🆃Nikola Tesla - Collected Quotes

"It is a mere question of time when men will succeed in attaching their machinery to the very wheelwork of nature." (Nikola Tesla, "The Inventions, Researches and Writings of Nikola Tesla", 1894)

"There is no subject more captivating, more worthy of study, than nature. To understand this great mechanism, to discover the forces which are active, and the laws which govern them, is the highest aim of the intellect of man." (Nikola Tesla, "The Inventions, Researches and Writings of Nikola Tesla", 1894)

"Throughout the infinite, the forces are in a perfect balance, and hence the energy of a single thought may determine the motion of a universe." (Nikola Tesla, "The Inventions, Researches and Writings of Nikola Tesla", 1894)

"To know each other we must reach beyond the sphere of our sense perceptions." (Nikola Tesla, "Electrical World and Engineer", 1905)

"But instinct is something which transcends knowledge. We have, undoubtedly, certain finer fibers that enable us to perceive truths when logical deduction, or any other willful effort of the brain, is futile." (Nikola Tesla, "My Inventions", 1919)

"Man, like the universe, is a machine. Nothing enters our minds or determines our actions which is not directly or indirectly a response to stimuli beating upon our sense organs from without." (Nikola Tesla, "My Inventions", 1919) 

"The progressive development of man is vitally dependent on invention. It is the most important product of his creative brain. Its ultimate purpose is the complete mastery of mind over the material world, the harnessing of the forces of nature to human needs. This is the difficult task of the inventor who is often misunderstood and unrewarded. But he finds ample compensation in the pleasing exercises of his powers and in the knowledge of being one of that exceptionally privileged class without whom the race would have long ago perished in the bitter struggle against pitiless elements. Speaking for myself, I have already had more than my full measure of this exquisite enjoyment; so much, that for many years my life was little short of continuous rapture." (Nikola Tesla, "My Inventions", 1919) 

"There is scarcely a subject that cannot be mathematically treated and the effects calculated or the results determined beforehand from the available theoretical and practical data." (Nikola Tesla, "My Inventions", 1919)

"We are automata entirely controlled by the forces of the medium being tossed about like corks on the surface of the water, but mistaking the resultant of the impulses from the outside for free will. The movements and other actions we perform are always life preservative and tho seemingly quite independent from one another, we are connected by invisible links." (Nikola Tesla, "My Inventions", 1919)

"The scientific man does not aim at an immediate result. He does not expect that his advanced ideas will be readily taken up. His work is like that of the planter - for the future. His duty is to lay the foundation for those who are to come, and point the way. He lives and labors and hopes." (Nikola Tesla, "Radio Power Will Revolutionize the World", Modern Mechanics and Inventions, 1934)

"Today's scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality." (Nikola Tesla, "Radio Power Will Revolutionize the World", Modern Mechanics and Inventions, 1934)

"Einstein's relativity work is a magnificent mathematical garb which fascinates, dazzles and makes people blind to the underlying errors. The theory is like a beggar clothed in purple whom ignorant people take for a king [...] its exponents are brilliant men but they are metaphysicists rather than scientists." (Nikola Tesla, New York Times, 1935)

“Life is and will ever remain an equation incapable of solution, but it contains certain known factors.” (Nikola Tesla, "A Machine to End War”, 1937)

"Every living being is an engine geared to the wheelwork of the universe. Though seemingly affected only by its immediate surrounding, the sphere of external influence extends to infinite distance." (Nikola Tesla)

"Misunderstandings are always caused by the inability of appreciating one another's point of view. This again is due to the ignorance of those concerned, not so much in their own, as in their mutual fields." (Nikola Tesla)

"Of all the endless variety of phenomena which nature presents to our senses, there is none that fills our minds with greater wonder than that inconceivably complex movement which, in its entirety, we designate as human life; Its mysterious origin is veiled in the forever impenetrable mist of the past, its character is rendered incomprehensible by its infinite intricacy, and its destination is hidden in the unfathomable depths of the future." (Nikola Tesla)

