Out of Context: On Curiosity (Definiions)

"Curiosity is only vanity. We usually only want to know something so that we can talk about it." (Blaise Pascal, "Pensées", 1669)

"Curiosity is, in great and generous minds, the first passion and the last." (Samuel Johnson, 1751)

"Curiosity is one of the permanent and certain characteristics of a vigorous intellect." (Samuel Johnson, 1751) 

"Curiosity is the most superficial of all the affections; it changes its object perpetually; it has an appetite which is very sharp, but very easily satisfied, and it has always an appearance of giddiness, restlessness and anxiety." (Edmund Burke, "A Philosophical Enquiry into the Origin of our Ideas of the Sublime and Beautiful", 1757)

"Curiosity is one of those insatiable passions that grow by gratification." (Sarah Scott, "A Description of Millenium Hall", 1762)

"Curiosity is lying in wait for every secret." (Ralph W Emerson, "Letters and Social Aims, Progress of Culture", 1884)

"Curiosity is the aspect of the universe seeking to realise itself, and the fruit of such activity is new reality, stimulating to new research." (Cassius J Keyser, "The Human Worth of Rigorous Thinking: Essays and Addresses", 1916)

"Curiosity and the urge to solve problems are the emotional hallmarks of our species [...]" (Carl E Sagan, "The Dragons of Eden", 1977)

"Curiosity, especially intellectual inquisitiveness, is what separates the truly alive from those who are merely going through the motions." (Tom Robbins, "Villa Incognito", 2003)

"Curiosity is the greatest source of ideas, retail revolutions, and insights." (Michael J Silverstein, "Rocket: Eight Lessons to Secure Infinite Growth", 2015)

"Curiosity is a delicate little plant which, aside from stimulation, stands mainly in need of freedom." (Albert Einstein)

"Curiosity is the one thing invincible in Nature." (Freya Stark)

"Curiosity is the wick in the candle of learning." (William A Ward)

On Curiosity (-1899)

"So blind is the curiosity by which mortals are possessed, that they often conduct their minds along unexplored routes, having no reason to hope for success, but merely being willing to risk the experiment of finding whether the truth they seek lies there." (René Descartes, "Le Discours de la Méthode", 1637)

"Curiosity is only vanity. We usually only want to know something so that we can talk about it." (Blaise Pascal, "Pensées", 1669)

"A strong curiosity has prompted men in all times to study nature; every useful art has some connexion with the science; and the unexhausted beauty and variety of things makes it ever agreeable, new and surprising." (Colin Maclaurin, "An Account of Sir Isaac Newton’s Philosophical Discoveries", 1748)

"In reality, all arguments from experience are founded on the similarity which we discover among natural objects, and by which we are induced to expect effects similar to those, which we have found to follow from such objects. And though none but a fool or madman will ever pretend to dispute the authority of experience, or to reject that great guide of human life; it may surely be allowed a philosopher to have so much curiosity at least, as to examine the principle of human nature, which gives this mighty authority to experience, and makes us draw advantage from that similarity, which nature has placed among different objects. From causes, which appear similar, we expect similar effects. This is the sum of all our experimental conclusions." (David Hume, "An Enquiry Concerning Human Understanding", 1748)

"In geometry, as in most sciences, it is very rare that an isolated proposition is of immediate utility. But the theories most powerful in practice are formed of propositions which curiosity alone brought to light, and which long remained useless without its being able to divine in what way they should one day cease to be so. In this sense it may be said, that in real science, no theory, no research, is in effect useless." (Voltaire, "A Philosophical Dictionary", 1764) 

"Look round the world: contemplate the whole and every part of it: You will find it to be nothing but one great machine, subdivided into an infinite number of lesser machines, which again admit of subdivisions, to a degree beyond what human senses and faculties can trace and explain. All these various machines, and even their most minute parts, are adjusted to each other with an accuracy, which ravishes into admiration all men, who have ever contemplated them. The curious adapting of means to ends, throughout all nature, resembles exactly, though it much exceeds, the productions of human contrivance; of human design, thought, wisdom, and intelligence." (David Hume, "Dialogues Concerning Natural Religion Dialogues Concerning Natural Religion", 1779)

"Every stage of science has its train of practical applications and systematic inferences, arising both from the demands of convenience and curiosity, and from the pleasure which, as we have already said, ingenious and active-minded men feel in exercising the process of deduction." (William Whewell, "The Philosophy of the Inductive Sciences Founded Upon Their History", 1840)

