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:
“This above all makes history useful and desirable: it unfolds before our eyes a glorious record of exemplary actions.”
—Titus Livius (Livy)
“All history is a record of the power of minorities, and of minorities of one.”
—Ralph Waldo Emerson (1803–1882)
“In front of these sinister facts, the first lesson of history is the good of evil. Good is a good doctor, but Bad is sometimes a better.”
—Ralph Waldo Emerson (1803–1882)