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In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. [1] [2] [3] Some conjectures, ...
Conjecture Field Comments Eponym(s) Cites 1/3–2/3 conjecture: order theory: n/a: 70 abc conjecture: number theory: ⇔Granville–Langevin conjecture, Vojta's conjecture in dimension 1 ⇒Erdős–Woods conjecture, Fermat–Catalan conjecture Formulated by David Masser and Joseph Oesterlé. [1] Proof claimed in 2012 by Shinichi Mochizuki: n/a ...
A conjecture is a proposition that is unproven. Conjectures are related to hypotheses , which in science are empirically testable conjectures. In mathematics , a conjecture is an unproven proposition that appears correct.
A proposition that has not been proved but is believed to be true is known as a conjecture, or a hypothesis if frequently used as an assumption for further mathematical work. Proofs employ logic expressed in mathematical symbols, along with natural language that usually admits some ambiguity.
The first Hardy–Littlewood conjecture (named after G. H. Hardy and John Littlewood) is a generalization of the twin prime conjecture. It is concerned with the distribution of prime constellations , including twin primes, in analogy to the prime number theorem .
The conjecture is known to hold in special cases; for other cases, the bound on could be improved depending on the degree , although no absolute bound < is known that holds for all . In 1989, Tischler showed that the conjecture is true for the optimal bound K = d − 1 d {\displaystyle K={\frac {d-1}{d}}} if f {\displaystyle f} has only real ...
Bold hypothesis or bold conjecture is a concept in the philosophy of science of Karl Popper, first explained in his debut The Logic of Scientific Discovery (1935) and subsequently elaborated in writings such as Conjectures and Refutations: The Growth of Scientific Knowledge (1963).
Conjecture—as in conjectural emendation—is a critical reconstruction of the original reading of a clearly corrupt, contaminated, nonsensical or illegible textual fragment. Conjecture is one of the techniques of textual criticism used by philologists while commenting on or preparing editions of manuscripts (e.g. biblical or other ancient ...