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Today in Science History - Quickie Quiz
Who said: “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”
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Unexpected Quotes (36 quotes)
Unexpectedly Quotes

After having a wash I proceeded to the bar where—believe it or not—there was a white-coated barman who was not only serving drinks but also cigarettes! I hastened forward and rather timidly said ‘Can I have some cigarettes?’
‘What’s your rank?’ was the slightly unexpected reply.
‘I am afraid I haven’t got one,’ I answered.
‘Nonsense—everyone who comes here has a rank.’
‘I’m sorry but I just don’t have one.’
‘Now that puts me in a spot,’ said the barman, ‘for orders about cigarettes in this camp are clear—twenty for officers and ten for other ranks. Tell me what exactly are you?’
Now I really wanted those cigarettes so I drew myself up and said ‘I am the Professor of Chemistry at Manchester University.’
The barman contemplated me for about thirty seconds and then said ‘I’ll give you five.’
Since that day I have had few illusions about the importance of professors!
In A Time to Remember: The Autobiography of a Chemist (1983), 59. This event took place after a visit to the Defence Research Establishment at Porton to observe a demonstration of a new chemical anti-tank weapon (1941).
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Although I was first drawn to math and science by the certainty they promised, today I find the unanswered questions and the unexpected connections at least as attractive.
In Warped Passages (2005), 65.
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Among people I have met, the few whom I would term “great” all share a kind of unquestioned, fierce dedication; an utter lack of doubt about the value of their activities (or at least an internal impulse that drives through any such angst); and above all, a capacity to work (or at least to be mentally alert for unexpected insights) at every available moment of every day of their lives.
From The Lying Stones of Marrakech: Penultimate Reflections in Natural History (2000), 76.
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Creating a new theory is not like destroying an old barn and erecting a skyscraper in its place. It is rather like climbing a mountain, gaining new and wider views, discovering unexpected connections between our starting point and its rich environment. But the point from which we started out still exists and can be seen, although it appears smaller and forms a tiny part of our broad view gained by the mastery of the obstacles on our adventurous way up.
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Each and every loss becomes an instance of ultimate tragedy–something that once was, but shall never be known to us. The hump of the giant deer–as a nonfossilizable item of soft anatomy–should have fallen into the maw of erased history. But our ancestors provided a wondrous rescue, and we should rejoice mightily. Every new item can instruct us; every unexpected object possesses beauty for its own sake; every rescue from history’s great shredding machine is–and I don’t know how else to say this–a holy act of salvation for a bit of totality.
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I learned this, at least, by my experiment: that if one advances confidently in the direction of his dreams, and endeavors to live the life which he has imagined, he will meet with a success unexpected in common hours.
In Walden: or, Life in the Woods (1854, 1893), 496.
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If the resident zoologist of Galaxy X had visited the earth 5 million years ago while making his inventory of inhabited planets in the universe, he would surely have corrected his earlier report that apes showed more promise than Old World monkeys and noted that monkeys had overcome an original disadvantage to gain domination among primates. (He will confirm this statement after his visit next year–but also add a footnote that one species from the ape bush has enjoyed an unusual and unexpected flowering, thus demanding closer monitoring.)
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In addition to this it [mathematics] provides its disciples with pleasures similar to painting and music. They admire the delicate harmony of the numbers and the forms; they marvel when a new discovery opens up to them an unexpected vista; and does the joy that they feel not have an aesthetic character even if the senses are not involved at all? … For this reason I do not hesitate to say that mathematics deserves to be cultivated for its own sake, and I mean the theories which cannot be applied to physics just as much as the others.
(1897) From the original French, “Et surtout, leurs adeptes y trouvent des jouissances analogues á celles que donnent la peinture et la musique. Ils admirent la délicate harmonie des nombres et des formes; ils s’émerveillent quand une découverte nouvelle leur ouvre une perspective inattendue; et la joie qu’ils éprouvent ainsi n’a-t-elle pas le caractère esthétique, bien que les sens n’y prennent aucune part?...C’est pourquoi je n’hésite pas à dire que les mathématiques méritent d’être cultivées pour elles-mêmes et que les théories qui ne peuvent être appliquées á la physique doivent l’être comme les autres.” Address read for him at the First International Congress of Mathematicians in Zurich: '‘Sur les rapports de l’analyse pure et de la physique', in Proceedings of that Congress 81-90, (1898). Also published as 'L’Analyse et la Physique', in La Valeur de la Science (1905), 137-151. As translated in Armand Borel, 'On the Place of Mathematics in Culture', in Armand Borel: Œvres: Collected Papers (1983), Vol. 4, 420-421.
