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Home > Dictionary of Science Quotations > Scientist Names Index D > René Descartes Quotes

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René Descartes
(31 Mar 1596 - 11 Feb 1650)

French philosopher and mathematician who is known as “the father of modern philosophy.” His name is remembered in the term Cartesian geometry in which he applied algebra to geometry.


Science Quotes by René Descartes (46 quotes)

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Apud me omnia fiunt Mathematicè in Natura
In my opinion, everything happens in nature in a mathematical way.
— René Descartes
In letter (11 Mar 1640) to Père Marin Mersenne. English version inspired by a translation of the original Latin in German, “Nach meiner Ansicht geschieht alles in der Natur auf mathematische Art,” in René Descartes and Artur Buchenau (trans., ed.), René Descartes' Philosophische Werke (1905), 246. The Latin is often seen misquoted as “omnia apud me mathematica fiunt.” See context in longer quote that begins, “I have no doubt….” on the René Descartes Quotes page of this website.
Science quotes on:  |  Happen (82)  |  Mathematics (1149)  |  Nature (1211)

Ego cogito, ergo sum.
I think, therefore I am.
— René Descartes
From the original Latin in Principia Philosophiæ (1644), Pars Prima, as collected in Charles Adam and Paul Tannery, Œuvres de Descartes (1905), Vol. 8, Proposition VII, 7. English version as given in John Veitch (trans.), The Method, Meditations, and Selections from the Principles of Descartes (1880), 195.
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Et ainsi nous rendre maîtres et possesseurs de la nature.
And thereby make ourselves, as it were, the lords and masters of nature.
— René Descartes
Discourse on Method in Discourse on Method and Related Writings (1637), trans. Desmond M. Clarke, Penguin edition (1999), Part 6, 44.
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Et j’espère que nos neveux me sauront gré, non seulement des choses que j'ai ici expliquées, mais aussi de celles que j'ai omises volontairement, afin de leur laisser le plaisir de les inventer.
I hope that posterity will judge me kindly, not only as to the things which I have explained, but also as to those which I have intentionally omitted so as to leave to others the pleasure of discovery.
— René Descartes
Concluding remark in Géométrie (1637), as translated by David Eugene Smith and Marcia L. Latham, in The Geometry of René Descartes (1925, 1954), 240.
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[About Pierre de Fermat] It cannot be denied that he has had many exceptional ideas, and that he is a highly intelligent man. For my part, however, I have always been taught to take a broad overview of things, in order to be able to deduce from them general rules, which might be applicable elsewhere.
— René Descartes
Quoted, without source, in The Grolier Library of Science Biographies (1996), Vol. 3, 191.
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A vacuum is repugnant to reason.
— René Descartes
A commonly seen shortened version of a longer quote. From the original Latin: “Repugnare ut detur vacuum, sive in quo nulla plane sit res.” Subtitle of Article XVI in Principia Philospphiæ (1644), Pars Secunda, XVI, 41-42. Also collected in Œuvres de Descartes (1905), Vol. 8, 49. As translated by John Veitch: “That a vacuum or space in which there is absolutely no body is repugnant to reason,” in Meditations and Selections from the Principles of Philosophy (1853, 1913), 185. [Note: In the French edition, the subtitle was translated as, “Qu'il ne peut y avoir aucun vuide au sens que les Philosophes prenent ce mot,” which in English would be, “That there can be no vacuum in the sense that Philosophers take this word.” In Les Principes de la Philosophie (1651), Seconde Partie, Article XVI, 75.]
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After that, I thought about what a proposition generally needs in order to be true and certain because, since I had just found one that I knew was such, I thought I should also know what this certainty consists in. Having noticed that there is nothing at all in the proposition “I think, therefore I am” [cogito ergo sum] which convinces me that I speak the truth, apart from the fact that I see very clearly that one has to exist in order to think, I judged that I could adopt as a general rule that those things we conceive very clearly and distinctly are all true. The only outstanding difficulty is in recognizing which ones we conceive distinctly.
— René Descartes
Discourse on Method in Discourse on Method and Related Writings (1637), trans. Desmond M. Clarke, Penguin edition (1999), Part 4, 25.
