(number theory) A famous open problem in mathematics, the hypothesis stating that, for every finite collection f_1,f_2,…,f_k of non-constant irreducible polynomials over the integers with positive leading coefficients, one of the following conditions holds: (i) there are infinitely many positive integers n such that all of f_1(n),f_2(n),…,f_k(n) are simultaneously prime numbers, or (ii) there is an integer m>1 (called a fixed divisor) which always divides the product f_1(n)f_2(n)⋯f_k(n).

An evolutionary hypothesis which proposes that organisms must constantly adapt, evolve, and proliferate not merely to gain reproductive advantage, but also simply to survive while pitted against other evolving organisms in an ever-changing environment.

The hypothesis that the evolution of life required an improbable combination of astrophysical and geological events and circumstances, and for this reason complex extraterrestrial life is a very improbable phenomenon and likely to be extremely rare.

(evolutionary theory) The hypothesis, in evolutionary biology, that a female animal's optimal choice among potential mates is a male whose genes will produce male offspring with the best chance of reproductive success, irrespective of the mate's capacity as a caregiver or any other direct benefits he can offer.