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In many ways, unexpected results are what have most inspired my photography.
As quoted, without source, in Gus Kayafas and Estelle Jussim, Stopping Time: The Photographs of Harold Edgerton (1987), 9.
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It is not always possible to know what one has learned, or when the dawning will arrive. You will continue to shift, sift, to shake out and to double back. The synthesis that finally occurs can be in the most unexpected place and the most unexpected time. My charge ... is to be alert to the dawnings.
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It is the tension between creativity and skepticism that has produced the stunning and unexpected findings of science.
In Broca’s Brain: Reflections on the Romance of Science (1974, 1986), 73.
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Mathematicians attach great importance to the elegance of their methods and their results. This is not pure dilettantism. What is it indeed that gives us the feeling of elegance in a solution, in a demonstration? It is the harmony of the diverse parts, their symmetry, their happy balance; in a word it is all that introduces order, all that gives unity, that permits us to see clearly and to comprehend at once both the ensemble and the details. But this is exactly what yields great results, in fact the more we see this aggregate clearly and at a single glance, the better we perceive its analogies with other neighboring objects, consequently the more chances we have of divining the possible generalizations. Elegance may produce the feeling of the unforeseen by the unexpected meeting of objects we are not accustomed to bring together; there again it is fruitful, since it thus unveils for us kinships before unrecognized. It is fruitful even when it results only from the contrast between the simplicity of the means and the complexity of the problem set; it makes us then think of the reason for this contrast and very often makes us see that chance is not the reason; that it is to be found in some unexpected law. In a word, the feeling of mathematical elegance is only the satisfaction due to any adaptation of the solution to the needs of our mind, and it is because of this very adaptation that this solution can be for us an instrument. Consequently this esthetic satisfaction is bound up with the economy of thought.
In 'The Future of Mathematics', Monist, 20, 80. Translated from the French by George Bruce Halsted.
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Nature never “fails.” Nature complies with its own laws. Nature is the law. When Man lacks understanding of Nature’s laws and a Man-contrived structure buckles unexpectedly, it does not fail. It only demonstrates that Man did not understand Nature’s laws and behaviors. Nothing failed. Man’s knowledge or estimating was inadequate.
In "How Little I Know", in Saturday Review (12 Nov 1966), 152. Excerpted in Buckminster Fuller and Answar Dil, Humans in Universe (1983), 31.
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Nothing afflicted Marcellus so much as the death of Archimedes, who was then, as fate would have it, intent upon working out some problem by a diagram, and having fixed his mind alike and his eyes upon the subject of his speculation, he never noticed the incursion of the Romans, nor that the city was taken. In this transport of study and contemplation, a soldier, unexpectedly coming up to him, commanded him to follow to Marcellus, which he declined to do before he had worked out his problem to a demonstration; the soldier, enraged, drew his sword and ran him through. Others write, that a Roman soldier, running upon him with a drawn sword, offered to kill him; and that Archimedes, looking back, earnestly besought him to hold his hand a little while, that he might not leave what he was at work upon inconclusive and imperfect; but the soldier, nothing moved by his entreaty, instantly killed him. Others again relate, that as Archimedes was carrying to Marcellus mathematical instruments, dials, spheres, and angles, by which the magnitude of the sun might be measured to the sight, some soldiers seeing him, and thinking that he carried gold in a vessel, slew him. Certain it is, that his death was very afflicting to Marcellus; and that Marcellus ever after regarded him that killed him as a murderer; and that he sought for his kindred and honoured them with signal favours.
Plutarch
In John Dryden (trans.), Life of Marcellus.
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Old age is the most unexpected of all things that happen to a man.
Diary entry (8 May 1936), collected in Diary in Exile (1959).
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Originality finds the unexpected but inevitable next step.
City Aphorisms, Twelfth Selection (1993).
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Perhaps the strongest bond of sympathy between mathematics and poetry, however, is the endless invention of each. Dr. Johnson remarked, “The essence of poetry is invention; such invention as, by producing something unexpected, surprises and delights”; but he might have said the same of mathematics.
In 'The Poetry of Mathematics', The Mathematics Teacher (May 1926), 19, No. 5, 295.
