hypothesis
Hypothesis
2007-06-13 18:41:26
2007-08-23 15:57:35
Definition
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In mathematics, a {\em 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.
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\bibitem{rc} R. Crandall \& C. Pomerance, {\it Prime Numbers: A Computational Perspective}, Springer, NY, 2001: 1.2.4
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