On Guesses (-1900)

"[…] our reasonings about the wonderful and intricate operations of Nature are so full of uncertainty, that, as the wise-man truly observes, hardly do we guess aright at the things that are upon earth, and with labour do we find the things that are before us." (Stephen Hales, "Vegetable Staticks", 1727)

"[....] advances in knowledge are not commonly made without the previous exercise of some boldness and license in guessing. The discovery of new truths requires, undoubtedly, minds careful and fertile in examining what is suggested; but it requires, no less, such as are quick and fertile in suggesting." (William Whewell, "History of the Inductive Sciences, from the Earliest to the Present Time" Vol. 1, 1837)

"The Conceptions by which Facts are bound together, are suggested by the sagacity of discoverers. This sagacity cannot be taught. It commonly succeeds by guessing; and this success seems to consist in framing several tentative hypotheses and selecting the right one. But a supply of appropriate hypotheses cannot be constructed by rules, nor without inventive talent." (William Whewell, "History of the Inductive Sciences, from the Earliest to the Present Time" Vol. 2, 1837)

"It is frequently analogy which guides the experienced to what are called good guesses." (Francis W Newman, "Lectures on Logic", 1838)

 "[...] it is always safe and philosophic to distinguish, as much as is in our power, fact from theory; the experience of past ages is sufficient to show us the wisdom of such a course; and considering the constant tendency of the mind to rest on an assumption, and, when it answers every present purpose, to forget that it is an assumption, we ought to remember that it, in such cases, becomes a prejudice, and inevitably interferes, more or less, with a clear-sighted judgment. I cannot doubt but that he who, as a wise philosopher, has most power of penetrating the secrets of nature, and guessing by hypothesis at her mode of working, will also be most careful, for his own safe progress and that of others, to distinguish that knowledge which consists of assumption, by which I mean theory and hypothesis, from that which is the knowledge of facts and laws; never raising the former to the dignity or authority of the latter, nor confusing the latter more than is inevitable with the former." (Michael Faraday, "A Speculation Touching Electric Conduction and the Nature of Matter", Philosophical Magazine Vol. XXIV, 1844)

"Summing up, then, it would seem as if the mind of the great discoverer must combine contradictory attributes. He must be fertile in theories and hypotheses, and yet full of facts and precise results of experience. He must entertain the feeblest analogies, and the merest guesses at truth, and yet he must hold them as worthless till they are verified in experiment. When there are any grounds of probability he must hold tenaciously to an old opinion, and yet he must be prepared at any moment to relinquish it when a clearly contradictory fact is encountered." (William S Jevons, "The Principles of Science: A Treatise on Logic and Scientific Method", 1874)

"It would be an error to suppose that the great discoverer seizes at once upon the truth, or has any unerring method of divining it. In all probability the errors of the great mind exceed in number those of the less vigorous one. Fertility of imagination and abundance of guesses at truth are among the first requisites of discovery; but the erroneous guesses must be many times as numerous as those that prove well founded. The weakest analogies, the most whimsical notions, the most apparently absurd theories, may pass through the teeming brain, and no record remain of more than the hundredth part. […] The truest theories involve suppositions which are inconceivable, and no limit can really be placed to the freedom of hypotheses." (W Stanley Jevons, "The Principles of Science: A Treatise on Logic and Scientific Method", 1877)

"When a great theory has grown into existence, and the general assent of competent judges has converted a sublime conception from the state of a provisional hypothesis to the position of a strengthening doctrine, there is unusual interest in glancing over the progress of science and noting the actual steps by which the guess became theory, and the theory, doctrine." (Alexander Winchell, "World-Life or Comparative Geology", 1883)

'No, no: I never guess. It is a shocking habit, - destructive to the logical faculty." (Sir Arthur C Doyle, "The Sign of the Four", 1890)

"The history of civilization proves beyond doubt just how sterile the repeated attempts of metaphysics to guess at nature’s laws have been. Instead, there is every reason to believe that when the human intellect ignores reality and concentrates within, it can no longer explain the simplest inner workings of life’s machinery or of the world around us." (Santiago Ramón y Cajal, "Reglas y Consejos sobre Investigacíon Cientifica: Los tónicos de la voluntad", 1897)

On Guesses (1975-1999)

