1 a hypothesis that has been formed by speculating or conjecturing (usually with little hard evidence); "speculations about the outcome of the election"; "he dismissed it as mere conjecture" [syn: speculation]
2 a message expressing an opinion based on incomplete evidence [syn: guess, supposition, surmise, surmisal, speculation, hypothesis]
3 reasoning that involves the formation of conclusions from incomplete evidence v : to believe especially on uncertain or tentative grounds; "Scientists supposed that large dinosaurs lived in swamps" [syn: speculate, theorize, theorise, hypothesize, hypothesise, hypothecate, suppose]
- A statement or idea which is unproven, but is thought to be
true; a guess.
- I explained it, but it is pure conjecture whether he understood, or not.
- A supposition
based upon incomplete evidence; a hypothesis.
- The physicist used his conjecture about subatomic particles to design an experiment.
- The interpretation of signs and omens.
An unproven statement; guess
A supposition based upon incomplete evidence; a hypothesis
- German: Vermutung
In mathematics, a conjecture is a mathematical statement which appears likely to be true, but has not been formally proven to be true under the rules of mathematical logic. Once a conjecture is formally proven true it is elevated to the status of theorem and may be used afterwards without risk in the construction of other formal mathematical proofs. Until that time, mathematicians may use the conjecture on a provisional basis, but any resulting work is itself provisional until the underlying conjecture is cleared up.
In scientific philosophy, Karl Popper pioneered the use of the term "conjecture" to indicate a proposition which is presumed to be real, true, or genuine, mostly based on inconclusive grounds, in contrast with a hypothesis (hence theory, axiom, principle), which is a testable statement based on accepted grounds.
Famous conjecturesUntil recently, the most famous conjecture was the mis-named Fermat's last theorem, mis-named because although Fermat claimed to have found a clever proof of it, none could be found among his notes after his death. The conjecture taunted mathematicians for over three centuries before Andrew Wiles, a Princeton University research mathematician, finally proved it in 1993, and now it may properly be called a theorem.
Other famous conjectures include:
The Langlands program is a far-reaching web of these ideas of 'unifying conjectures' that link different subfields of mathematics, e.g. number theory and the representation theory of Lie groups; some of these conjectures have since been proved.
Unlike the empirical sciences, formal mathematics is based on provable truth; one cannot simply try a huge number of cases and conclude that since no counter-examples could be found, therefore the statement must be true. Of course a single counter-example would immediately bring down the conjecture, after which it is sometimes referred to as a false conjecture. (c.f. Pólya conjecture)
Mathematical journals sometimes publish the minor results of research teams having extended a given search farther than previously done before. 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 million millions). In practice, however, it is extremely rare for this type of work to yield a counter-example and such efforts are generally regarded as mere displays of computing power, rather than meaningful contributions to formal mathematics.
Use of conjectures in conditional proofs
Sometimes a conjecture is called a hypothesis when it is used frequently and repeatedly as an assumption in proofs of other results. For example, the Riemann hypothesis is a conjecture from number theory that (amongst other things) makes predictions about the distribution of prime numbers. Few number theorists doubt that the Riemann hypothesis is true (it is said that Atle Selberg was once a sceptic, and J. E. Littlewood always was). In anticipation of its eventual proof, some have proceeded to develop further proofs which are contingent on the truth of this conjecture. These are called conditional proofs: the conjectures assumed appear in the hypotheses of the theorem, for the time being.
These "proofs", however, would fall apart if it turned out that the hypothesis was false, so there is considerable interest in verifying the truth or falsity of conjectures of this type.
Not every conjecture ends up being proven true or false. The continuum hypothesis, which tries to ascertain the relative cardinality of certain infinite sets, was eventually shown to be undecidable (or independent) from the generally accepted set of axioms of set theory. It is therefore possible to adopt this statement, or its negation, as a new axiom in a consistent manner (much as we can take Euclid's parallel postulate as either true or false).
In this case, if a proof uses this statement, researchers will often look for a new proof that doesn't require the hypothesis (in the same way that it is desirable that statements in Euclidean geometry be proved using only the axioms of neutral geometry, i.e. no parallel postulate.) The one major exception to this in practice is the axiom of choice—unless studying this axiom in particular, the majority of researchers do not usually worry whether a result requires the axiom of choice.
conjecture in Simple English: Conjecture
conjecture in Danish: Formodning (matematik)
conjecture in German: Vermutung
conjecture in Spanish: Conjetura
conjecture in French: Conjecture
conjecture in Scottish Gaelic: Baralachas
conjecture in Italian: Congettura
conjecture in Hebrew: השערה (מתמטיקה)
conjecture in Hungarian: Sejtés
conjecture in Dutch: Vermoeden
conjecture in Japanese: 予想
conjecture in Portuguese: Conjectura
conjecture in Russian: Гипотеза
conjecture in Serbian: Конјектура
conjecture in Finnish: Konjektuuri
conjecture in Swedish: Förmodan
conjecture in Thai: ข้อความคาดการณ์
conjecture in Turkish: Konjektür
conjecture in Chinese: 猜想
assume, assumption, axiom, believe, blind guess, bold conjecture, conceive, conclude, deem, estimate, expect, fancy, feel, gather, give a guess, glean, guess, guesswork, hazard a conjecture, hunch, hypothesis, imagine, infer, inference, judge, perhaps, postulate, postulation, postulatum, premise, presume, presumption, presupposal, presupposition, pretend, proposition, risk assuming, rough guess, set of postulates, shot, speculation, stab, supposal, suppose, supposing, supposition, surmise, suspect, take for granted, tentatively suggest, thesis, think, unverified supposition, venture a guess, wild guess, working hypothesis