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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 question is whether or not, for all problems for which an algorithm can verify a given solution quickly (that is, in polynomial time), an algorithm can also find that solution quickly. Since the former describes the class of problems termed NP, while the latter describes P, the question is equivalent to asking whether all problems in NP are ...
Smale's problems is a list of eighteen unsolved problems in mathematics proposed by Steve Smale in 1998 [1] and republished in 1999. [2] Smale composed this list in reply to a request from Vladimir Arnold, then vice-president of the International Mathematical Union, who asked several mathematicians to propose a list of problems for the 21st century.
Huge breakthroughs in math and science are usually the work of many people over many years. Seven math problems were given a $1 million bounty each in 2000, and just one has been solved so far.
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Let n be an odd square-free integer. Assuming the Birch and Swinnerton-Dyer conjecture, n is the area of a right triangle with rational side lengths (a congruent number ) if and only if the number of triplets of integers ( x , y , z ) satisfying 2 x 2 + y 2 + 8 z 2 = n is twice the number of triplets satisfying 2 x 2 + y 2 + 32 z 2 = n .
Encyclopedia of Mathematics. EMS Press. 2001 [1994]. "Original text of Hilbert's talk, in German". Archived from the original on 2012-02-05 "David Hilbert's "Mathematical Problems": A lecture delivered before the International Congress of Mathematicians at Paris in 1900" (PDF). Mathematical Problems public domain audiobook at LibriVox