Probabilistic number theory is a subfield of number theory, which explicitly uses probability to answer questions of number theory. One basic idea underlying it is that different prime numbers are, in some serious sense, like independent random variables. This however is not an idea that has a unique useful formal expression.
The founders of the theory were Paul Erdős, Aurel Wintner and Mark Kac during the 1930s, one of the most intense periods of investigation in analytic number theory. The Erdős–Wintner theorem and the Erdős–Kac theorem on additive functions were foundational results.
Read more about Probabilistic Number Theory: See Also
Famous quotes containing the words number and/or theory:
“In this world, which is so plainly the antechamber of another, there are no happy men. The true division of humanity is between those who live in light and those who live in darkness. Our aim must be to diminish the number of the latter and increase the number of the former. That is why we demand education and knowledge.”
—Victor Hugo (1802–1885)
“There is in him, hidden deep-down, a great instinctive artist, and hence the makings of an aristocrat. In his muddled way, held back by the manacles of his race and time, and his steps made uncertain by a guiding theory which too often eludes his own comprehension, he yet manages to produce works of unquestionable beauty and authority, and to interpret life in a manner that is poignant and illuminating.”
—H.L. (Henry Lewis)