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:
“What you don’t understand is that it is possible to be an atheist, it is possible not to know if God exists or why He should, and yet to believe that man does not live in a state of nature but in history, and that history as we know it now began with Christ, it was founded by Him on the Gospels.”
—Boris Pasternak (1890–1960)
“... in America ... children are instructed in the virtues of the system they live under, as though history had achieved a happy ending in American civics.”
—Mary McCarthy (1912–1989)
“History ... is, indeed, little more than the register of the crimes, follies, and misfortunes of mankind.
But what experience and history teach is this—that peoples and governments have never learned anything from history, or acted on principles deduced from it.”
—Georg Wilhelm Friedrich Hegel (1770–1831)