TPTP (Thousands of Problems for Theorem Provers) is a freely available collection of problems for automated theorem proving. It is used to evaluate the...

Interactive provers are used for a variety of tasks, but even fully automatic systems have proved a number of interesting and hard theorems, including...

by others and credited as theorems of Fermat (for example, Fermat's theorem on sums of two squares), Fermat's Last Theorem resisted proof, leading to...

mathematics, the four color theorem, or the four color map theorem, states that no more than four colors are required to color the regions of any map so that no...

University of Miami, and is of both British and Australian nationality. Geoff Sutcliffe is the developer of the Thousands of Problems for Theorem Provers (TPTP)...

most for any mathematical theorem. The proofs are diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years...

where this problem is applied, are in image editing, lighting problems of a stage or installation of infrastructures for the warning of natural disasters...

deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems. In mainstream mathematics, the axioms...

impossibility theorem is a key result in social choice theory showing that no ranked-choice procedure for group decision-making can satisfy the requirements of rational...

abbreviation and may refer to Thousands of Problems for Theorem Provers Test & Performance Tools Platform, a platform of Eclipse This disambiguation page...

unsatisfiable. SAT is the first problem that was proven to be NP-complete—this is the Cook–Levin theorem. This means that all problems in the complexity class...

problem the halting problem for Z. [...] Theorem 2.2 There exists a Turing machine whose halting problem is recursively unsolvable. A related problem...

because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes...

Hilbert's problems are 23 problems in mathematics published by German mathematician David Hilbert in 1900. They were all unsolved at the time, and several...

proposition which is used to prove a larger statement. For that reason, it is also known as a "helping theorem" or an "auxiliary theorem". In many cases, a lemma...

the University of Illinois at Urbana–Champaign, solved the four-color theorem, one of the most famous problems in mathematics. They proved that any two-dimensional...

algorithm. For this kind of stable matching problem, the rural hospitals theorem states that: The set of assigned doctors, and the number of filled positions...

In mathematics, the classification of finite simple groups (popularly called the enormous theorem) is a result of group theory stating that every finite...

he had proved Fermat's Last Theorem, Savant published the book The World's Most Famous Math Problem (October 1993), which surveys the history of Fermat's...

foundations of algebraic geometry covers many thousands of pages. Although this is not a proof of a single theorem, there are several theorems in it whose...

list of some of the more commonly known problems that are NP-complete when expressed as decision problems. As there are thousands of such problems known...

systems (in particular, expert systems), symbolic mathematics, automated theorem provers, ontologies, the semantic web, and automated planning and scheduling...

scan Computer studies of Turing machine problems, Journal of the ACM 12/1965 Radó's theorem (Riemann surfaces) Radó's theorem (harmonic functions) Douglas...

(1970, p. 80) See Euler's theorem. L. Euler "Theoremata arithmetica nova methodo demonstrata" (An arithmetic theorem proved by a new method), Novi commentarii...

possible exception of the parallel postulate) that theorems proved from them were deemed absolutely true, and thus no other sorts of geometry were possible...

This is a list of misnamed theorems in mathematics. It includes theorems (and lemmas, corollaries, conjectures, laws, and perhaps even the odd object)...

theory, NP-complete problems are the hardest of the problems to which solutions can be verified quickly. Somewhat more precisely, a problem is NP-complete...

number of possible positions in the game tree of that problem. The first proof of the four colour theorem was a proof by exhaustion with 1834 cases. This...

planar graphs of degree at most 3. For bipartite graphs, the equivalence between vertex cover and maximum matching described by Kőnig's theorem allows the...

arXiv. Many other important problems have been solved in this century. Examples include the Green–Tao theorem (2004), existence of bounded gaps between arbitrarily...