"Science is opposed to theological dogmas because science is founded on fact. To me, the universe is simply a great machine which never came into being and never will end. The human being is no exception to the natural order. Man, like the universe, is a machine." (Nikola Tesla)

"The practical success of an idea, irrespective of its inherent merit, is dependent on the attitude of the contemporaries. If timely it is quickly adopted; if not, it is apt to fare like a sprout lured out of the ground by warm sunshine, only to be injured and retarded in its growth by the succeeding frost." (Nikola Tesla)

"Today's scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality." (Nikola Tesla)

"What one man calls God, another calls the laws of physics." (Nikola Tesla)

🚀On Invention (-1799)

"[...] because the origin of arts and sciences is to be considered according to the present revolution of the universe, we must affirm, in conformity with the most general tradition, that geometry was first invented by the Egyptians, deriving its origin from the mensuration of their fields: since this, indeed, was necessary to them, on account of the inundation of the Nile washing away the boundaries of land belonging to each. Nor ought It to seem wonderful, that the invention of this as well as of other sciences, should receive its commencement from convenience and opportunity. Since whatever is carried in the circle of generation proceeds from the imperfect to the perfect." (Proclus Lycaeus, cca 5th century)

"Reflexion is careful and laborious thought, and watchful attention directed to the agreeable effect of one's plan. Invention, on the other hand, is the solving of intricate problems and the discovery of new principles by means of brilliancy and versatility." (Marcus Vitruvius Pollio, "De architectura" ["On Architecture], cca. 15BC) 

"To invent is to discover that we know not, and not to recover or resummon that which we already know." (Francis Bacon, "Advancement of Learning", 1605)

"Moreover, the works already known are due to chance and experiment rather than to sciences; for the sciences we now possess are merely systems for the nice ordering and setting forth of things already invented; not methods of invention or directions for new works." (Sir Francis Bacon, "Novum Organum", 1620)

"To apply oneself to great inventions, starting from the smallest beginnings, is no task for ordinary minds; to divine that wonderful arts lie hid behind trivial and childish things is a conception for superhuman talents." (Galileo Galilei, "Dialogue Concerning the Two Chief World Systems", 1632) 

"Invention, strictly speaking, is little more than a new combination of those images which have been previously gathered and deposited in the memory: nothing can come of nothing." (Joshua Reynolds, "Discourses on Art", 1769) 

"Nothing, in truth, has such a tendency to weaken not only the powers of invention, but the intellectual powers in general, as a habit of extensive and various reading without reflection." (Dugald Stewart, "Elements of the Philosophy of the Human Mind", 1792) 

🚀On Invention (2000-2019)

"The passion and beauty and joy of science is that we humans have invented a process to understand the universe in a way that is true for everyone. We are finding universal truths." (Bill Nye, 2000) 

"The best reaction to a paradox is to invent a genuinely new and deep idea. (Ian Hacking, "An Introduction to Probability and Inductive Logic", 2001)

"The brain highlights what it imagines as patterns; it disregards contradictory information. Human nature yearns to see order and hierarchy in the world. It will invent it where it cannot find it." (Benoît Mandelbrot, "The (Mis)Behavior of Markets", 2004)

"Metaphorizing is a manner of thinking, not a property of thinking. It is a capacity of thought, not its quality. It represents a mental operation by which a previously existing entity is described in the characteristics of another one on the basis of some similarity or by reasoning. When we say that something is (like) something else, we have already performed a mental operation. This operation includes elements such as comparison, paralleling and shaping of the new image by ignoring its less satisfactory traits in order that this image obtains an aesthetic value. By this process, for an instant we invent a device, which serves as the pole vault for the comparison’s jump. Once the jump is made the pole vault is removed. This device could be a lightning-speed logical syllogism, or a momentary created term, which successfully merges the traits of the compared objects." (Ivan Mladenov, “Conceptualizing Metaphors: On Charles Peirce’s marginalia”, 2006)

"The strength of a theory is not what it allows, but what it prohibits; if you can invent an equally persuasive explanation for any outcome, you have zero knowledge." (Eliezer Yudkowsky, "An Alien God", 2007)