"The determination of the average man is not merely a matter of speculative curiosity; it may be of the most important service to the science of man and the social system. It ought necessarily to precede every other inquiry into social physics, since it is, as it were, the basis. The average man, indeed, is in a nation what the centre of gravity is in a body; it is by having that central point in view that we arrive at the apprehension of all the phenomena of equilibrium and motion." (Adolphe Quetelet, "A Treatise on Man and the Development of his Faculties", 1842)

On Curiosity (Unsourced)

 "Anytime new insight replaces an old assumption, or a fossilized perception is the spring. New understandings sprout, new tolerances appear, and new curiosity draws you to previously dark places. Just as the sun shines earlier and longer in the spring, changes that seemed impossible appear to be possible with each new insight into your own health." (Gary Zukav)

"Curiosity is the one thing invincible in Nature." (Freya Stark)

"Learning is by nature curiosity, prying into everything, reluctant to leave anything, material or immaterial, unexplained." (Philo of Alexandria)

"Mathematics originates in the mind of an individual, as it doubtless originated historically in the collective life of mankind, with the recognition of certain recurrent abstract features in common experience, and the development of processes of counting, measuring, and calculating, by which order can be brought into the manipulations of these features. It originated in this manner, indeed; but already at a very early stage it begins to transcend the practical sphere and its character undergoes a corresponding change. Intellectual curiosity progressively takes charge, despite the fact that practical considerations may for long continue to be the main source of interest and may indeed never cease to stimulate the creation of new concepts and new methods. As mathematics breaks from its early dependence on practical utility, its ‘immediate’ significance is at the same time lost and the goal is to discover what it is that makes 'emancipated' mathematics valid. (Geoffrey T Kneebone)

"Most students have to do some work to resuscitate their childlike curiosity. The best way to do that is to start asking questions again - lots of them." (Hal Gregersen)

"Satisfaction of one’s curiosity is one of the greatest sources of happiness in life." (Linus Pauling)

"The important thing is not to stop questioning. Curiosity has its own reason for existing. One cannot help but be in awe when he contemplates the mysteries of eternity, of life, of the marvelous structure of reality. It is enough if one tries merely to comprehend a little of this mystery every day. Never lose a holy curiosity." (Albert Einstein)

"The whole art of teaching is only the art of awakening the natural curiosity of the mind for the purpose of satisfying it afterwards." (Anatole France)

"Thinkers aren’t limited by what they know because they can always increase what they know. Rather they’re limited by what puzzles them because there’s no way to become curious about something that doesn’t puzzle you." (Daniel Quinn)

On Curiosity (2000-)

 "Learning emerges from discovery, not directives; reflection, not rules; possibilities, not prescriptions; diversity, not dogma; creativity and curiosity, not conformity and certainty; and meaning, not mandates." (Stephanie P Marshall, "The Power to Transform: Leadership That Brings Learning and Schooling to Life", 2006)

"The complexities of the universe are reflected in the complexities of our brains and in that natural, intimate and solitary activity that we call mind. In this process of matching up and representing, the inexhaustible human curiosity accepts the ancestral challenge of exploring the enormity of what we have yet to know. Chess, a world of fixed rules but with almost infinite borders, is an approachable model of that profound and endless human search." (Diego Rasskin-Gutman, "Chess Metaphors: Artificial Intelligence and the Human Mind", 2009)

"There is no way to guarantee in advance what pure mathematics will later find application. We can only let the process of curiosity and abstraction take place, let mathematicians obsessively take results to their logical extremes, leaving relevance far behind, and wait to see which topics turn out to be extremely useful. If not, when the challenges of the future arrive, we won’t have the right piece of seemingly pointless mathematics to hand." (Peter Rowlett, "The Unplanned Impact of Mathematics", Nature Vol. 475 (7355), 2011)

"What makes a mathematician is not technical skill or encyclopedic knowledge but insatiable curiosity and a desire for simple beauty. […] Part of becoming a mathematician is learning to ask such questions, to poke your stick around looking for new and exciting truths to uncover." (Paul Lockhart, "Measurement", 2012)

"Machines that replace physical labor have allowed us to focus more on what makes us human: our minds. Intelligent machines will continue that process, taking over the more menial aspects of cognition and elevating our mental lives toward creativity, curiosity, beauty, and joy. These are what truly make us human, not any particular activity or skill like swinging a hammer - or even playing chess." (Garry Kasparov, "Deep Thinking", 2017)

"If we don’t understand the statistics, we’re likely to be badly mistaken about the way the world is. It is all too easy to convince ourselves that whatever we’ve seen with our own eyes is the whole truth; it isn’t. Understanding causation is tough even with good statistics, but hopeless without them. [...] And yet, if we understand only the statistics, we understand little. We need to be curious about the world that we see, hear, touch, and smell, as well as the world we can examine through a spreadsheet." (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)