"[…] the distinction between rigorous thinking and more vague ‘imaginings’; even in mathematics itself, all is not a question of rigor, but rather, at the start, of reasoned intuition and imagination, and, also, repeated guessing. After all, most thinking is a synthesis or juxtaposition of advances along a line of syllogisms - perhaps in a continuous and persistent ‘forward'’ movement, with searching, so to speak ‘sideways’, in directions which are not necessarily present from the very beginning and which I describe as ‘sending out exploratory patrols’ and trying alternative routes." (Stanislaw M Ulam, "Adventures of a Mathematician", 1976)

"Mathematics does not grow through a monotonous increase of the number of indubitably established theorems, but through the incessant improvement of guesses by speculation and criticism." (Imre Lakatos, "Proofs and Refutations", 1976)

"That an educated guess about something would sound better if he called it a model?" (Robert L Bates, "Petulant Questions", Geotimes Vol. 22 (6), 1977)

"The truth is not in nature waiting to declare itself, and we cannot know a priori which observations are relevant and which are not; every discovery, every enlargement of the understanding begins as an imaginative preconception of what the truth might be. This imaginative preconception - a 'hypothesis' - arises by a process as easy or as difficult to understand as any other creative act of mind; it is a brainwave, an inspired guess, the product of a blaze of insight. It comes, anyway, from within and cannot be arrived at by the exercise of any known calculus of discovery." (Sir Peter B Medawar, "Advice to a Young Scientist", 1979)

"A mathematician’s work is mostly a tangle of guesswork, analogy, wishful thinking and frustration, and proof, far from being the core of discovery, is more often than not a way of making sure that our minds are not playing tricks." (Gian-Carlo Rota, 1981)

"We often hear that mathematics consists mainly in ‘proving theorems’. Is a writer’s job mainly that of ‘writing sentences’? A mathematician’s work is mostly a tangle of guesswork, analogy, wishful thinking and frustration, and proof, far from being the core of discovery, is more often than not a way of making sure that our minds are not playing tricks." (Gian-Carlo Rota, "Complicating Mathematics" in "Discrete Thoughts", 1981)

"Valid physical questions face us for which our physics is utterly inadequate. This can only be a sign that we stand at a great frontier of science, one that will form a cutting edge of inquiry for generations to come, with results we cannot guess." (Alan MacRobert, "Beyond the Big Bang", Sky & Telescope, Vol 65–66, 1983)

"Mathematics is not a deductive science - that’s a cliché. When you try to prove a theorem, you don’t just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork." (Paul R Halmos, "I Want to Be a Mathematician", 1985)

"Because mathematical proofs are long, they are also difficult to invent. One has to construct, without making any mistakes, long chains of assertions, and see what one is doing, see where one is going. To see means to be able to guess what is true and what is false, what is useful and what is not. To see means to have a feeling for which definitions one should introduce, and what the key assertions are that will allow one to develop a theory in a natural manner." (David Ruelle, "Chance and Chaos", 1991)

"Even distinguished philosophers of science [...] recognize the failure of philosophy to help understand the nature of science. They have not discovered a scientific method that provides a formula or prescriptions for how to make discoveries. But many famous scientists have given advice: try many things; do what makes your heart leap; think big; dare to explore where there is no light; challenge expectation; cherchez le paradox; be sloppy so that something unexpected happens, but not so sloppy that you can’t tell what happened; turn it on its head; never try to solve a problem until you can guess the answer; precision encourages the imagination; seek simplicity; seek beauty. [...] One could do no better than to try them all." (Lewis Wolpert, "The Unnatural Nature of Science", 1992)

"Scientists reach their conclusions for the damnedest of reasons: intuition, guesses, redirections after wild-goose chases, all combing with a dollop of rigorous observation and logical reasoning to be sure […] This messy and personal side of science should not be disparaged, or covered up, by scientists for two major reasons. First, scientists should proudly show this human face to display their kinship with all other modes of creative human thought […] Second, while biases and references often impede understanding, these mental idiosyncrasies may also serve as powerful, if quirky and personal, guides to solutions." (Stephen J Gould, "Dinosaur in a Haystack: Reflections in natural history", 1995)

On Guesses (1950-1974)