"We didn't invent nature. Nature invented us. Nature bats last, the saying goes, but, even more importantly, it's her playing field. We would be wise to learn the ground rules and play by them." (Kenny Ausubel, [speech at Bioneers Conference, 2003)

"Scientists often invent words to fill the holes in their understanding. These words are meant as conveniences until real understanding can be found. […] Words such as dimension and field and infinity […] are not descriptions of reality, yet we accept them as such because everyone is sure someone else knows what the words mean." (Scott Adams, "God's Debris: A Thought Experiment", 2004)

"The urge to discover, to invent, to know the unknown, seems so deeply human that we cannot imagine our history without it." (Alan Lightman, "The Discoveries: Great Breakthroughs in 20th-Century Science, Including the Original Papers", 2009)

🚀On Invention (1975-1999)

"Mathematicians do not agree among themselves whether mathematics is invented or discovered, whether such a thing as mathematical reality exists or is illusory." (Albert L Hammond, "Mathematics - Our invisible culture", 1978)

"For the great majority of mathematicians, mathematics is […] a whole world of invention and discovery - an art. The construction of a new theorem, the intuition of some new principle, or the creation of a new branch of mathematics is the triumph of the creative imagination of the mathematician, which can be compared to that of a poet, the painter and the sculptor." (George F J Temple, "100 Years of Mathematics: a Personal Viewpoint", 1981)

"The purpose of scientific enquiry is not to compile an inventory of factual information, nor to build up a totalitarian world picture of Natural Laws in which every event that is not compulsory is forbidden. We should think of it rather as a logically articulated structure of justifiable beliefs about nature. It begins as a story about a Possible World - a story which we invent and criticize and modify as we go along, so that it winds by being, as nearly as we can make it, a story about real life." (Sir Peter B Medawar, "Pluto’s Republic: Incorporating the Art of the Soluble and Induction Intuition in Scientific Thought", 1982)

"[…] a mathematician's ultimate concern is that his or her inventions be logical, not realistic. This is not to say, however, that mathematical inventions do not correspond to real things. They do, in most, and possibly all, cases. The coincidence between mathematical ideas and natural reality is so extensive and well documented, in fact, that it requires an explanation. Keep in mind that the coincidence is not the outcome of mathematicians trying to be realistic - quite to the contrary, their ideas are often very abstract and do not initially appear to have any correspondence to the real world. Typically, however, mathematical ideas are eventually successfully applied to describe real phenomena […]"(Michael Guillen, "Bridges to Infinity: The Human Side of Mathematics", 1983)

"I shall here present the view that numbers, even whole numbers, are words, parts of speech, and that mathematics is their grammar. Numbers were therefore invented by people in the same sense that language, both written and spoken, was invented. Grammar is also an invention. Words and numbers have no existence separate from the people who use them. Knowledge of mathematics is transmitted from one generation to another, and it changes in the same slow way that language changes. Continuity is provided by the process of oral or written transmission." (Carl Eckart, "Our Modern Idol: Mathematical Science", 1984) 

"Theoretical scientists, inching away from the safe and known, skirting the point of no return, confront nature with a free invention of the intellect. They strip the discovery down and wire it into place in the form of mathematical models or other abstractions that define the perceived relation exactly. The now-naked idea is scrutinized with as much coldness and outward lack of pity as the naturally warm human heart can muster. They try to put it to use, devising experiments or field observations to test its claims. By the rules of scientific procedure it is then either discarded or temporarily sustained. Either way, the central theory encompassing it grows. If the abstractions survive they generate new knowledge from which further exploratory trips of the mind can be planned. Through the repeated alternation between flights of the imagination and the accretion of hard data, a mutual agreement on the workings of the world is written, in the form of natural law." (Edward O Wilson, "Biophilia", 1984)

