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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 ...
The Hauptvermutung (German for main conjecture) of geometric topology is the conjecture that any two triangulations of a triangulable space have a common refinement, a single triangulation that is a subdivision of both of them. It was originally formulated in 1908, by Steinitz and Tietze. [14] This conjecture is now known to be false.
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.
The Erdős–Turán conjecture on additive bases of natural numbers. A conjecture on quickly growing integer sequences with rational reciprocal series. A conjecture with Norman Oler [2] on circle packing in an equilateral triangle with a number of circles one less than a triangular number. The minimum overlap problem to estimate the limit of M(n).
The full Taniyama–Shimura–Weil conjecture was finally proved by Diamond (1996), [10] Conrad et al. (1999), [11] and Breuil et al. (2001) [12] who, building on Wiles's work, incrementally chipped away at the remaining cases until the full result was proved. The now fully proved conjecture became known as the modularity theorem.
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.
Collins, Graham P., "Henri Poincaré, His Conjecture, Copacabana and Higher Dimensions," Scientific American, 9 June 2004. BBC in Our Time, "Discussion of the Poincaré conjecture," 2 November 2006, hosted by Melvyn Bragg. Poincare Contemplates Copernicus at MathPages
The Kepler conjecture postulated an optimal solution for packing spheres hundreds of years before it was proven correct by Thomas Callister Hales. Many other shapes have received attention, including ellipsoids, [ 2 ] Platonic and Archimedean solids [ 3 ] including tetrahedra , [ 4 ] [ 5 ] tripods (unions of cubes along three positive axis ...