"[...] if there is one important result that comes out of our inquiry into the nature of the Universe it is this: when by patient inquiry we learn the answer to any problem, we always find, both as a whole and in detail, that the answer thus revealed is fi ner in concept and design than anything we could ever have arrived at by a random guess." (Sir Fred Hoyle, "The Nature of the Universe", 1950)

"The scientist who discovers a theory is usually guided to his discovery by guesses; he cannot name a method by means of which he found the theory and can only say that it appeared plausible to him, that he had the right hunch or that he saw intuitively which assumption would fit the facts." (Hans Reichenbach, "The Rise of Scientific Philosophy", 1951)

"Sometimes [the word theory] is used for a hypothesis, sometimes for a confirmed hypothesis; sometimes for a train of thought; sometimes for a wild guess at some fact, or for a reasoned claim of what some fact is - or even for a philosophical speculation." (John O Wisdom, "Foundations of Inference in Natural Sciences", 1952)

"On every scientist’s desk there is a drawer labeled UNKNOWN in which he fi les what are at the moment unsolved questions, lest through guess-work or impatient speculation he come upon incorrect answers that will do him more harm than good. Man’s worst fault is opening the drawer too soon. His task is not to discover final answers but to win the best partial answers that he can, from which others may move confidently against the unknown, to win better ones." (Homer W Smith, "From Fish to Philosopher", 1953)

"Anything new that we learn about the world involves plausible reasoning, which is the only kind of reasoning for which we care in everyday affairs.[...] Certainly, let us learn proving, but also let us learn guessing." (George Pólya, "Mathematics and Plausible Reasoning" Vol. 1, 1954)

"In an honest search for knowledge you quite often have to abide by ignorance for an indefinite period. Instead of filling a gap by guesswork, genuine science prefers to put up with it; and this, not so much from conscientious scruples above telling lies, as from the consideration that, however irksome the gap may be, its obliteration by a fake removes the urge to seek after a tenable answer." (Erwin Schrödinger, "Nature and the Greeks", 1954)

"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)

"You have to guess the mathematical theorem before you prove it: you have to guess the idea of the proof before you carry through the details. You have to combine observations and follow analogies: you have to try and try again. The result of the mathematician’s creative work is demonstrative reasoning, a proof; but the proof is discovered by plausible reasoning, by guessing" (George Polya, "Mathematics and plausible reasoning" Vol. 1, 1954)

"There never was a great scientist who did not make bold guesses, and there never was a bold man whose guesses were not sometimes wild." (Jacob Bronowski, "Science and Human Values", 1956)

"The shrewd guess, the fertile hypothesis, the courageous leap to a tentative conclusion - these are the most valuable coin of the thinker at work." (Jerome S Bruner, "The Process of Education", 1960)

"The way in which knowledge progresses, and especially our scientific knowledge, is by unjustified (and unjustifiable) anticipations, by guesses, by tentative solutions to our problems, by conjectures. These conjectures are controlled by criticism; that is, by attempted refutations, which include severely critical tests. They may survive these tests; but they can never be positively justified: they can neither be established as certainly true nor as 'probable' (in the sense of probability calculus). Criticism of our conjectures is of decisive importance: by bringing out our mistakes it makes us understand the difficulties of the problem which we are trying to solve. This is how we become better acquainted with our problems, and able to propose more mature solutions: the very refutation of a theory - that is, of any serious tentative solution to our problem - is always a step forward that takes us nearer to the truth. And this is how we can learn from our mistakes." (Karl R Popper, "Conjectures and Refutations: The Growth of Scientific Knowledge", 1963)

"We know many laws of nature and we hope and expect to discover more. Nobody can foresee the next such law that will be discovered. Nevertheless, there is a structure in laws of nature which we call the laws of invariance. This structure is so far-reaching in some cases that laws of nature were guessed on the basis of the postulate that they fit into the invariance structure." (Eugene P Wigner, "The Role of Invariance Principles in Natural Philosophy", 1963)

"Another thing I must point out is that you cannot prove a vague theory wrong. If the guess that you make is poorly expressed and rather vague, and the method that you use for figuring out the consequences is a little vague - you are not sure, and you say, 'I think everything's right because it's all due to so and so, and such and such do this and that more or less, and I can sort of explain how this works' […] then you see that this theory is good, because it cannot be proved wrong! Also if the process of computing the consequences is indefinite, then with a little skill any experimental results can be made to look like the expected consequences." (Richard P Feynman, "The Character of Physical Law", 1965)

