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Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
Goldbach’s Conjecture. One of the greatest unsolved mysteries in math is also very easy to write. Goldbach’s Conjecture is, “Every even number (greater than two) is the sum of two primes ...
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 problem, Riemann hypothesis, Yang–Mills existence and mass gap, and the Poincaré conjecture at the ...
Problems 1, 2, 5, 6, [g] 9, 11, 12, 15, 21, and 22 have solutions that have partial acceptance, but there exists some controversy as to whether they resolve the problems. That leaves 8 (the Riemann hypothesis ), 13 and 16 [ h ] unresolved, and 4 and 23 as too vague to ever be described as solved.
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In earlier years, the twelve questions were worth one point each, with no partial credit given. The competition is considered to be very difficult: it is typically attempted by students specializing in mathematics, but the median score is usually zero or one point out of 120 possible, and there have been only five perfect scores as of 2021.
There are many longstanding unsolved problems in mathematics for which a solution has still not yet been found. The notable unsolved problems in statistics are generally of a different flavor; according to John Tukey, [1] "difficulties in identifying problems have delayed statistics far more than difficulties in solving problems."
[7] Jeffrey Lagarias stated in 2010 that the Collatz conjecture "is an extraordinarily difficult problem, completely out of reach of present day mathematics". [8] However, though the Collatz conjecture itself remains open, efforts to solve the problem have led to new techniques and many partial results.
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