"One cannot ‘invent’ the structure of an object. The most we can do is to patiently bring it to the light of day, with humility - in making it known, it is ‘discovered’. If there is some sort of inventiveness in this work, and if it happens that we find ourselves the maker or indefatigable builder, we are in no sense ‘making’ or ’building’ these ‘structures’. They have not waited for us to find them in order to exist, exactly as they are! But it is in order to express, as faithfully as possible, the things that we have been detecting or discovering, the reticent structure which we are trying to grasp at, perhaps with a language no better than babbling. Thereby are we constantly driven to ‘invent’ the language most appropriate to express, with increasing refinement, the intimate structure of the mathematical object, and to ‘construct’ with the help of this language, bit by bit, those ‘theories’ which claim to give a fair account of what has been apprehended and seen. There is a continual coming and going, uninterrupted, between the apprehension of things, and the means of expressing them by a language in constant state improvement [...]. The sole thing that constitutes the true inventiveness and imagination of the researcher is the quality of his attention as he listens to the voices of things." (Alexander Grothendieck, "Récoltes et semailles –Rélexions et témoignage sur un passé de mathématicien", 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)

"There is one qualitative aspect of reality that sticks out from all others in both profundity and mystery. It is the consistent success of mathematics as a description of the workings of reality and the ability of the human mind to discover and invent mathematical truths." (John D Barrow, "Theories of Everything", 1991)

"Ultimately, discovery and invention are both problems of classification, and classification is fundamentally a problem of finding sameness. When we classify, we seek to group things that have a common structure or exhibit a common behavior." (Grady Booch, "Object-oriented design: With Applications", 1991)

"As a result, surprisingly enough, scientific advance rarely comes solely through the accumulation of new facts. It comes most often through the construction of new theoretical frameworks. [..] To understand scientific development, it is not enough merely to chronicle new discoveries and inventions. We must also trace the succession of worldviews" (Nancy R Pearcey & Charles B Thaxton, "The Soul of Science: Christian Faith and Natural Philosophy", 1994)

"Mathematicians tells us that it is easy to invent mathematical theorems which are true, but that it is hard to find interesting ones. In analyzing music or writing its history, we meet the same difficulty, and it is compounded by another." (Charles Rosen, "The Frontiers of Meaning: Three Informal Lectures on Music", 1994)

"The controversy between those who think mathematics is discovered and those who think it is invented may run and run, like many perennial problems of philosophy. Controversies such as those between idealists and realists, and between dogmatists and sceptics, have already lasted more than two and a half thousand years. I do not expect to be able to convert those committed to the discovery view of mathematics to the inventionist view." (Paul Ernst, "Is Mathematics Discovered or Invented", 1996)

🚀On Invention (1950-1974)

"The construction of hypotheses is a creative act of inspiration, intuition, invention; its essence is the vision of something new in familiar material. The process must be discussed in psychological, not logical, categories; studied in autobiographies and biographies, not treatises on scientific method; and promoted by maxim and example, not syllogism or theorem." (Milton Friedman, "Essays in Positive Economics", 1953) 

"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)

"Invention is not the product of logical thought, even though the final product is tied to a logical structure." (Albert Einstein, "Autobiographische Skizze", 1955) 

"No part of the aim of normal science is to call forth new sorts of phenomena; indeed those that will not fit the box are often not seen at all. Nor do scientists normally aim to invent new theories, and they are often intolerant of those invented by others." (Thomas Kuhn, "The Structure of Scientific Revolutions", 1962) 

"We must now ask how changes of this sort can come about, considering first discoveries, or novelties of fact, and then inventions, or novelties of theory. That distinction between discovery and invention or between fact and theory will, however, immediately prove to be exceedingly artificial." (Thomas Kuhn, "The Structure of Scientific Revolutions", 1962) 

"The mathematicians and physics men Have their mythology; they work alongside the truth, Never touching it; their equations are false But the things work. Or, when gross error appears, They invent new ones; they drop the theory of waves In universal ether and imagine curved space." (Robinson Jeffers," The Beginning and the End and Other Poems, The Great Wound", 1963) 

"When the problems in physics become difficult we may often look to the mathematician who may already have studied such things and have prepared a line of reasoning for us to follow. On the other hand they may not have, in which case we have to invent our own line of reasoning, which we then pass back to the mathematician." (Richard Feynman,"The Character of Physical Law" , 1965) 

