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Cameron–Erdős conjecture: sum-free sets: 2003: Nils Dencker: Nirenberg–Treves conjecture: pseudo-differential operators: 2004 (see comment) Nobuo Iiyori and Hiroshi Yamaki: Frobenius conjecture: group theory: A consequence of the classification of finite simple groups, completed in 2004 by the usual standards of pure mathematics. 2004 ...
For example, a Fourier series of sine and cosine functions, all continuous, may converge pointwise to a discontinuous function such as a step function. Carmichael's totient function conjecture was stated as a theorem by Robert Daniel Carmichael in 1907, but in 1922 he pointed out that his proof was incomplete. As of 2016 the problem is still open.
The Clay Institute has pledged a US $1 million prize for the first correct solution to each problem. The Clay Mathematics Institute officially designated the title Millennium Problem for the seven unsolved mathematical problems, the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP ...
In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. [1] [2] [3] Some conjectures, such as the Riemann hypothesis or Fermat's conjecture (now a theorem, proven in 1995 by Andrew Wiles), have shaped much of mathematical history as new areas of mathematics are developed in order to ...
In mathematics, the Birch and Swinnerton-Dyer conjecture (often called the Birch–Swinnerton-Dyer conjecture) describes the set of rational solutions to equations defining an elliptic curve. It is an open problem in the field of number theory and is widely recognized as one of the most challenging mathematical problems.
The conjecture is known to hold in special cases; for other cases, the bound on could be improved depending on the degree , although no absolute bound < is known that holds for all . In 1989, Tischler showed that the conjecture is true for the optimal bound K = d − 1 d {\displaystyle K={\frac {d-1}{d}}} if f {\displaystyle f} has only real ...
Schanuel's conjecture; Schinzel's hypothesis H; Scholz conjecture; Second Hardy–Littlewood conjecture; Serre's conjecture II; Sexy prime; Sierpiński number; Singmaster's conjecture; Safe and Sophie Germain primes; Stark conjectures; Sums of three cubes; Superperfect number; Supersingular prime (algebraic number theory) Szpiro's conjecture
A conjecture with Norman Oler [2] on circle packing in an equilateral triangle with a number of circles one less than a triangular number. The minimum overlap problem to estimate the limit of M(n). A conjecture that the ternary expansion of contains at least one digit 2 for every >. [3]