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Science is a human activity, and the best way to understand it is to understand the individual human beings who practise it. Science is an art form and not a philosophical method. The great advances in science usually result from new tools rather than from new doctrines. ... Every time we introduce a new tool, it always leads to new and unexpected discoveries, because Nature's imagination is richer than ours.
Concluding remark from 'The Scientist As Rebel' American Mathemtical Monthly (1996), 103, 805. Reprinted in The Scientist as Rebel (2006), 17-18, identified as originally written for a lecture (1992), then published as an essay in the New York Review.
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The history of mathematics may be instructive as well as agreeable; it may not only remind us of what we have, but may also teach us to increase our store. Says De Morgan, “The early history of the mind of men with regards to mathematics leads us to point out our own errors; and in this respect it is well to pay attention to the history of mathematics.” It warns us against hasty conclusions; it points out the importance of a good notation upon the progress of the science; it discourages excessive specialization on the part of the investigator, by showing how apparently distinct branches have been found to possess unexpected connecting links; it saves the student from wasting time and energy upon problems which were, perhaps, solved long since; it discourages him from attacking an unsolved problem by the same method which has led other mathematicians to failure; it teaches that fortifications can be taken by other ways than by direct attack, that when repulsed from a direct assault it is well to reconnoiter and occupy the surrounding ground and to discover the secret paths by which the apparently unconquerable position can be taken.
In History of Mathematics (1897), 1-2.
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The hybridoma technology was a by-product of basic research. Its success in practical applications is to a large extent the result of unexpected and unpredictable properties of the method. It thus represents another clear-cut example of the enormous practical impact of an investment in research which might not have been considered commercially worthwhile, or of immediate medical relevance. It resulted from esoteric speculations, for curiosity’s sake, only motivated by a desire to understand nature.
From Nobel Lecture (8 Dec 1984), collected in Tore Frängsmyr and Jan Lindsten (eds.), Nobel Lectures in Physiology Or Medicine: 1981-1990 (1993), 267-268.
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The test of a theory is its ability to cope with all the relevant phenomena, not its a priori 'reasonableness'. The latter would have proved a poor guide in the development of science, which often makes progress by its encounter with the totally unexpected and initially extremely puzzling.
'From DAMTP [Department of Applied Mathematics and Theoretical Physics] to Westcott House', Cambridge Review (1981), 103, 61.
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The unexpected and the incredible belong in this world. Only then is life whole.
Carl Jung
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The Unexpected stalks a farm in big boots like a vagrant bent on havoc. Not every farmer is an inventor, but the good ones have the seeds of invention within them. Economy and efficiency move their relentless tinkering and yet the real motive often seems to be aesthetic. The mind that first designed a cutter bar is not far different from a mind that can take the intractable steel of an outsized sickle blade and make it hum in the end. The question is how to reduce the simplicity that constitutes a problem (“It's simple; it's broke.”) to the greater simplicity that constitutes a solution.
In Making Hay (2003), 33-34.
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There are almost unlimited possibilities for making discoveries and to uncover the unknown. It is in the nature of the discovery that it can not be planned or programmed. On the contrary it consists of surprises and appears many times in the most unexpected places.
Nobel Banquet speech (10 Dec 1982). In Wilhelm Odelberg (ed.), Les Prix Nobel. The Nobel Prizes 1982 (1983)
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There is not wholly unexpected surprise, but surprise nevertheless, that mathematics has direct application to the physical world about us.
In The American Mathematical Monthly (1949), 56, 19. Excerpted in John Ewing (ed,), A Century of Mathematics: Through the Eyes of the Monthly (1996), 186.
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This science, Geometry, is one of indispensable use and constant reference, for every student of the laws of nature; for the relations of space and number are the alphabet in which those laws are written. But besides the interest and importance of this kind which geometry possesses, it has a great and peculiar value for all who wish to understand the foundations of human knowledge, and the methods by which it is acquired. For the student of geometry acquires, with a degree of insight and clearness which the unmathematical reader can but feebly imagine, a conviction that there are necessary truths, many of them of a very complex and striking character; and that a few of the most simple and self-evident truths which it is possible for the mind of man to apprehend, may, by systematic deduction, lead to the most remote and unexpected results.
In The Philosophy of the Inductive Sciences Part 1, Bk. 2, chap. 4, sect. 8 (1868).
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To expect the unexpected shows a thoroughly modern intellect.
In Lily Splane, Quantum Consciousness (2004), 309

Unless you expect the unexpected you will never find it, for it is hard to discover and hard to attain.