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And there are absolutely no judgments (or rules) in Mechanics which do not also pertain to Physics, of which Mechanics is a part or type: and it is as natural for a clock, composed of wheels of a certain kind, to indicate the hours, as for a tree, grown from a certain kind of seed, to produce the corresponding fruit. Accordingly, just as when those who are accustomed to considering automata know the use of some machine and see some of its parts, they easily conjecture from this how the other parts which they do not see are made: so, from the perceptible effects and parts of natural bodies, I have attempted to investigate the nature of their causes and of their imperceptible parts.
— René Descartes
Principles of Philosophy (1644), trans. V. R. and R. P. Miller (1983), 285-6.
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But from the time I was in college I learned that there is nothing one could imagine which is so strange and incredible that it was not said by some philosopher; and since that time, I have recognized through my travels that all those whose views are different from our own are not necessarily, for that reason, barbarians or savages, but that many of them use their reason either as much as or even more than we do. I also considered how the same person, with the same mind, who was brought up from infancy either among the French or the Germans, becomes different from what they would have been if they had always lived among the Chinese or among the cannibals, and how, even in our clothes fashions, the very thing that we liked ten years ago, and that we may like again within the next ten years, appears extravagant and ridiculous to us today. Thus our convictions result from custom and example very much more than from any knowledge that is certain... truths will be discovered by an individual rather than a whole people.
— René Descartes
Discourse on Method in Discourse on Method and Related Writings (1637), trans. Desmond M. Clarke, Penguin edition (1999), Part 2, 14-5.
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Common sense is the most widely shared commodity in the world, for every man is convinced that he is well supplied with it.
— René Descartes
Epigraph in Ian Glynn, An Anatomy of Thought: The Origin and Machinery of the Mind (), Chap. 2, 7. A more freely translated version of the Descartes (longer) quote beginning, “Good sense is, of all things among men…” also on the René Descartes Quotes page on this website.
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Considering that, among all those who up to this time made discoveries in the sciences, it was the mathematicians alone who had been able to arrive at demonstrations—that is to say, at proofs certain and evident—I did not doubt that I should begin with the same truths that they have investigated, although I had looked for no other advantage from them than to accustom my mind to nourish itself upon truths and not to be satisfied with false reasons.
— René Descartes
In Discourse upon Method, Part 2, in Henry A. Torrey (ed., trans. )Philosophy of Descartes in Extracts from His Writings , (1892), 47-48.
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Each problem that I solved became a rule which served afterwards to solve other problems.
— René Descartes
In Discours de la Méthode (1637), collected in Œuvres, vol. VI, 20-21. As translated and cited in epigraph, George Polya, Mathematical Discovery (1981), 1.
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Even the mind depends so much on temperament and the disposition of one’s bodily organs that, if it is possible to find a way to make people generally more wise and more skilful than they have been in the past, I believe that we should look for it in medicine. It is true that medicine as it is currently practiced contains little of much use.
— René Descartes
In Discourse on Method as translated by Desmond M. Clarke, in Discourse on Method and Related Writings (1999), 44. Also see an earlier translation that begins “For the mind…” on this web page.
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Finally, since I thought that we could have all the same thoughts, while asleep, as we have while we are awake, although none of them is true at that time, I decided to pretend that nothing that ever entered my mind was any more true than the illusions of my dreams. But I noticed, immediately afterwards, that while I thus wished to think that everything was false, it was necessarily the case that I, who was thinking this, was something. When I noticed that this truth “I think, therefore I am” was so firm and certain that all the most extravagant assumptions of the sceptics were unable to shake it, I judged that I could accept it without scruple as the first principle of the philosophy for which I was searching. Then, when I was examining what I was, I realized that I could pretend that I had no body, and that there was no world nor any place in which I was present, but I could not pretend in the same way that I did not exist. On the contrary, from the very fact that I was thinking of doubting the truth of other things, it followed very evidently and very certainly that I existed; whereas if I merely ceased to think, even if all the rest of what I had ever imagined were true, I would have no reason to believe that I existed. I knew from this that I was a substance, the whole essence or nature of which was to think and which, in order to exist, has no need of any place and does not depend on anything material. Thus this self—that is, the soul by which I am what I am—is completely distinct from the body and is even easier to know than it, and even if the body did not exist the soul would still be everything that it is.
— René Descartes
Discourse on Method in Discourse on Method and Related Writings (1637), trans. Desmond M. Clarke, Penguin edition (1999), Part 4, 24-5.
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For the mind is so intimately dependent upon the condition and relation of the organs of the body, that if any means can ever be found to render men wiser and more ingenious than hitherto, I believe that it is in medicine they must be sought for. It is true that the science of medicine, as it now exists, contains few things whose utility is very remarkable.
