two children together. Tur\u00e1n was awarded the Kossuth Prize twice, in 1948 and 1952, and was invited as a speaker at the International Congress of Mathematicians (ICM) in 1970.<\/p>\n
Paul Tur\u00e1n passed away on September 26, 1976, in Budapest due to leukemia. Over the course of his career, he produced more than 150 published works. Tur\u00e1n's story is a powerful reminder that even in the harshest conditions, the mind of a mathematician can still create beautiful ideas and change the academic world forever.<\/p>\n