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.
References
- 1 R. Crandall & C. Pomerance, Prime Numbers^{}: A Computational Perspective, Springer, NY, 2001: 1.2.4
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 |