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The Clay Mathematics Institute officially designated the title Millennium Problem for the seven unsolved mathematical problems, the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Riemann hypothesis, Yang–Mills existence and mass gap, and the Poincaré conjecture at the ...
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 ...
In computational complexity, problems that are in the complexity class NP but are neither in the class P nor NP-complete are called NP-intermediate, and the class of such problems is called NPI. Ladner's theorem , shown in 1975 by Richard E. Ladner , [ 1 ] is a result asserting that, if P ≠ NP , then NPI is not empty; that is, NP contains ...
In mathematical logic, Tarski's high school algebra problem was a question posed by Alfred Tarski. It asks whether there are identities involving addition , multiplication , and exponentiation over the positive integers that cannot be proved using eleven axioms about these operations that are taught in high-school-level mathematics .
The answer to the problem as proposed was given in the 1749 issue of the magazine by a Mr. Heath, and stated as 76,257.86 sq.yds. which was arrived at partly by "trial and a table of logarithms". The answer is not so accurate as the number of digits of precision would suggest.
The competition consists of 15 questions of increasing difficulty, where each answer is an integer between 000 and 999 inclusive. Thus the competition effectively removes the element of chance afforded by a multiple-choice test while preserving the ease of automated grading; answers are entered onto an OMR sheet, similar to the way grid-in math questions are answered on the SAT.
This category is intended for all unsolved problems in mathematics, including conjectures. Conjectures are qualified by having a suggested or proposed hypothesis. Conjectures are qualified by having a suggested or proposed hypothesis.