History
Euler stated that every arithmetic progression beginning with 1 contains an infinite number of primes. The theorem in the above form was first conjectured by Legendre in his attempted unsuccessful proofs of quadratic reciprocity and proved by Dirichlet in (Dirichlet 1837) with Dirichlet L-series. The proof is modeled on Euler's earlier work relating the Riemann zeta function to the distribution of primes. The theorem represents the beginning of rigorous analytic number theory.
Atle Selberg (1949) gave an elementary proof.
Read more about this topic: Dirichlet's Theorem On Arithmetic Progressions
Famous quotes containing the word history:
“Let us not underrate the value of a fact; it will one day flower in a truth. It is astonishing how few facts of importance are added in a century to the natural history of any animal. The natural history of man himself is still being gradually written.”
—Henry David Thoreau (1817–1862)
“You treat world history as a mathematician does mathematics, in which nothing but laws and formulas exist, no reality, no good and evil, no time, no yesterday, no tomorrow, nothing but an eternal, shallow, mathematical present.”
—Hermann Hesse (1877–1962)
“To history therefore I must refer for answer, in which it would be an unhappy passage indeed, which should shew by what fatal indulgence of subordinate views and passions, a contest for an atom had defeated well founded prospects of giving liberty to half the globe.”
—Thomas Jefferson (1743–1826)