"To say that observations of the past are certain, whereas predictions are merely probable, is not the ultimate answer to the question of induction; it is only a sort of intermediate answer, which is incomplete unless a theory of probability is developed that explains what we should mean by ‘probable’ and on what ground we can assert probabilities." (Hans Reichenbach, "The Rise of Scientific Philosophy", 1951)
"The result of the mathematician's creative work is demonstrative reasoning, a proof; but the proof is discovered by plausible reasoning, by guessing. If the learning of mathematics reflects to any degree the invention of mathematics, it must have a place for guessing, for plausible inference." (George Pólya, "Induction and Analogy in Mathematics", 1954)
"[…] the human reason discovers new relations between things not by deduction, but by that unpredictable blend of speculation and insight […] induction, which - like other forms of imagination - cannot be formalized." (Jacob Bronowski, "The Reach of Imagination", 1967)
"Innocent, unbiased observation is a myth." (Sir Peter B Medawar, "Induction and Intuition in Scientific Thought", 1969)
"Induction is aimed at revealing regularities and relationships that are hidden behind the outer aspects of the phenomena under study. Its most common tools are generalization, specialization, and analogy. Generalization arises from an attempt to grasp the significance of observed facts and is then verified by further particular cases." (Yakov Khurgin, "Did You Say Mathematics?", 1974)
"Induction is the process of eliciting general laws via observation and the correlation of particular instances. All sciences, including mathematics, make use of the induction method. Now, mathematical induction is applied only by mathematicians in the proof of theorems of a particular kind." (Yakov Khurgin, "Did You Say Mathematics?", 1974)
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