"The essential functions of the mind consist in understanding and in inventing, in other words, in building up structures by structuring reality." (Jean Piaget, 1971)

"All perceiving is also thinking, all reasoning is also intuition, all observation is also invention." (Rudolf Arnheim, "Entropy and Art: An Essay on Disorder and Order", 1974)

🚀On Invention (1900-1949)

“With the extension of mathematical knowledge will it not finally become impossible for the single investigator to embrace all departments of this knowledge? In answer let me point out how thoroughly it is ingrained in mathematical science that every real advance goes hand in hand with the invention of sharper tools and simpler methods which at the same time assist in understanding earlier theories and to cast aside some more complicated developments. It is therefore possible for the individual investigator, when he makes these sharper tools and simpler methods his own, to find his way more easily in the various branches of mathematics than is possible in any other science.” (David Hilbert, “Mathematical Problems”, Bulletin of the American Mathematical Society Vol. 8, 1902)

"The chief end of mathematical instruction is to develop certain powers of the mind, and among these the intuition is not the least precious. By it the mathematical world comes in contact with the real world, and even if pure mathematics could do without it, it would always be necessary to turn to it to bridge the gulf between symbol and reality. The practician will always need it, and for one mathematician there are a hundred practicians. However, for the mathematician himself the power is necessary, for while we demonstrate by logic, we create by intuition; and we have more to do than to criticize others’ theorems, we must invent new ones, this art, intuition teaches us." (Henri Poincaré, "The Value of Science", 1905)

"It is the intuition of pure number, that of pure logical forms, which illumines and directs those we have called analysts. This it is which enables them not alone to demonstrate, but also to invent." (Henri Poincaré, "The Value of Science", 1905)

"Unadulterated, unsweetened observations are what the real nature-lover craves. No man can invent incidents and traits as interesting as the reality." (John Burroughs, "Ways of Nature", 1905)

"Reduced to their most pregnant difference, empiricism means the habit of explaining wholes by parts, and rationalism means the habit of explaining parts by wholes. Rationalism thus preserves affinities with monism, since wholeness goes with union, while empiricism inclines to pluralistic views. No philosophy can ever be anything but a summary sketch, a picture of the world in abridgment, a foreshortened bird's-eye view of the perspective of events. And the first thing to notice is this, that the only material we have at our disposal for making a picture of the whole world is supplied by the various portions of that world of which we have already had experience. We can invent no new forms of conception, applicable to the whole exclusively, and not suggested originally by the parts." (William James, "A Pluralistic Universe", 1908)

"The progressive development of man is vitally dependent on invention. It is the most important product of his creative brain. Its ultimate purpose is the complete mastery of mind over the material world, the harnessing of the forces of nature to human needs. This is the difficult task of the inventor who is often misunderstood and unrewarded. But he finds ample compensation in the pleasing exercises of his powers and in the knowledge of being one of that exceptionally privileged class without whom the race would have long ago perished in the bitter struggle against pitiless elements. Speaking for myself, I have already had more than my full measure of this exquisite enjoyment; so much, that for many years my life was little short of continuous rapture." (Nikola Tesla, "My Inventions", 1919) 

“We can invent as many theories we like, and any one of them can be made to fit the facts. But that theory is always preferred which makes the fewest number of assumptions.” (Albert Einstein [interview] 1929)

"It seems that the human mind has first to construct forms independently, before we can find them in things. Kepler’s marvelous achievement is a particularly fine example of the truth that knowledge cannot spring from experience alone, but only from the comparison of the inventions of the intellect with observed fact." (Albert Einstein, 1930)

"Mathematics has been called the science of the infinite. Indeed, the mathematician invents finite constructions by which questions are decided that by their very nature refer to the infinite. This is his glory." (Hermann Weyl, "Levels of Infinity", cca. 1930)

"The discoveries in physical science, the triumphs in invention, attest the value of the process of trial and error. In large measure, these advances have been due to experimentation." (Louis Brandeis, "Judicial opinions", 1932)

"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)

