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Elementary proof of the prime number theorem — Atle Selberg and Paul Erdős

1949 AD · Transmission: Disputed
MathematicsMethodNordic

Atle Selberg publishes in 1949, at the Institute for Advanced Study in Princeton, an "elementary" proof of the prime number theorem — that is, without resorting to complex-variable analysis, unlike the classical proofs of Hadamard and de la Vallée Poussin from 1896. Almost simultaneously and independently, the Hungarian mathematician Paul Erdős arrived at a related result using similar ideas, sparking a public priority dispute between the two over who had first reached the decisive step of the proof. The controversy, documented in correspondence from the time, marked the relationship between the two mathematicians for years. Selberg received the Fields Medal in 1950; Erdős, despite being an independent co-discoverer, was never awarded this distinction.

InstitutionInstitute for Advanced Study, Princeton
Historical regionNorway / USA (Selberg) / Hungary (Erdős)
Primary sourceSelberg, A. — "An Elementary Proof of the Prime-Number Theorem" (Annals of Mathematics, 50, April 1949); Erdős, P. — related result published independently in 1949
Secondary sourceInternational Mathematical Union — Fields Medal citation 1950
Original languageEnglish
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