— René Descartes
In A Discourse on Method (1637) as translated by John Veitch, Everyman’s Library: Philosophy & Theology: A Discourse on Method, Etc. (1912, 1916), 49-50. A later translation of this quote begins “Even the mind…” on this web page.
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Give me extension and motion, and I will construct the Universe.
— René Descartes
As quoted, without citation, in Morris Kline, Mathematics in Western Culture (1964), 106. Webmaster has not yet located this in a primary source. Can you help?
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Good sense is, of all things among men, the most equally distributed ; for every one thinks himself so abundantly provided with it, that those even who are the most difficult to satisfy in everything else, do not usually desire a larger measure of this quality than they already possess.
— René Descartes
In Discours de la Méthode (1637), Part 1. English version as given in John Veitch (trans.), The Method, Meditations, and Selections from the Principles of Descartes (1880), 3. Also seen translated as “Of all things, good sense is the most fairly distributed: everyone thinks he is so well supplied with it that even those who are the hardest to satisfy in every other respect never desire more of it than they already have,” or “Good sense is of all things in the world the most equally distributed, for everybody thinks he is so well supplied with it that even those most difficult to please in all other matters never desire more of it than they already possess.” From the original French, “Le bon sens est la chose du monde la mieux partagée; car chacun pense en être si bien pourvu, que ceux même qui sont les plus difficiles à contenter en toute autre chose n'ont point coutume d'en désirer plus qu'ils en ont.”
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I believed that, instead of the multiplicity of rules that comprise logic, I would have enough in the following four, as long as I made a firm and steadfast resolution never to fail to observe them.
The first was never to accept anything as true if I did not know clearly that it was so; that is, carefully to avoid prejudice and jumping to conclusions, and to include nothing in my judgments apart from whatever appeared so clearly and distinctly to my mind that I had no opportunity to cast doubt upon it.
The second was to subdivide each on the problems I was about to examine: into as many parts as would be possible and necessary to resolve them better.
The third was to guide my thoughts in an orderly way by beginning, as if by steps, to knowledge of the most complex, and even by assuming an order of the most complex, and even by assuming an order among objects in! cases where there is no natural order among them.
And the final rule was: in all cases, to make such comprehensive enumerations and such general review that I was certain not to omit anything.
The long chains of inferences, all of them simple and easy, that geometers normally use to construct their most difficult demonstrations had given me an opportunity to think that all the things that can fall within the scope of human knowledge follow from each other in a similar way, and as long as one avoids accepting something as true which is not so, and as long as one always observes the order required to deduce them from each other, there cannot be anything so remote that it cannot be reached nor anything so hidden that it cannot be uncovered.
— René Descartes
Discourse on Method in Discourse on Method and Related Writings (1637), trans. Desmond M. Clarke, Penguin edition (1999), Part 2, 16.
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I concluded that I might take as a general rule the principle that all things which we very clearly and obviously conceive are true: only observing, however, that there is some difficulty in rightly determining the objects which we distinctly conceive.
— René Descartes
In Discours de la Méthode (1637), as translated by J. Veitch, A Discourse on Method (1912), 27.
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I could not possibly be of such a nature as I am, and yet have in my mind the idea of a God, if God did not in reality exist.
— René Descartes
In Meditations (1641), Part 3. English as given in John Veitch (trans.), 'Of God: That He Exists', Meditation III, The Method, Meditations, and Selections from the Principles of Descartes (1880), 132. Also seen translated as, “It is not possible that I could have in myself the idea of God, if God did not truly exist.”
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I have no doubt that many small strikes of a hammer will finally have as much effect as one very heavy blow: I say as much in quantity, although they may be different in mode, but in my opinion, everything happens in nature in a mathematical way, and there is no quantity that is not divisible into an infinity of parts; and Force, Movement, Impact etc. are types of quantities.
— René Descartes
From the original French, “Ie ne doute point que plusieurs petits coups de Marteau ne fassent enfin autant d’effet qu’vn fort grand coup, ie dis autant en quantité, bien qu’ils puissent estre différents, in modo; mais apud me omnia fiunt Mathematicè in Natura, & il n’y a point de quantité qui ne soit divisible en une infinité de parties; Or la Force, le Mouuement, la Percussion, &c. sont des Especes de quantitez,” in letter (11 Mar 1640) to Père Marin Mersenne (AT III 36), collected in Lettres de Mr Descartes (1659), Vol. 2, 211-212. English version by Webmaster using online resources.
