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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 ...
The question is whether knowing the warden's answer changes the prisoner's chances of being pardoned. This problem is equivalent to the Monty Hall problem; the prisoner asking the question still has a 1 / 3 chance of being pardoned but his unnamed colleague has a 2 / 3 chance.
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.
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.
In A simple solution to the hardest logic puzzle ever, [6] B. Rabern and L. Rabern offer a variant of the puzzle: a god, confronted with a paradox, will say neither ja nor da and instead not answer at all. For example, if the question "Are you going to answer this question with the word that means no in your language?" is put to True, he cannot ...
The Zebra Puzzle is a well-known logic puzzle.Many versions of the puzzle exist, including a version published in Life International magazine on December 17, 1962. The March 25, 1963, issue of Life contained the solution and the names of several hundred successful solvers from around the world.