"Those of us in the business of communicating ideas need to go beyond the fact-check and the statistical smackdown. Facts are valuable things, and so is fact-checking. But if we really want people to understand complex issues, we need to engage their curiosity. If people are curious, they will learn." (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)

On Curiosity (1950-1999)

"The characteristic feature of our age results from the wedding of science and engineering. It is the working together of disciplined curiosity and purposeful ingenuity to create new materials, new forces, and new opportunities which powerfully affect our manner of living and ways of thinking." (Karl T Compton, "A Scientist Speaks: Excerpts from Addresses by Karl Taylor Compton - During the Years 1930-1949", 1955)

"No one will get very far or become a real mathematician without certain indispensable qualities; he must have hope, faith, and curiosity, and prime necessity is curiosity."(Louis J Mordell, "Reflections of a Mathematician", 1959)

"No one will get very far or become a real mathematician without certain indispensable qualities. He must have hope, faith, and curiosity, and prime necessity is curiosity." (Louis J Mordell, "Reflections of a Mathematician", 1959)

"Many teachers and textbook writers have never recognized the power of sheer intellectual curiosity as a motive for the highest type of work in mathematics, and as a consequence they have failed to organize and present the work in a manner designed to stimulate the student’s interest through a challenge to his curiosity." (Charles H Butler & F Lynwood Wren, "The Teaching of Secondary Mathematics" 5th Ed., 1970)

"Questions are the engines of intellect, the cerebral machines which convert energy to motion, and curiosity to controlled inquiry." (David H Fischer, "Historians’ Fallacies", 1970)

"Curiosity, a healthy curiosity, and a desire to learn is what leads the scientist from one problem to another. Once that feeling is lost and there is no excitement or pleasure in learning new facts, the scientist will no longer be able to discover anything new." (Yakov Khurgin, "Did You Say Mathematics?", 1974) 

"A branch of physics, once it becomes obsolete or unproductive, tends to be forever part of the past. It may be a historical curiosity, perhaps the source of some inspiration to a modern scientist, but dead physics is usually dead for good reason. Mathematics, by contrast, is full of channels and byways that seem to lead nowhere in one era and become major areas of study in another." (James Gleick, "Chaos: Making a New Science", 1987)

"Mathematics is a remarkable sprawling riot of imagination, ranging from pure intellectual curiosity to nuts-and-bolts utility; and it is all one thing." (Ian Stewart, "Game, Set, and Math: Enigmas and Conundrums", 1989)

"Some methods, such as those governing the design of experiments or the statistical treatment of data, can be written down and studied. But many methods are learned only through personal experience and interactions with other scientists. Some are even harder to describe or teach. Many of the intangible influences on scientific discovery - curiosity, intuition, creativity - largely defy rational analysis, yet they are often the tools that scientists bring to their work." (Committee on the Conduct of Science, "On Being a Scientist", 1989)

"The life of a mathematician is dominated by an insatiable curiosity, a desire bordering on passion to solve the problems he is studying." (Jean Dieudonné, "Mathematics - The Music of Reason", 1992) 

On Curiosity (1900-1949)

"Knowledge for the sake of knowledge, as the history of science proves, is an aim with an irresistible fascination for mankind, and which needs no defense. The mere fact that science does, to a great extent, gratify our intellectual curiosity, is a sufficient reason for its existence." (John W N Sullivan, "The Limitations of Science", 1915)

"Curiosity is the aspect of the universe seeking to realise itself, and the fruit of such activity is new reality, stimulating to new research." (Cassius J Keyser, "The Human Worth of Rigorous Thinking: Essays and Addresses", 1916)

"We have come to believe that a pupil in school should feel that he is living his own life naturally. with a minimum of restraint and without tasks that are unduly irksome; that he should find his way through arithmetic largely hoy his own spirit of curiosity; and that he should be directed in arithmetic as he would he directed in any other game, - not harshly driven, hardly even led, but proceeding with the feeling that he is being accompanied and that he is doing his share in finding the way." (David E Smith, "The Progress of Arithmetic", 1923)

"The curves treated by the calculus are normal and healthy; they possess no idiosyncrasies. But mathematicians would not be happy merely with simple, lusty configurations. Beyond these their curiosity extends to psychopathic patients, each of whom has an individual case history resembling no other; these are the pathological curves in mathematics." (Edward Kasner & James R Newman, "Mathematics and the Imagination", 1940)

