# 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**

### 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.