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Unsolved problems in mathematics

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magic square
sums of each row, column, and main diagonals are equal
Hilbert's problems
twenty-three problems in mathematics published in 1900
P versus NP problem
unsolved problem in computer science about time complexity
Millennium Problems
seven mathematical problems whose solution is awarded with a US$1 million prize each
list of unsolved problems in mathematics
Wikimedia list article
Hadamard matrix
real square matrix whose all columns (rows) are mutually orthogonal and which only 1 or −1 as entries
Generalized Riemann hypothesis
Various conjectures about the zeroes of some functions similar to the Riemann zeta function
Navier–Stokes existence and smoothness
Millennium Prize Problem
Erdős conjecture on arithmetic progressions
Characterization of large sets
Smale's problems
collection of 18 then-unsolved mathematical problems proposed by S. Smale in 1998
Burnside's problem
mathematical problem in group theory
Szilassi polyhedron
nonconvex polyhedron with seven faces all of which abut each other
Yang–Mills existence and mass gap
Millennium Prize Problem
Hilbert–Pólya conjecture
Mathematical conjecture about the Riemann zeta function.
Thomson problem
mathematical problem
inverse Galois problem
unsolved problem in mathematics
Bloch's theorem
Theorem in complex analysis named after André Bloch
discrepancy theory
theory of irregularities of distribution
Köthe conjecture
open Problem in Ring Theory (Mathematics)
Eternity II puzzle
puzzle competition released in 2007, published by Lord Christopher Monckton, marketed and copyrighted by TOMY UK Ltd.; a 2 million USD prize was offered for a solution, but the competition ended in 2010 with no solutions found
Birch–Tate conjecture
mathematical conjecture
mutually unbiased bases
a set of orthonormal bases, where each vector of a given basis has the same overlap with all the vectors of other bases