"Research is formalized curiosity. It is poking and prying with a purpose. It is a seeking that he who wishes may know the cosmic secrets of the world and they that dwell therein." (Zora Neale Hurston, "Dust Tracks on a Road", 1942)

"A great discovery solves a great problem but there is a grain of discovery in the solution of any problem. Your problem may be modest; but if it challenges your curiosity and brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery." (George Polya, "How to solve it", 1944) 

"Scientific progress on a broad front results from free play of free intellects, working on subjects of their own choice, in the manner dictated by their curiosity for the exploration of the unknown." (Vannevar Bush, "Science: The Endless Frontier", 1945)

"When a student makes really silly blunders or is exasperatingly slow, the trouble is almost always the same; he has no desire at all to solve the problem, even no desire to understand it properly, and so he has not understood it. Therefore, a teacher wishing seriously to help the student should. first of all, stir up his curiosity, give him some desire to solve the problem. The teacher should also allow some time to the student to make up his mind to settle down to his task. Teaching to solve problems is education of the will. Solving problems which are not too easy for him, the student learns to persevere through success, to appreciate small advance, to wait for the essential idea, to concentrate with all his might when it appears, If the student had no opportunity in school to familiarize himself with the varying emotions of the struggle for the solution his mathematical education failed in the most vital point." (George Pólya, "How to Solve It", 1945) 

"Science cannot be stopped. Men will gather knowledge no matter what the consequences. Science will go on whether we are pessimistic or optimistic, as I am. More interesting discoveries than we can imagine will be made, and I am awaiting them, full of curiosity and enthusiasm." (Linus Pauling, "Chemical Achievement and Hope for the Future", 1947)

On Learning: Aphorisms

"For the things we have to learn before we can do, we learn by doing." (Aristotle, "Nicomachean Ethics", Book II, 349 BC)

"A little learning is a dangerous thing." (Alexander Pope)

"A few moments to learn, a lifetime to master." (proverb)

"Poor is the pupil who does not surpass his master." (Leonardo da Vinci)

"Much learning does not teach understanding." (Heraclitus, "Fragments", 6th c. BC)

"The learning of many things does not teach intelligence […]." (Pythagoras of Samos)

"Much learning does not teach a man to have intelligence." (Heraclitus of Ephesus)

"Curiosity is the wick in the candle of learning." (William A Ward)

"Learning is a treasure which accompanies its owner everywhere." (proverb)

"Learning is its own exceeding great reward." (William Hazlitt, "The Plain Speaker", 1826)

"What we learn with pleasure we never forget." (Louis Mercier)

"Whatever is good to know is difficult to learn." (Greek proverb)

"We learn to walk by stumbling." (Bulgarian proverb)

"He who is afraid to ask is ashamed of learning." (Danish proverb)

"It takes ten pounds of common sense to carry one pound of learning." (Persian proverb)

"He who has imagination without learning has wings but no feet." (Joseph Joubert)

"Learning is not attained by chance. It must be sought for with ardor and attended to with diligence." (Abigail Adams)

"Learning hath gained most by those books by which the printers have lost." (Thomas Fuller)

"[…] education is not something which the teacher does, but that it is a natural process which develops spontaneously in the human being." (Maria Montessori)

On Problem Solving VII: Mathematicians I

"An expert problem solver must be endowed with two incompatible qualities, a restless imagination and a patient pertinacity." (Howard W Eves) 

"Finding the right answer is important, of course. But more important is developing the ability to see that problems have multiple solutions, that getting from X to Y demands basic skills and mental agility, imagination, persistence, patience." (Mary H Futrell)

"I knew nothing, except how to think, how to grapple with a problem and then go on grappling with it until you had solved it." (Sir Barnes Wallis) 

"It’s not that I’m so smart, it’s just that I stay with problems longer." (Albert Einstein)

"Man is not born to solve the problems of the universe, but to find out where the problems begin, and then to take his stand within the limits of the intelligible." (Johann Wolfgang von Goethe) 

"Solving problems is a practical skill like, let us say, swimming. We acquire any practical skill by imitation and practice." (George Polya) 

"The life of a mathematician is dominated by an insatiable curiosity, a desire bordering on passion to solve the problems he is studying." (Jean Dieudonne)

"The measure of our intellectual capacity is the capacity to feel less and less satisfied with our answers to better and better problems." (Charles W Churchman) 

"The real raison d’etre for the mathematician’s existence is simply to solve problems. So what mathematics really consists of is problems and solutions." (John Casti) 

"When I am working on a problem I never think about beauty. I only think about how to solve the problem. But when I have finished, if the solution is not beautiful, I know it is wrong." (Buckminster Fuller) 

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