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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 ...
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 ...
This conjecture is known as Lemoine's conjecture and is also called Levy's conjecture. The Goldbach conjecture for practical numbers, a prime-like sequence of integers, was stated by Margenstern in 1984, [33] and proved by Melfi in 1996: [34] every even number is a sum of two practical numbers.
The Poincaré conjecture was a mathematical problem in the field of geometric topology. In terms of the vocabulary of that field, it says the following: Poincaré conjecture. Every three-dimensional topological manifold which is closed, connected, and has trivial fundamental group is homeomorphic to the three-dimensional sphere.
The abc conjecture (also known as the Oesterlé–Masser conjecture) is a conjecture in number theory that arose out of a discussion of Joseph Oesterlé and David Masser in 1985. [ 1 ] [ 2 ] It is stated in terms of three positive integers a , b {\displaystyle a,b} and c {\displaystyle c} (hence the name) that are relatively prime and satisfy a ...
The Collatz conjecture [a] is one of the most famous unsolved problems in mathematics. ... As an example, 9 780 657 631 has 1132 steps, as does 9 780 657 630.
The conjecture was formulated in 1993 by Andrew Beal, a banker and amateur mathematician, while investigating generalizations of Fermat's Last Theorem. [2] [3] Since 1997, Beal has offered a monetary prize for a peer-reviewed proof of this conjecture or a counterexample. [4] The value of the prize has increased several times and is currently $1 ...
The now fully proved conjecture became known as the modularity theorem. Several other theorems in number theory similar to Fermat's Last Theorem also follow from the same reasoning, using the modularity theorem. For example: no cube can be written as a sum of two coprime nth powers, n ≥ 3. (The case n = 3 was already known by Euler.)