A hypothesis (from Greek ὑπόθεσις) consists either of a suggested explanation for a phenomenon or of a reasoned proposal suggesting a possible correlation between multiple phenomena. The term derives from the Greek, hypotithenai meaning "to put under" or "to suppose." The scientific method requires that one can test a scientific hypothesis. Scientists generally base such hypotheses on previous observations or on extensions of scientific theories.
In early usage, scholars often referred to a clever idea or to a convenient mathematical approach that simplified cumbersome calculations as a hypothesis; when used this way, the word did not necessarily have any specific meaning. Cardinal Bellarmine gave a famous example of the older sense of the word in the warning issued to Galileo in the early 17th century: that he must not treat the motion of the Earth as a reality, but merely as a hypothesis.
In common usage in the 21st century, a hypothesis refers to a provisional idea whose merit needs evaluation. For proper evaluation, the framer of a hypothesis needs to define specifics in operational terms. A hypothesis requires more work by the researcher in order to either confirm or disprove it. In due course, a confirmed hypothesis may become part of a theory or occasionally may grow to become a theory itself. Normally, scientific hypotheses have the form of a mathematical model. Sometimes, but not always, one can also formulate them as existential statements, stating that some particular instance of the phenomenon under examination has some characteristic and causal explanations, which have the general form of universal statements, stating that every instance of the phenomenon has a particular characteristic.
Any useful hypothesis will enable predictions, by reasoning (including deductive reasoning). It might predict the outcome of an experiment in a laboratory setting or the observation of a phenomenon in nature. The prediction may also invoke statistics and only talk about probabilities. Karl Popper, following others, has argued that a hypothesis must be falsifiable, and that a proposition or theory cannot be called scientific if it does not admit the possibility of being shown false. To meet this additional criterion, it must at least in principle be possible to make an observation that would disprove the proposition as false, even if one has not actually (yet) made that observation. A falsifiable hypothesis can greatly simplify the process of testing to determine whether the hypothesis has instances in which it is false.
It is essential in framing a hypothesis that the investigator does not currently know the outcome of a potentially falsifying test or that it remains reasonably under continuing investigation. Only in such cases does the experiment, test or study potentially increase the probability of showing the truth of a hypothesis. If the researcher already knows the outcome, it counts as a "consequence" — and the researcher should have already considered this while formulating the hypothesis. If one cannot assess the predictions by observation or by experience, the hypothesis classes as not yet useful, and must wait for others who might come afterward to make possible the needed observations. For example, a new technology or theory might make the necessary experiments feasible.