"It is only through refined measurements and careful experimentation that we can have a wider vision. And then we see unexpected things: we see things that are far from what we would guess - far from what we could have imagined. Our imagination is stretched to the utmost, not, as in fiction, to imagine things which are not really there, but just to comprehend those things which are there." (Richard P Feynman, "The Character of Physical Law", 1965)

"Never make a calculation until you know the answer: Make an estimate before every calculation, try a simple physical argument (symmetry! invariance! conservation!) before every derivation, guess the answer to every puzzle. Courage: no one else needs to know what the guess is. Therefore make it quickly, by instinct. A right guess reinforces this instinct. A wrong guess brings the refreshment of surprise. In either case, life as a spacetime expert, however long, is more fun!" (Edwin F  Taylor & John A Wheeler, "Spacetime Physics", 1965)

"The method of guessing the equation seems to be a pretty effective way of guessing new laws. This shows again that mathematics is a deep way of expressing nature, and any attempt to express nature in philosophical principles, or in seat-of-the-pants mechanical feelings, is not an efficient way." (Richard Feynman, "The Character of Physical Law", 1965)

"What are the facts? Again and again and again - what are the facts? Shun wishful thinking, ignore divine revelation, forget what ‘the stars foretell,’ avoid opinion, care not what the neighbors think, never mind the unguessable ‘verdict of history', - what are the facts, and to how many decimal places? You pilot always into an unknown future; facts are your only clue. Get the facts!" (Robert A Heinlein, "Time Enough for Love", 1973)

On Guesses (1900-1949)

"It is best to prove things by actual experiment; then you know; whereas if you depend on guessing and supposing and conjecturing, you will never get educated." (Mark Twain [Samuel L Clemens], "Eve’s Diary", 1905)

"Some things you can’t find out; but you will never know you can’t by guessing and supposing: no, you have to be patient and go on experimenting until you find out that you can’t find out. And it is delightful to have it that way, it makes the world so interesting. If there wasn’t anything to find out, it would be dull. Even trying to find out and not finding out is just as interesting as trying to find out and finding out; and I don’t know but more so." (Mark Twain [Samuel L Clemens], "Eve’s Diary", 1905)

"In the degree in which life is uneasy and troubled, fancy is stirred to frame pictures of a contrary state of things. By reading the characteristic features of any man’s castles in the air you can make a shrewd guess as to his underlying desires which are frustrated." (John Dewey, "Reconstruction in Philosophy", 1920)

"[...] unless science is to degenerate into idle guessing, the test of value of any theory must be whether it expresses with as little redundancy as possible the facts which it intended to cover." (Sir Arthur S Eddington, "Space, Time and Gravitation: An Outline of the General Relativity", 1920)

"In regions where our ignorance is great, occasional guesses are permissible." (Sir Oliver Lodge, "On the Supposed Weight and Ultimate Fate of Radiation", Philosophical Magazine Vol. 41, 1921)

"This is called the inductive method. Hypothesis, my dear young friend, establishes itself by a cumulative process: or, to use popular language, if you make the same guess often enough it ceases to be a guess and becomes a Scientific Fact." Clive S Lewis, "The Pilgrim’s Regress: An Allegorical Apology for Christianity, Reason and Romanticism", 1933)

"I think that we shall have to get accustomed to the idea that we must not look upon science as a 'body of knowledge,' but rather as a system of hypotheses; that is to say, as a system of guesses or anticipations which in principle cannot be justified, but with which we work as long as they stand up to tests, and of which we are never justified in saying that we know they are 'true' or 'more or less certain' or even 'probable’." (Karl R Popper, "The Logic of Scientific Discovery", 1934)

"Heuristic reasoning is reasoning not regarded as final and strict but as provisional and plausible only, whose purpose is to discover the solution of the present problem. We are often obliged to use heuristic reasoning. We shall attain complete certainty when we shall have obtained the complete solution, but before obtaining certainty we must often be satisfied with a more or less plausible guess. We may need the provisional before we attain the final. We need heuristic reasoning when we construct a strict proof as we need scaffolding when we erect a building." (George Pólya, "How to solve it", 1945)