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Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories...

In mathematics, an impossibility theorem is a theorem that demonstrates a problem or general set of problems cannot be solved. These are also known as...

Arrow's impossibility theorem is a key result in social choice, discovered by Kenneth Arrow, showing that no ranked voting rule can behave rationally...

In mathematics, the Abel–Ruffini theorem (also known as Abel's impossibility theorem) states that there is no solution in radicals to general polynomial...

In mathematics and formal logic, a theorem is a statement that has been proven, or can be proven. The proof of a theorem is a logical argument that uses...

Euler's sum of powers conjecture Proof of impossibility Sums of powers, a list of related conjectures and theorems Wall–Sun–Sun prime If the exponent n were...

is to help prove a more substantial theorem – a step in the direction of proof. Some powerful results in mathematics are known as lemmas, first named for...

Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving mathematical...

solve. The difference between this impossibility and that of the no-go theorems is that a proof of impossibility states a category of logical proposition...

time it was thought that certain theorems, like the prime number theorem, could only be proved using "higher" mathematics. However, over time, many of these...

Social choice theory Arrow's impossibility theorem Condorcet paradox Gibbard–Satterthwaite theorem Gibbard's theorem ^ May, Kenneth O. 1952. "A set...

binomial theorem (combinatorics) Abel's curve theorem (mathematical analysis) Abel's theorem (mathematical analysis) Abelian and Tauberian theorems (mathematical...

theory showed that almost all ordinary mathematics can be formalized in terms of sets, although there are some theorems that cannot be proven in common axiom...

systematically applied in Euclid's Elements. A mathematical assertion is considered as truth only if it is a theorem that is proved from true premises by means...

Ribet's theorem, it provides a proof for Fermat's Last Theorem. Both Fermat's Last Theorem and the modularity theorem were believed to be impossible to prove...

Reverse mathematics is a program in mathematical logic that seeks to determine which axioms are required to prove theorems of mathematics. Its defining...

hundreds of fixed-point theorems, Brouwer's is particularly well known, due in part to its use across numerous fields of mathematics. In its original field...

prime numbers to number theory and mathematics in general stems from the fundamental theorem of arithmetic. This theorem states that every integer larger...

In mathematics and computer science, the Entscheidungsproblem (German for 'decision problem'; pronounced [ɛntˈʃaɪ̯dʊŋspʁoˌbleːm]) is a challenge posed...

In 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...