Conjecture

conjecturalconjecturesconjecturedconjecturingguessmathematical conjecturetextual criticismunsolved problem
In mathematics, a conjecture is a conclusion or a proposition which is suspected to be true due to preliminary supporting evidence, but for which no proof or disproof has yet been found.wikipedia
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Mathematics

mathematicalmathmathematician
In mathematics, a conjecture is a conclusion or a proposition which is suspected to be true due to preliminary supporting evidence, but for which no proof or disproof has yet been found.
Mathematicians seek and use patterns to formulate new conjectures; they resolve the truth or falsity of conjectures by mathematical proof.

Riemann hypothesis

Critical line theoremcritical line1st
Some conjectures, such as the Riemann hypothesis (still a conjecture) or Fermat's Last Theorem (a conjecture until proven in 1995 by Andrew Wiles), have shaped much of mathematical history as new areas of mathematics are developed in order to prove them.
In mathematics, the Riemann hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part 1⁄2.

Fermat's Last Theorem

Fermat’s Last TheoremLast Theorema long-standing problem
Some conjectures, such as the Riemann hypothesis (still a conjecture) or Fermat's Last Theorem (a conjecture until proven in 1995 by Andrew Wiles), have shaped much of mathematical history as new areas of mathematics are developed in order to prove them. In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c can satisfy the equation for any integer value of n greater than two.
The proposition was first conjectured by Pierre de Fermat in 1637 in the margin of a copy of Arithmetica; Fermat added that he had a proof that was too large to fit in the margin.

Algebraic number theory

placefinite placealgebraic
The unsolved problem stimulated the development of algebraic number theory in the 19th century, and the proof of the modularity theorem in the 20th century.
Fermat's last theorem was first conjectured by Pierre de Fermat in 1637, famously in the margin of a copy of Arithmetica where he claimed he had a proof that was too large to fit in the margin.

Counterexample

counter-examplecounterexamples
A number of false proofs and false counterexamples have appeared since the first statement of the four color theorem in 1852.
She conjectures that "All rectangles are squares", and she is interesting in knowing whether this statement is true or false.

Theorem

theoremspropositionconverse
It was the first major theorem to be [[computer-assisted proof#List of theorems proved with the help of computer programs|proved using a computer]].
In this case, A is called the hypothesis of the theorem ("hypothesis" here means something very different from a conjecture), and B the conclusion of the theorem.

Collatz conjecture

Collatz problemCollatz sequenceHasse's algorithm
For instance, the Collatz conjecture, which concerns whether or not certain sequences of integers terminate, has been tested for all integers up to 1.2 × 10 12 (over a trillion).
The Collatz conjecture is a conjecture in mathematics that concerns a sequence defined as follows: start with any positive integer n. Then each term is obtained from the previous term as follows: if the previous term is even, the next term is one half the previous term.

Euler's sum of powers conjecture

conjecturedEuler conjectureEuler proposed
the Pólya conjecture and Euler's sum of powers conjecture).
Euler's conjecture is a disproved conjecture in mathematics related to Fermat's last theorem.

Langlands program

Langlands philosophyLanglands correspondenceLanglands conjectures
In mathematics, the Langlands program is a web of far-reaching and influential conjectures about connections between number theory and geometry.

Mathematical proof

proofproofsprove
There are various methods of doing so; see methods of mathematical proof for more details.
An unproven proposition that is believed to be true is known as a conjecture, or a hypothesis if the proposition is frequently used as an assumption to build upon similar mathematical work.

List of conjectures

several conjectures
This is a list of mathematical conjectures.

Pólya conjecture

conjecture by George PólyaPolya conjecture
the Pólya conjecture and Euler's sum of powers conjecture).
The conjecture was posited by the Hungarian mathematician George Pólya in 1919, and proved false in 1958 by C. Brian Haselgrove.

Continuum hypothesis

generalized continuum hypothesisGCHHilbert's first problem
The continuum hypothesis, which tries to ascertain the relative cardinality of certain infinite sets, was eventually shown to be independent from the generally accepted set of Zermelo–Fraenkel axioms of set theory.
As a result of its independence, many substantial conjectures in those fields have subsequently been shown to be independent as well.

Conditional proof

conditional resultConditional Introductionconditionals
These are called conditional proofs: the conjectures assumed appear in the hypotheses of the theorem, for the time being.
Conditional proofs exist linking several otherwise unproven conjectures, so that a proof of one conjecture may immediately imply the validity of several others.

Science

scientificsciencesscientific knowledge
Conjecture is related to hypothesis, which in science refers to a testable conjecture.
Still, philosophical perspectives, conjectures, and presuppositions, often overlooked, remain necessary in natural science.

Hypothesis

hypotheseshypotheticalhypothesized
Conjecture is related to hypothesis, which in science refers to a testable conjecture.

Consequent

conclusionApodosisconclusions
In mathematics, a conjecture is a conclusion or a proposition which is suspected to be true due to preliminary supporting evidence, but for which no proof or disproof has yet been found.

Proposition

propositionspropositionalclaim
In mathematics, a conjecture is a conclusion or a proposition which is suspected to be true due to preliminary supporting evidence, but for which no proof or disproof has yet been found.

Formal proof

prooflogical prooflogical proofs
In mathematics, a conjecture is a conclusion or a proposition which is suspected to be true due to preliminary supporting evidence, but for which no proof or disproof has yet been found.

Andrew Wiles

Andrew John WilesSir Andrew WilesAndrew J. Wiles
Some conjectures, such as the Riemann hypothesis (still a conjecture) or Fermat's Last Theorem (a conjecture until proven in 1995 by Andrew Wiles), have shaped much of mathematical history as new areas of mathematics are developed in order to prove them.

Number theory

number theoristcombinatorial number theorytheory of numbers
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c can satisfy the equation for any integer value of n greater than two.

Sign (mathematics)

positivenon-negativesign
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c can satisfy the equation for any integer value of n greater than two.

Integer

integersintegralZ
For instance, the Collatz conjecture, which concerns whether or not certain sequences of integers terminate, has been tested for all integers up to 1.2 × 10 12 (over a trillion). In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c can satisfy the equation for any integer value of n greater than two.

Pierre de Fermat

FermatPierre FermatFermat, Pierre de
This theorem was first conjectured by Pierre de Fermat in 1637 in the margin of a copy of Arithmetica, where he claimed that he had a proof that was too large to fit in the margin.

Arithmetica

This theorem was first conjectured by Pierre de Fermat in 1637 in the margin of a copy of Arithmetica, where he claimed that he had a proof that was too large to fit in the margin.