Paul Erdos

He was one of the most prolific mathematicians and producers of mathematical conjectures of the 20th century.

Paul Erdos

founded the field of discrete mathematics

One of his best known contributions in popular mathematics is the Erdős-Straus conjecture that every number of the form 4/n has a three-term Egyptian fraction.

The Erdős-Straus conjecture was formulated in 1948 by Paul Erdős and Ernst G.

The theorem was proved by Nicolaas Govert de Bruijn and Paul Erdős, after whom it is named.

This result was first conjectured by Erdős, and proven by Beck.

Paul Erdős, Chao Ko, and Richard Rado proved the theorem in 1938, but did not publish it until 1961.

While Ramsey's theorem makes it easy to prove that every infinite sequence of distinct real numbers contains a monotonically increasing infinite subsequence or a monotonically decreasing infinite subsequence, the result proved by Paul Erdős and George Szekeres goes further.

The theorem was published in 1960 by Paul Erdős and Tibor Gallai, after whom it is named.

It is named after Paul Erdős and Louis Mordell.

It is named after Paul Erdős and Arthur Stone, who proved it in 1946, and it has been described as the “fundamental theorem of extremal graph theory”.

In number theory, the Erdős-Kac theorem, named after Paul Erdős and Mark Kac, and also known as the fundamental theorem of probabilistic number theory, states that if ω(n) is the number of distinct prime factors of n, then, loosely speaking, the probability distribution of ω ( n ) − log ⁡ log ⁡ n log ⁡ log ⁡ n {\displaystyle {\frac {\omega (n)-\log \log n}{\sqrt {\log \log n}}}} is the standard normal distribution. ( ω ( n ) {\displaystyle \omega (n)} is sequence A001221 in the OEIS.)

It is named after Paul Erdős and Richard Rado.

The theorem is named after Paul Erdős and Norman H.

In incidence geometry, the De Bruijn-Erdős theorem, originally published by Nicolaas Govert de Bruijn and Paul Erdős in 1948, states a lower bound on the number of lines determined by n points in a projective plane.

In the mathematical discipline of graph theory, the Erdős-Pósa theorem, named after Paul Erdős and Lajos Pósa, relates two parameters of a graph: The size of the largest collection of vertex-disjoint cycles contained in the graph; The size of the smallest feedback vertex set in the graph: a set that contains one vertex from every cycle.

under the supervision of László Fejes Tóth and Paul Erdős

named after Paul Erdős and Lajos Pósa