He wrote 18 papers with Paul Erdős.

He wrote 32 joint papers with Paul Erdős, the most well-known of which are his papers introducing the Erdős – Rényi model of random graphs.

Erdős wrote of Turán, " In 1940 – 1941 he created the area of extremal problems in graph theory which is now one of the fastest-growing subjects in combinatorics.

Guy wrote four papers with Paul Erdős, giving him an Erdős number of 1.

Lovász wrote 6 papers with Paul Erdős, a mathematician who was famous for writing papers with co-authors, which earned Lovász an Erdős number of one.

Among over 700 scholarly articles Harary wrote, two were co-authored with Paul Erdős, giving Harary an Erdős number of 1.

Marcus wrote a paper together with Paul Erdős (" Sur la décomposition de l ' espace euclidien en ensembles homogènes ", Acta Math.

Bayer wrote a paper with Persi Diaconis, who has an Erdős number of 1 due to a jointly authored 1977 Stanford University technical report, later published in a 2004 compilation.

Proofs of the prime number theorem not using the zeta function or complex analysis were found around 1948 by Atle Selberg and by Paul Erdős ( for the most part independently ).

He had 511 direct collaborators ; these are the people with Erdős number 1.

The people who have collaborated with them ( but not with Erdős himself ) have an Erdős number of 2 ( 9267 people as of 2010 ), those who have collaborated with people who have an Erdős number of 2 ( but not with Erdős or anyone with an Erdős number of 1 ) have an Erdős number of 3, and so forth.

The Erdős number was most likely first defined in print by Casper Goffman, an analyst whose own Erdős number is 1.

In 1940, Paul Erdős showed that there is a constant c < 1 and infinitely many primes p such that ( p ′ − p ) < ( c ln p ) where p ′ denotes the next prime after p. This result was successively improved ; in 1986 Helmut Maier showed that a constant c < 0. 25 can be used.

Graham's Erdős number is 1.

They were close friends of the mathematician Paul Erdős, and have both published papers with him – 13 in her case ; thus, both have Erdős numbers of 1.

The existence of ω < sub > 1 </ sub >- Erdős cardinals implies the existence of 0 < sup >#</ sup >.

# If K has no ω < sub > 1 </ sub >- Erdős cardinals, then for a particular countable ( in K ) and definable in K sequence of functions from ordinals to ordinals, every set of ordinals closed under these functions is a union of a countable number of sets in K. If L = K, these are simply the primitive recursive functions.

In 1936 Erdős and Turán conjectured for every value d called density 0 < d < 1 and every integer k there is a number N ( d, k ) such that every subset A of

Alavi's Erdős number is 1 due to eight joint papers with Paul Erdős, who frequently visited him in Kalamazoo.

His Erdős number is 1: he cowrote 50 joint papers with Paul Erdős beginning in 1976 and is among the three mathematicians that most frequently co-authored with Erdős.

His Erdős number is 1 ..

Thus, no cardinal can be ω < sub > 1 </ sub >- Erdős in L. While L does contain the initial ordinals of those large cardinals ( when they exist in a supermodel of L ), and they are still initial ordinals in L, it excludes the auxiliary structures ( e. g. measures ) which endow those cardinals with their large cardinal properties.

Paul Erdős said, allegedly, about the Collatz conjecture: " Mathematics is not yet ripe for such problems " and also offered $ 500 for its solution.

Paul Erdős originally offered US $ 50 for proving the conjecture in the affirmative, and later raised the reward to US $ 500.

* Erdős discrepancy problem-Homogeneous arithmetic progressions ( Erdős, $ 500 )

The Erdős number () describes the " collaborative distance " between a person and mathematician Paul Erdős, as measured by authorship of mathematical papers.

The idea of the Erdős number was created by friends as a humorous tribute to the enormous output of Erdős, one of the most prolific modern writers of mathematical papers, and has become well known in scientific circles as a tongue-in-cheek measurement of mathematical prominence.

* Erdős number, collaborations on mathematical papers with Paul Erdős

Paul Erdős, the eccentric and extremely prolific Hungarian-born mathematician, referred to the notion of deus deceptor in a humorous context when he called God " the Supreme Fascist ", who deliberately hid things from people, ranging from socks and passports to the most elegant of mathematical proofs.

Paul Erdős is legendary for having posed hundreds, if not thousands, of mathematical problems, many of them profound.

Erdős often stayed with Graham, and allowed him to look after his mathematical papers and even his income.

The prolific mathematician Paul Erdős and his various collaborators made many famous mathematical conjectures, over a wide field of subjects.

Through his film credits, combined with his research publications in mathematical physics, Greene is one of the few people to have a defined Erdős – Bacon number.

He has published more than 200 mathematical papers on these topics together with such notable mathematicians as Béla Bollobás, Stefan Burr, Paul Erdős, Ron Gould, András Gyárfás, Brendan McKay, Cecil Rousseau, Richard Schelp, Miklós Simonovits, Joel Spencer, and Vera Sós.

Paul Erdős was famous for offering mathematical bounties.

* Paul Erdős ' concept of " The Book " in which God maintains the most elegant proofs from THE BOOK of mathematical theorems

To restore Folkman's confidence, Erdős immediately challenged him to solve mathematical problem s.

As soon as Folkman received Graham and Erdős at the hospital, Erdős challenged Folkman with mathematical problems, helping to rebuild his confidence.

As a young woman in Budpaest, Klein was a member of a group of Hungarians including Paul Erdős, George Szekeres, and Paul Turán that convened over interesting mathematical problems.

A person's Erdős – Bacon number is the sum of one's Erdős number — which measures the " collaborative distance " in authoring mathematical papers between that person and Hungarian mathematician Paul Erdős — and one's Bacon number — which represents the number of links, through roles in films, by which the individual is separated from American actor Kevin Bacon.

The Erdős criterion technically refers to collaboration on mathematical papers, but it is often relaxed to include general research articles for the Erdős – Bacon number.