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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.
The seven selected problems span a number of mathematical fields, namely algebraic geometry, arithmetic geometry, geometric topology, mathematical physics, number theory, partial differential equations, and theoretical computer science. Unlike Hilbert's problems, the problems selected by the Clay Institute were already renowned among ...
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 ...
[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.
10. Determination of the solvability of a Diophantine equation. 11. Quadratic forms with any algebraic numerical coefficients 12. Extensions of Kronecker's theorem on Abelian fields to any algebraic realm of rationality 13. Impossibility of the solution of the general equation of 7th degree by means of functions of only two arguments. 14.
Fermat's Last Theorem considers solutions to the Fermat equation: a n + b n = c n with positive integers a, b, and c and an integer n greater than 2. There are several generalizations of the Fermat equation to more general equations that allow the exponent n to be a negative integer or rational, or to consider three different exponents.
A polynomial equation, also called an algebraic equation, is an equation of the form [24] ... Solving Diophantine equations is generally a very hard task.
An algebraic solution of a polynomial equation is an expression involving the four basic arithmetic operations (addition, subtraction, multiplication, and division), and root extractions. Such an expression may be viewed as the description of a computation that starts from the coefficients of the equation to be solved and proceeds by computing ...