hypothesis

In mathematics, a hypothesis is an unproven statement which is supported by all the available data and by many weaker results. An unproven mathematical statement is usually called a “conjecture”, and while experimentation can sometimes produce millions of examples to support a conjecture, usually nothing short of a proof can convince experts in the field. But when a conjecture is supported not only but all the available data but also by numerous weaker results, it is upgraded in label to a hypothesis. The most famous conjecture in mathematics is the Riemann hypothesis, which despite many attempts at a proof, is supported by many related results. The convexity conjecture, on the other hand, is considered “incompatible” with the $n$-tuples conjecture and more results appear to support the latter, thus neither is upgraded to hypothesis.

Title	hypothesis
Canonical name	Hypothesis
Date of creation	2013-03-22 17:15:18
Last modified on	2013-03-22 17:15:18
Owner	PrimeFan (13766)
Last modified by	PrimeFan (13766)
Numerical id	6
Author	PrimeFan (13766)
Entry type	Definition
Classification	msc 00A05