As quoted in Peter Pešic, Labyrinth: A Search for the Hidden Meaning of Science (2001), 2.
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We knew that DNA was important. We knew it was an important molecule. And we knew that its shape was likely to be important. But we didn’t realise I think just how important it would be. Put in other words, we didn’t realise that the shape would give us a clue to the replication mechanism. And this turned out to be really an unexpected dividend from finding out what the shape was.
From Transcript of BBC TV program, The Prizewinners (1962).
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We may see how unexpectedly recondite parts of pure mathematics may bear upon physical science, by calling to mind the circumstance that Fresnel obtained one of the most curious confirmations of the theory (the laws of Circular Polarization by reflection) through an interpretation of an algebraical expression, which, according to the original conventional meaning of the symbols, involved an impossible quantity.
In History of Scientific Ideas, Bk. 2, chap. 14, sect. 8.
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What is peculiar and new to the [19th] century, differentiating it from all its predecessors, is its technology. It was not merely the introduction of some great isolated inventions. It is impossible not to feel that something more than that was involved. … The process of change was slow, unconscious, and unexpected. In the nineteeth century, the process became quick, conscious, and expected. … The whole change has arisen from the new scientific information. Science, conceived not so much in its principles as in its results, is an obvious storehouse of ideas for utilisation. … Also, it is a great mistake to think that the bare scientific idea is the required invention, so that it has only to be picked up and used. An intense period of imaginative design lies between. One element in the new method is just the discovery of how to set about bridging the gap between the scientific ideas, and the ultimate product. It is a process of disciplined attack upon one difficulty after another This discipline of knowledge applies beyond technology to pure science, and beyond science to general scholarship. It represents the change from amateurs to professionals. … But the full self-conscious realisation of the power of professionalism in knowledge in all its departments, and of the way to produce the professionals, and of the importance of knowledge to the advance of technology, and of the methods by which abstract knowledge can be connected with technology, and of the boundless possibilities of technological advance,—the realisation of all these things was first completely attained in the nineteeth century.
In Science and the Modern World (1925, 1997), 96.
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[A significant invention] must be startling, unexpected. It must come to a world that is not prepared for it.
Speaking at a shareholders' meeting (1975) as quoted by Victor K. McElheny, in Insisting On The Impossible: The Life Of Edwin Land (1999), 403-404.
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[In the case of research director, Willis R. Whitney, whose style was to give talented investigators as much freedom as possible, you may define “serendipity” as] the art of profiting from unexpected occurrences. When you do things in that way you get unexpected results. Then you do something else and you get unexpected results in another line, and you do that on a third line and then all of a sudden you see that one of these lines has something to do with the other. Then you make a discovery that you never could have made by going on a direct road.
Quoted in Guy Suits, 'Willis Rodney Whitney', National Academy of Sciences, Biographical Memoirs (1960), 355.
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[It] is not the nature of things for any one man to make a sudden, violent discovery; science goes step by step and every man depends on the work of his predecessors. When you hear of a sudden unexpected discovery—a bolt from the blue—you can always be sure that it has grown up by the influence of one man or another, and it is the mutual influence which makes the enormous possibility of scientific advance. Scientists are not dependent on the ideas of a single man, but on the combined wisdom of thousands of men, all thinking of the same problem and each doing his little bit to add to the great structure of knowledge which is gradually being erected.
Concluding remark in Lecture ii (1936) on 'Forty Years of Physics', revised and prepared for publication by J.A. Ratcliffe, collected in Needham and Pagel (eds.), Background to Modern Science: Ten Lectures at Cambridge Arranged by the History of Science Committee, (1938), 73-74. Note that the words as prepared for publication may not be verbatim as spoken in the original lecture by the then late Lord Rutherford.
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[Science] is not perfect. It can be misused. It is only a tool. But it is by far the best tool we have, self-correcting, ongoing, applicable to everything. It has two rules. First: there are no sacred truths; all assumptions must be critically examined; arguments from authority are worthless. Second: whatever is inconsistent with the facts must be discarded or revised. ... The obvious is sometimes false; the unexpected is sometimes true.
Cosmos (1985), 277.
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[The purpose of flight research] is to separate the real from the imagined problems and to make known the overlooked and the unexpected.
Description of the purpose of the X-15 program given in a meeting at the Langley Research Center (Oct 1956). Quoted in Michael H. Gorn, Expanding the Envelope (2001), 3.
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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