"The straight line of the geometers does not exist in the material universe. It is a pure abstraction, an invention of the imagination or, if one prefers, an idea of the Eternal Mind." (Eric T Bell, "The Magic of Numbers", 1946)

🚀On Invention (1850-1899)

"Our inventions are wont to be pretty toys, which distract our attention from serious things. They are but improved means to an unimproved end." (Henry D Thoreau, "Walden ou la vie dans les bois", 1854) 

"They say that each generation inherits from those that have gone before; if this were so there would be no limit to man's improvements or to his power of reaching perfection. But he is very far from receiving intact that storehouse of knowledge which the centuries have piled up before him; he may perfect some inventions, but in others, he lags behind the originators, and a great many inventions have been lost entirely. What he gains on the one hand, he loses on the other." (Eugène Delacroix, 1854) 

"Nevertheless so profound is our ignorance, and so high our presumption, that we marvel when we hear of the extinction of an organic being; and as we do not see the cause, we invoke cataclysms to desolate the world, or invent laws on the duration of the forms of life!" (Charles Darwin, "On the Origin of Species by Means of Natural Selection", 1866)

"As the prerogative of Natural Science is to cultivate a taste for observation, so that of Mathematics is, almost from the starting point, to stimulate the faculty of invention." (James J Sylvester, "A plea for the mathematician", Nature Vol. 1, 1870) 

"The culture of the geometric imagination, tending to produce precision in remembrance and invention of visible forms will, therefore, tend directly to increase the appreciation of works of belles-letters." (Thomas Hill, "Uses of Mathesis", Bibliotheca Sacra Vol. 32, 1875)

"Great inventions are never, and great discoveries are seldom, the work of any one mind. Every great invention is really an aggregation of minor inventions, or the final step of a progression. It is not usually a creation, but a growth, as truly so as is the growth of the trees in the forest." (Robert H Thurston, "The Growth of the Steam Engine", Popular Science, 1877) 

"A discoverer is a tester of scientific ideas; he must not only be able to imagine likely hypotheses, and to select suitable ones for investigation, but, as hypotheses may be true or untrue, he must also be competent to invent appropriate experiments for testing them, and to devise the requisite apparatus and arrangements." (George Gore, "The Art of Scientific Discovery", 1878) 

"Mathematics renders its best service through the immediate furthering of rigorous thought and the spirit of invention."  (Johann F Herbart, "Mathematischer Lehrplan fur Realschulen", 1890)

"The natural world has its laws, and no man must interfere with them in the way of presentment any more than in the way of use; but they themselves may suggest laws of other kinds, and man may, if he pleases, invent a little world of his own, with its own laws; for there is that in him which delights in calling up new forms - which is the nearest, perhaps, he can come to creation. When such forms are new embodiments of old truths, we call them products of the Imagination; when they are mere inventions, however lovely, I should call them the work of the Fancy: in either case, Law has been diligently at work." (George MacDonald, "The Fantastic Imagination", 1893)

"In scientific investigations, it is permitted to invent any hypothesis and, if it explains various large and independent classes of facts, it rises to the ranks of a well-grounded theory." (Charles Darwin, "The Variations of Animals and Plants Under Domestication" Vol. 1, 1896) 

On Discovery (until 1699)

"Reflexion is careful and laborious thought, and watchful attention directed to the agreeable effect of one's plan. Invention, on the other hand, is the solving of intricate problems and the discovery of new principles by means of brilliancy and versatility." (Marcus Vitruvius Pollio, "De architectura" ["On Architecture"], cca. 15 BC)

"Reasoning draws a conclusion and makes us grant the conclusion, but does not make the conclusion certain, nor does it remove doubt so that the mind may rest on the intuition of truth, unless the mind discovers it by the path of experience." (Roger Bacon, "Opus Major", 1267)

"In the discovery of hidden things and the investigation of hidden causes, stronger reasons are obtained from sure experiments and demonstrated arguments than from probable conjectures and the opinions of philosophical speculators of the common sort […]" (William Gilbert, "De Magnete", 1600)

