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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 ...
[7] Jeffrey Lagarias stated in 2010 that the Collatz conjecture "is an extraordinarily difficult problem, completely out of reach of present day mathematics". [8] However, though the Collatz conjecture itself remains open, efforts to solve the problem have led to new techniques and many partial results.
In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. [ 1 ] [ 2 ] [ 3 ] Some conjectures, such as the Riemann hypothesis or Fermat's conjecture (now a theorem , proven in 1995 by Andrew Wiles ), have shaped much of mathematical history as new areas of mathematics are developed in ...
In mathematics, the common fixed point problem is the conjecture that, for any two continuous functions that map the unit interval into itself and commute under functional composition, there must be a point that is a fixed point of both functions.
In mathematics, the standard conjectures about algebraic cycles are several conjectures describing the relationship of algebraic cycles and Weil cohomology theories.One of the original applications of these conjectures, envisaged by Alexander Grothendieck, was to prove that his construction of pure motives gave an abelian category that is semisimple.
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 conjecture, also referred to as Greenberg's invariants conjecture, firstly appeared in Greenberg's Princeton University thesis of 1971 and originally stated that, assuming that is a totally real number field and that / is the cyclotomic -extension, (/) = (/) =, i.e. the power of dividing the class number of is bounded as .
The Borsuk problem in geometry, for historical reasons [note 1] incorrectly called Borsuk's conjecture, is a question in discrete geometry. It is named after Karol Borsuk . Problem