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I specifically paused to show that, if there were such machines with the organs and shape of a monkey or of some other non-rational animal, we would have no way of discovering that they are not the same as these animals. But if there were machines that resembled our bodies and if they imitated our actions as much as is morally possible, we would always have two very certain means for recognizing that, none the less, they are not genuinely human. The first is that they would never be able to use speech, or other signs composed by themselves, as we do to express our thoughts to others. For one could easily conceive of a machine that is made in such a way that it utters words, and even that it would utter some words in response to physical actions that cause a change in its organs—for example, if someone touched it in a particular place, it would ask what one wishes to say to it, or if it were touched somewhere else, it would cry out that it was being hurt, and so on. But it could not arrange words in different ways to reply to the meaning of everything that is said in its presence, as even the most unintelligent human beings can do. The second means is that, even if they did many things as well as or, possibly, better than anyone of us, they would infallibly fail in others. Thus one would discover that they did not act on the basis of knowledge, but merely as a result of the disposition of their organs. For whereas reason is a universal instrument that can be used in all kinds of situations, these organs need a specific disposition for every particular action.
— René Descartes
Discourse on Method in Discourse on Method and Related Writings (1637), trans. Desmond M. Clarke, Penguin edition (1999), Part 5, 40.
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I suppose the body to be just a statue or a machine made of earth.
— René Descartes
The World and Other Writings (1633), trans. and ed. Stephen Gaukroger (1998), 99.
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I was then in Germany, where I had been drafted because of the wars that are still going on there, and as I was returning to the army from the emperor's coronation, the arrival of winter delayed me in quarters where, finding no company to distract me and, luckily, having no cares or passions to trouble me, I used to spend the whole day alone in a room, that was heated by a stove, where I had plenty of time to concentrate on my own thoughts.
— René Descartes
Discourse on Method in Discourse, on Method and Related Writings (1637), trans. Desmond M. Clarke, Penguin edition (1999), Part 2, 11.
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I would think I knew nothing in physics if I could say only how things could be but, without demonstrating that they can’t be otherwise.
— René Descartes
From the original French, “Pour la Physique, ie croyrois n’y rien sçauoir, si ie ne sçauois que dire comment les choses peuuent estre, sans demonstrer qu’elles ne peuuent estre autrement,” in letter (11 Mar 1640) to Père Marin Mersenne, collected in Lettres de Mr Descartes (1659), Vol. 2, 213. As translated by John Cottingham, et al., (trans.), in The Philosophical Writings of Descartes: Volume 3, The Correspondence (1991), 145.
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If I had been taught from my youth all the truths of which I have since sought out demonstrations, and had thus learned them without labour, I should never, perhaps, have known any beyond these; at least, I should never have acquired the habit and the facility which I think I possess in always discovering new truths in proportion as I give myself to the search.
— René Descartes
In Discours de la Méthode (1637). In English from John Veitch (trans.), A Discourse on Method (1912), 57.
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If I have succeeded in discovering any truths in the sciences…, I can declare that they are but the consequences and results of five or six principal difficulties which I have surmounted, and my encounters with which I reckoned as battles in which victory declared for me.
— René Descartes
In Discours de la Méthode (1637), as translated by J. Veitch, A Discourse on Method (1912), 53. Also seen translated as, “If I found any new truths in the sciences…, I can say that they follow from, or depend on, five or six principal problems which I succeeded in solving and which I regard as so many battles where the fortunes of war were on my side.”
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If there is any work in the world which cannot be so well finished by another as by him who has commenced it, it is that at which I labour.
— René Descartes
In Discours de la Méthode (1637). In English from John Veitch (trans.), A Discourse on Method (1912), 57.
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If we had a thorough knowledge of all the parts of the seed of any animal (e.g., man), we could from that alone, by reasons entirely mathematical and certain, deduce the whole conformation and figure of each of its members, and, conversely, if we knew several peculiarities of this conformation, we would from those deduce the nature of its seed.
— René Descartes
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In order to seek truth, it is necessary once in the course of our life, to doubt, as far as possible, of all things.
— René Descartes
From the original Latin: “Veritatem inquirenti, semel in vita de omnibus, quantum fieri potest, esse dubitandum,” Principles of Philosophy (1644). Pars Prima, as collected in Charles Adam and Paul Tannery, Œuvres de Descartes (1905), Vol. 8, Proposition I, 5. English version as given in John Veitch (trans.), The Method, Meditations, and Selections from the Principles of Descartes (1880), 193. Also seen translated as: “If you would be a real seeker after truth, you must at least once in your life doubt, as far as possible, all things.”
