Pál Turán
Who was Pál Turán?
Hungarian mathematician (1910–1976)
Biographical data adapted from Wikipedia’s article on Pál Turán (CC BY-SA 4.0).
Biography
Pál Turán was born on August 18, 1910, in Budapest, Hungary, and became one of the most important mathematicians of the 20th century, focusing mainly on extremal combinatorics, number theory, and analysis. He studied at Eötvös Loránd University in Budapest, where he laid the groundwork for his future in mathematics. He married Vera T. Sós, a respected mathematician as well, and together, they were key figures in Hungarian mathematics for many years.
During World War II, Turán faced significant challenges. In 1940, because he was Jewish, he was arrested and sent to a Nazi labor camp in Transylvania. Over the years, he was moved between camps and had to endure terrible conditions. Despite this, Turán continued to work on mathematical problems and later published ideas he developed during this tough period. His ability to maintain high-level thinking under such stress deeply impressed those around him and highlighted his strong character.
After the war, Turán returned to academic life in Budapest and had a highly productive research career. He is best known for Turán's theorem in extremal graph theory, addressing how many edges a graph with a certain number of vertices can have without forming a complete subgraph of a specified size. This theorem provided a clear answer and led to a whole new area in combinatorics. He also came up with Turán's brick factory problem, a challenge in combinatorial geometry about reducing crossings in specific drawings of complete bipartite graphs, a question that continues to intrigue researchers.
Besides his work in combinatorics, Turán made important contributions to analytic number theory and approximation theory, including the Turán inequalities, the Erdős–Turán inequality, and the Turán–Kubilius inequality. His long-lasting collaboration with Paul Erdős is one of the most famous in 20th-century mathematics. Their partnership, spanning 46 years and resulting in 28 papers, was pivotal in establishing a culture of teamwork and problem-focused mathematics that gained worldwide attention for the Hungarian school.
Turán was recognized with the Kossuth Prize twice, in 1948 and 1952, for his contributions to Hungarian science, and he received the Szele Tibor commemorative medal in 1975. He continued his work and teaching in Budapest until he passed away on September 26, 1976, leaving a legacy that remains important to various active areas of mathematical research.
Before Fame
Pál Turán grew up in Budapest in the early 1900s, when the city was known for its strong mathematical and scientific education. He studied at Eötvös Loránd University, which had a great tradition in mathematics and had already produced several internationally recognized figures. During his student years and early career, he was influenced by the Hungarian math culture, which emphasized problem-solving and collaboration through competitions and close networks among young mathematicians.
His early research focused on number theory and the distribution of prime numbers, where he quickly made a name for himself. His friendship and working relationship with Paul Erdős began during this time, providing an intellectual partnership that boosted both men's productivity. By the late 1930s, before the war disrupted things, Turán had already started developing ideas in extremal combinatorics, which would eventually earn him lasting recognition.
Key Achievements
- Proved Turán's theorem, a foundational result in extremal graph theory determining the maximum edges in a graph without a complete subgraph of a given order
- Formulated Turán's brick factory problem, a still-unsolved combinatorial geometry problem about crossing numbers in complete bipartite graphs
- Made major contributions to analytic number theory through the Erdős–Turán inequality and the Turán–Kubilius inequality
- Sustained a 46-year collaboration with Paul Erdős resulting in 28 joint papers across number theory and combinatorics
- Received the Kossuth Prize twice (1948, 1952), reflecting his standing as one of Hungary's leading scientific figures
Did You Know?
- 01.Turán developed some of his most significant mathematical ideas while imprisoned in Nazi labour camps during the Second World War, working through problems mentally under conditions that allowed no access to libraries or writing materials.
- 02.His collaboration with Paul Erdős lasted 46 years and produced 28 joint papers, making it one of the longest and most prolific partnerships in the history of mathematics.
- 03.Turán's brick factory problem, which asks for the minimum number of crossings when connecting m kilns to n storage sites with no shared rail segments, was inspired by the layout of an actual brick factory where Turán was forced to work as a prisoner.
- 04.He won the Kossuth Prize, Hungary's highest state honor in science and culture, on two separate occasions: in 1948 and again in 1952.
- 05.Turán's wife, Vera T. Sós, was also a prominent mathematician specializing in combinatorics and graph theory, making them one of the few married couples both recognized at the highest level of the same mathematical discipline.
Family & Personal Life
Awards & Honors
| Award | Year | Details |
|---|---|---|
| Kossuth Prize | 1948 | — |
| Kossuth Prize | 1952 | — |
| Szele Tibor commemorative medal | 1975 | — |