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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 ...
Hilbert's problems ranged greatly in topic and precision. Some of them, like the 3rd problem, which was the first to be solved, or the 8th problem (the Riemann hypothesis), which still remains unresolved, were presented precisely enough to enable a clear affirmative or negative answer.
Then in binary, the number n can be written as the concatenation of strings w k w k−1... w 1 where each w h is a finite and contiguous extract from the representation of 1 / 3 h . [23] The representation of n therefore holds the repetends of 1 / 3 h , where each repetend is optionally rotated and then replicated up to a finite ...
2008: The answer to one question in a GCSE Music paper was given away by accident in the copyright declaration printed on the back of the question paper. [9] 2011: OCR set an impossible maths question in the 2011 AS Mathematics paper. [10]
The Hardest Logic Puzzle Ever is a logic puzzle so called by American philosopher and logician George Boolos and published in The Harvard Review of Philosophy in 1996. [1] [2] Boolos' article includes multiple ways of solving the problem.
The classification of the simple quasithin groups by Aschbacher and Smith was 1221 pages long, one of the longest single papers ever written. 2004 Classification of finite simple groups. The proof of this is spread out over hundreds of journal articles which makes it hard to estimate its total length, which is probably around 10000 to 20000 pages.