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# 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

## Mathematics Subject Classification

00A05*no label found*

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## Comments

## hypothesis

> In mathematics, the term "hypothesis" is not used as often as in the sciences.

Then why are there 104 references to this entry?

Perhaps it would be more appropriate to give the definition of "hypothesis" that is often used in mathematics (i.e., a synonym is "assumption"). Or maybe this other definition of "hypothesis" should be a separate entry.