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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 ...
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.
It is among the most notable theorems in the history of mathematics and prior to its proof was in the Guinness Book of World Records as the "most difficult mathematical problem", in part because the theorem has the largest number of unsuccessful proofs. [3]
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.
Find the most general law of the reciprocity theorem in any algebraic number field. Partially resolved. Solved by Emil Artin in 1927 for Abelian extensions of the rational numbers during the development of class field theory. The non-abelian case remains unsolved, if one interprets that as meaning non-abelian class field theory. — 10th
Consequently, it is one of the toughest exams in the world. To put it to perspective, some people who are considered to be in the top 98 percent high IQ individuals in standardized tests have ...
Most of the points have orbits that diverge to infinity. Coloring these points based on how fast they diverge produces the image on the left, for h ( z ) ≜ 0 {\displaystyle h(z)\triangleq 0} . The inner black regions and the outer region are the Fatou components , and the boundary between them is the Julia set of f {\displaystyle f} , which ...