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Margulis proved the conjecture with ergodic theory methods. 1989: Vladimir I. Chernousov: Weil's conjecture on Tamagawa numbers: algebraic groups: The problem, based on Siegel's theory for quadratic forms, submitted to a long series of case analysis steps. 1990: Ken Ribet: epsilon conjecture: modular forms: 1992: Richard Borcherds: Conway ...
In mathematics, the common fixed point problem is the conjecture that, for any two continuous functions that map the unit interval into itself and commute under functional composition, there must be a point that is a fixed point of both functions.
The Collatz conjecture states that all paths eventually lead to 1. The Collatz conjecture [a] is one of the most famous unsolved problems in mathematics. The conjecture asks whether repeating two simple arithmetic operations will eventually transform every positive integer into 1.
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 ...
Download as PDF; Printable version ... In mathematics, Fujita's conjecture is a problem in the theories of algebraic geometry and complex ... J. Amer. Math. Soc., 6 ...
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 ...
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] The conjecture that the Erdős–Moser equation, 1 k + 2 k + ⋯ + (m – 1) k = m k, has no solutions except 1 1 + 2 1 = 3 1.
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 ...