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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.
The Millennium Prize Problems are seven well-known complex mathematical problems selected by the Clay Mathematics Institute in 2000. The Clay Institute has pledged a US $1 million prize for the first correct solution to each problem.
In Task 1, students are given two questions but need to answer only one. For Task 2, students select another fragment from the same work and answer one of the two provided questions. Task 3 involves analyzing a poem, with two questions provided, from which students choose one to answer. Task 4 requires comparing the poem from Task 3 with ...
The competition consists of 15 questions of increasing difficulty, where each answer is an integer between 0 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.
A student receives 6 points for each question answered correctly, 1.5 points for each question left blank, and 0 points for incorrect answers. Thus, a student who answers 24 correctly, leaves 1 blank, and misses 0 gets 24 × 6 + 1.5 × 1 = 145.5 {\displaystyle 24\times 6+1.5\times 1=145.5} points.
Such questions are usually more difficult to solve than regular mathematical exercises like "5 − 3", even if one knows the mathematics required to solve the problem. Known as word problems , they are used in mathematics education to teach students to connect real-world situations to the abstract language of mathematics.