"A scientist, whether theorist or experimenter, puts forward statements, or systems of statements, and tests them step by step. In the field of the empirical sciences, more particularly, he constructs hypotheses, or systems of theories, and tests them against experience by observation and experiment." (Karl R Popper, "The Logic of Scientific Discovery", 1934)
"It is sometimes said of two expositions of one and the same mathematical proof that the one is simpler or more elegant than the other. This is a distinction which has little interest from the point of view of the theory of knowledge; it does not fall within the province of logic, but merely indicates a preference of an aesthetic or pragmatic character." (Karl R Popper, "The Logic of Scientific Discovery", 1934)
"Modern positivists are apt to see more clearly that science is not a system of concepts but rather a system of statements." (Karl R Popper, "The Logic of Scientific Discovery", 1934)
"Science is not a system of certain, or -established, statements; nor is it a system which steadily advances towards a state of finality […] And our guesses are guided by the unscientific, the metaphysical (though biologically explicable) faith in laws, in regularities which we can uncover - discover. Like Bacon, we might describe our own contemporary science - 'the method of reasoning which men now ordinarily apply to nature' - as consisting of 'anticipations, rash and premature' and as 'prejudices'." (Karl R Popper, "The Logic of Scientific Discovery", 1934)
"Science does not aim, primarily, at high probabilities. It aims at a high informative content, well backed by experience. But a hypothesis may be very probable simply because it tells us nothing, or very little." (Karl R Popper, "The Logic of Scientific Discovery", 1934)
"The most important application of the theory of probability is to what we may call 'chance-like' or 'random' events, or occurrences. These seem to be characterized by a peculiar kind of incalculability which makes one disposed to believe - after many unsuccessful attempts - that all known rational methods of prediction must fail in their case. We have, as it were, the feeling that not a scientist but only a prophet could predict them. And yet, it is just this incalculability that makes us conclude that the calculus of probability can be applied to these events." (Karl R Popper, "The Logic of Scientific Discovery", 1934)
"There is no such thing as a logical method of having new ideas or a logical reconstruction of this process […] very discovery contains an ‘irrational element’ or a ‘creative intuition’." (Karl R Popper, "The logic of scientific discovery", 1934)
"It is his intuition, his mystical insight into the nature of things, rather than his reasoning which makes a great scientist." (Karl R Popper, "The Open Society and Its Enemies", 1945)
“It is easy to obtain confirmations, or verifications, for nearly every theory - if we look for confirmations. Confirmations should count only if they are the result of risky predictions. […] A theory which is not refutable by any conceivable event is non-scientific. Irrefutability is not a virtue of a theory (as people often think) but a vice. Every genuine test of a theory is an attempt to falsify it, or refute it.” (Karl R Popper, “Conjectures and Refutations: The Growth of Scientific Knowledge”, 1963)
"Higher organisms are able to learn through trial and error how a certain problem should be solved. We may say that they too make testing movements - mental testings - and that to learn is essentially to tryout one testing movement after another until one is found that solves the problem. We might compare the animal's successful solution to an expectation and hence to a hypothesis or a theory. For the animal's behaviour shows us that it expects (perhaps unconsciously or dispositionally) that in a similar case the same testing movements will again solve the problem in question." (Karl R Popper, "The Logic and Evolution of Scientific Theory", [in "All Life is Problem Solving", 1999] 1972)
"The natural as well as the social sciences always start from problems, from the fact that something inspires amazement in us, as the Greek philosophers used to say. To solve these problems, the sciences use fundamentally the same method that common sense employs, the method of trial and error. To be more precise, it is the method of trying out solutions to our problem and then discarding the false ones as erroneous. This method assumes that we work with a large number of experimental solutions. One solution after another is put to the test and eliminated." (Karl R Popper, "The Logic and Evolution of Scientific Theory", [in "All Life is Problem Solving", 1999] 1972)
"Scientists, like all organisms, work with the method of trial and error. The trial is a solution to a problem. In the evolution of the plant or animal kingdom, error or, to be more precise, the correction of error usually means eradication of the organism; in science it usually means eradication of the hypothesis or theory." (Karl R Popper, "Epistemology and the Problem of Peace", [lecture in "All Life is Problem Solving", 1999] 1985)
"[...] we learn only through trial and error. Our trials, however, are always our hypotheses. They stem from us, not from the external world. All we learn from the external world is that some of our efforts are mistaken." (Karl R Popper, "The Epistemological Position of Evolutionary Epistemology", ["All Life is Problem Solving", 1999] 1987)
"Classical models tell us more than we at first can know." (Karl R Popper)
"A theory is just a mathematical model to describe the observations." (Karl R Popper)
"Science starts from problems, and not from observations." (Karl R Popper)
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