Mertens Conjecture

In mathematics, the Mertens conjecture is the incorrect statement that the Mertens function M(n) is bounded by √n, which implies the Riemann hypothesis. It was conjectured by Stieltjes in a 1885 letter to Hermite (reprinted in Stieltjes 1905) and Mertens (1897), and disproved by Odlyzko & te Riele (1985). It is a striking example of a mathematical proof contradicting a large amount of computational evidence in favor of a conjecture.

Read more about Mertens Conjecture:  Definition, Disproof of The Conjecture, Connection To The Riemann Hypothesis

Famous quotes containing the word conjecture:

    “There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact.”
    —Mark Twain [Samuel Langhorne Clemens] (1835–1910)