Erdős, Pál

(Budapest, March 26th, 1913 – Warsaw, September 20th, 1996)

Erdős, Pál

He was a brilliant mind of the 20th century, a roving ambassador of Hungarian mathematics. Nobody did more than he to make Hungarian mathematics and our talented mathematicians known beyond our borders.

He passed his final examinations at Szent István Grammar School, and his name was to be found among those who were the best problem solvers of the Mathematics and Physics of Secondary School periodicals. From September 1930 he continued his studies at the Faculty of Mathematics and Physics of the Péter Pázmány University of Sciences Külső csatoló in Budapest. At the age of 18, he proved that a prime number with forms of 4k+1 and 4k+3 could always be found between n and 2n. His first paper was published with László Kalmár's aid in a periodical entitled Acta Scientiarum Mathematicarum in Szeged.

Erdős graduated from university in 1934, attained a Ph.D. from Lipót Fejér, then obtained a scholarship and went to L.J. Mordell in England for three years. Mathematics took him captive for life; the continuous concentrating, problem raising and solving became his natural element. In 1938, he went to the United States and made his home there. However, he kept his Hungarian citizenship all the time.

The number of his publications is 1500 or so, which is more by an order of magnitude than his contemporaries. He worked together with 500 co-authors. He achieved, probably, his most significant result in the second half of the 1930's when he, with Mark Kacc and Aurel Wintner, established the number theory of probability. With Pál Turán, they obtained immortality in the approximation theory and the statistical group theory.

He reached his most frequently quoted result in 1949, when with Atle Selberg he produced primary evidence for the prime number thesis, which had been proved only by means of the complex function theory up to that time. In 1951 he did receive the Cole Prize of the American Mathematical Society for his many papers on the number theory, and in particular for the above mentioned paper On a new method in elementary number theory which leads to an elementary proof of the prime number theorem.

In the 1940's, he was the first who pointed out the basic fact that the mathematical analysis of a random process can be traced back to an investigation of Brownian motion.

In the theory of sets he founded the partition calculus with András Hajnal and Richárd Radó and the theory of random graphs with Alfréd Rényi.

Erdős contributions to mathematics were rich and broad. However, he was not theory builder but he wanted to solve problems in an elegant and elementary way.

Erdős won several prizes including the Wolf Prize. Because his lifestyle needed little expenses, most of the money he had earned from lecturing at different conferences, he spent to help students or devoted on personal prizes for solving problems he had posed.

Memberships: member of the Hungarian Academy of Sciences Web link (1956, 1962), the American Academy of Sciences (1974), the Dutch Academy of Sciences (1977), the Australian Academy of Sciences (1985), the Indian Academy of Sciences (1988), the Polish Academy of Sciences (1994), the Royal Society (1989), honorary doctor: University of Wisconsin, USA (1973), Technische Hochschule, Hannover (1977), York University of Western Ontario, Canada (1985), Université de Lomoges, France (1986), Cambridge University, UK (1991), Technion, Haifa, Israel (1992), Western Michigan University, Kalamazzo, USA (1992), Eötvös Lóránd University of Sciences, Budapest, Hungary (1993), University of Illinois, Urbana-Champaign, USA (1993), University of Haifa, Israel (1994), Emory University Atlanta, USA (1995).

Honours: Cole Prize (1951), Kossuth Prize (1958), Tibor Szele Prize (1971), State Prize (1983), Wolf Prize (1983), Gold Medal of the Hungarian Academy of Sciences (1991)