History
The conjecture was considered as early as the early 1940s by Atle Selberg who never formally stated the conjecture. A special case of the conjecture is mentioned in a 1944 paper of Leonidas Alaoglu and Paul Erdős who suggest that it had been considered by Carl Ludwig Siegel. An equivalent statement was first mentioned in print by Theodor Schneider who set it as the first of eight important, open problems in transcendental number theory in 1957.
The related six exponentials theorem was first explicitly mentioned in the 1960s by Serge Lang and Kanakanahalli Ramachandra, and both also explicitly conjecture the above result. Indeed, after proving the six exponentials theorem Lang mentions the difficulty in dropping the number of exponents from six to four — the proof used for six exponentials “just misses” when one tries to apply it to four.
Read more about this topic: Four Exponentials Conjecture
Famous quotes containing the word history:
“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)
“I believe that history has shape, order, and meaning; that exceptional men, as much as economic forces, produce change; and that passé abstractions like beauty, nobility, and greatness have a shifting but continuing validity.”
—Camille Paglia (b. 1947)
“If you look at the 150 years of modern China’s history since the Opium Wars, then you can’t avoid the conclusion that the last 15 years are the best 15 years in China’s modern history.”
—J. Stapleton Roy (b. 1935)