"To invent is to discover that we know not, and not to recover or resummon that which we already know." (Francis Bacon, Advancement of Learning", 1605)

"It cannot be that axioms established by argumentation should avail for the discovery of new works, since the subtlety of nature is greater many times over than the subtlety of argument. But axioms duly and orderly formed from particulars easily discover the way to new particulars, and thus render sciences active." (Francis Bacon, "Novum Organum", 1620)

"The entire method consists in the order and arrangement of the things to which the mind's eye must turn so that we can discover some truth." (René Descartes, "Rules for the Direction of the Mind", 1628)

"We do not yet pretend to have discovered all things, or that what we have discovered can receive no addition; and therefore, pray let us agree, there are yet many things to be done in the ages to come." (Bernard Le Bovier de Fontenelle, "Conversations on the Plurality of Worlds", 1686)

"For the understanding, like the eye, judging of objects only by its own sight, cannot but be pleased with what it discovers, having less regret for what has escaped it, because it is unknown." (John Locke, "An Essay Concerning Human Understanding", 1689)

🅷Jacques S Hadamard - Collected Quotes

"Bernhard Riemann, whose extraordinary intuitive powers we have already mentioned, has especially renovated our knowledge of the distribution of prime numbers, also one of the most mysterious questions in mathematics. He has taught us to deduce results in that line from considerations borrowed from the integral calculus: more precisely, from the study of a certain quantity, a function of a variable s which may assume not only real, but also imaginary values. He proved some important properties of that function, but enunciated two or three as important ones without giving the proof. At the death of Riemann, a note was found among his papers, saying 'These properties of ζ(s) (the function in question) are deduced from an expression of it which, however, I did not succeed in simplifying enough to publish it.' We still have not the slightest idea of what the expression could be. As to the properties he simply enunciated, some thirty years elapsed before I was able to prove all of them but one. The question concerning that last one remains unsolved as yet, though, by an immense labor pursued throughout this last half century, some highly interesting discoveries in that direction have been achieved. It seems more and more probable, but still not at all certain, that the 'Riemann hypothesis' is true." (Jacques Hadamard, "The Psychology of Invention in the Mathematical Field", 1945) 

"It is important for him who wants to discover not to confine himself to one chapter of science, but to keep in touch with various others." (Jacques S Hadamard, "An Essay on the Psychology of Invention in the Mathematical Field", 1945)

"Practical application is found by not looking for it, and one can say that the whole progress of civilization rests on that principle." (Jacques S Hadamard, "An Essay on the Psychology of Invention in the Mathematical Field", 1945)

"The rules of algebra show that the square of any number, whether positive or negative, is a positive number: therefore, to speak of the square root of a negative number is mere absurdity. Now, Cardan deliberately commits that absurdity and begins to calculate on such 'imaginary' quantities. [...] One would describe this as pure madness; and yet the whole development of algebra and analysis would have been impossible without that fundament - which, of course, was, in the nineteenth century, established on solid and rigorous bases. It has been written that the shortest and best way between two truths of the real domain often passes through the imaginary one." (Jacque S Hadamard, "An Essay on the Psychology of Invention in the Mathematical Field", 1945)

"When I undertake some geometrical research, I have generally a mental view of the diagram itself, though generally an inadequate or incomplete one, in spite of which it affords the necessary synthesis - a tendency which, it would appear, results from a training which goes back to my very earliest childhood." (Jacques S Hadamard, "The Psychology of Invention in the Mathematical Field", 1945)

"The creation of a word or a notation for a class of ideas may be, and often is, a scientific fact of very great importance, because it means connecting these ideas together in our subsequent thought" (Jacques S Hadamard, "Newton and the Infinitesimal Calculus", 1947)

"Develop a honeybee mind, gathering ideas everywhere and associating them fully." (Jacques S Hadamard, "But You Don't Understand the Problem", Electronic News, 1967)

"Logic merely sanctions the conquests of the intuition." (Jacques S Hadamard)

"The object of mathematical rigor is to sanction and legitimize the conquests of intuition, and there never was any other object for it." (Jacques S Hadamard)