Search results
Results From The WOW.Com Content Network
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. 2004 Robertson–Seymour theorem. The proof takes about 500 pages spread over about 20 papers. 2005 Kepler conjecture.
The definition of a formal proof is intended to capture the concept of proofs as written in the practice of mathematics. The soundness of this definition amounts to the belief that a published proof can, in principle, be converted into a formal proof.
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.
The proof was completed by Werner Ballmann about 50 years later. Littlewood–Richardson rule. Robinson published an incomplete proof in 1938, though the gaps were not noticed for many years. The first complete proofs were given by Marcel-Paul Schützenberger in 1977 and Thomas in 1974. Class numbers of imaginary quadratic fields.
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 idea is to try and apply formal math ideas, like proofs, to knots, like … well, what you tie your shoes with. For example, you might know how to tie a “square knot” and a “granny knot.”
Significantly, these proofs can be checked automatically, also by computer. Checking formal proofs is usually simple, whereas finding proofs (automated theorem proving) is generally hard. An informal proof in the mathematics literature, by contrast, requires weeks of peer review to be checked, and may still contain errors.
Fermat's little theorem and some proofs; Gödel's completeness theorem and its original proof; Mathematical induction and a proof; Proof that 0.999... equals 1; Proof that 22/7 exceeds π; Proof that e is irrational; Proof that π is irrational; Proof that the sum of the reciprocals of the primes diverges