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It is not enough to have a good mind. The main thing is to use it well.
— René Descartes
…...
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It is well to know something of the manners of various peoples, in order more sanely to judge our own, and that we do not think that everything against our modes is ridiculous, and against reason, as those who have seen nothing are accustomed to think.
— René Descartes
In Discourse on Method (1637).

It must not be thought that it is ever possible to reach the interior earth by any perseverance in mining: both because the exterior earth is too thick, in comparison with human strength; and especially because of the intermediate waters, which would gush forth with greater impetus, the deeper the place in which their veins were first opened; and which would drown all miners.
— René Descartes
Principles of Philosophy (1644), trans. V. R. and R. P. Miller (1983), 217-8.
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Let us now declare the means whereby our understanding can rise to knowledge without fear of error. There are two such means: intuition and deduction. By intuition I mean not the varying testimony of the senses, nor the deductive judgment of imagination naturally extravagant, but the conception of an attentive mind so distinct and so clear that no doubt remains to it with regard to that which it comprehends; or, what amounts to the same thing, the self-evidencing conception of a sound and attentive mind, a conception which springs from the light of reason alone, and is more certain, because more simple, than deduction itself. …
It may perhaps be asked why to intuition we add this other mode of knowing, by deduction, that is to say, the process which, from something of which we have certain knowledge, draws consequences which necessarily follow therefrom. But we are obliged to admit this second step; for there are a great many things which, without being evident of themselves, nevertheless bear the marks of certainty if only they are deduced from true and incontestable principles by a continuous and uninterrupted movement of thought, with distinct intuition of each thing; just as we know that the last link of a long chain holds to the first, although we can not take in with one glance of the eye the intermediate links, provided that, after having run over them in succession, we can recall them all, each as being joined to its fellows, from the first up to the last. Thus we distinguish intuition from deduction, inasmuch as in the latter case there is conceived a certain progress or succession, while it is not so in the former; … whence it follows that primary propositions, derived immediately from principles, may be said to be known, according to the way we view them, now by intuition, now by deduction; although the principles themselves can be known only by intuition, the remote consequences only by deduction.
— René Descartes
In Rules for the Direction of the Mind, Philosophy of Descartes. [Torrey] (1892), 64-65.
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Many small strikes of a hammer will finally have as much effect as one very heavy blow.
— René Descartes
From the original French, “Plusieurs petits coups de Marteau ne fassent enfin autant d’effet qu’vn fort grand coup,” in letter (11 Mar 1640) to Père Marin Mersenne (AT III 36), collected in Lettres de Mr Descartes (1659), Vol. 2, 211-212. English version by Webmaster using online resources. See context in longer quote that begins, “I have no doubt….” on the René Descartes Quotes page of this website.
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The nature of matter, or body considered in general, consists not in its being something which is hard or heavy or coloured, or which affects the senses in any way, but simply in its being something which is extended in length, breadth and depth.
— René Descartes
Principles of Philosophy (1644), trans. V. R. and R. P. Miller (1983), 40.
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The seeker after truth must, once in the course of his life, doubt everything, as far as is possible.
— René Descartes
In Principles of Philosophy Part 1, 1, As translated by Cottingham, Stoothoff and Murdoch in Descartes: Selected Philosophical Writings (1988, 1999), 160.
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Then I had shown, in the same place, what the structure of the nerves and muscles of the human body would have to be in order for the animal spirits in the body to have the power to move its members, as one sees when heads, soon after they have been cut off, still move and bite the ground even though they are no longer alive; what changes must be made in the brain to cause waking, sleep and dreams; how light, sounds, odours, tastes, warmth and all the other qualities of external objects can impress different ideas on it through the senses; how hunger, thirst, and the other internal passions can also send their ideas there; what part of the brain should be taken as “the common sense”, where these ideas are received; what should be taken as the memory, which stores the ideas, and as the imagination, which can vary them in different ways and compose new ones and, by the same means, distribute the animal spirits to the muscles, cause the limbs of the body to move in as many different ways as our own bodies can move without the will directing them, depending on the objects that are present to the senses and the internal passions in the body. This will not seem strange to those who know how many different automata or moving machines can be devised by human ingenuity, by using only very few pieces in comparison with the larger number of bones, muscles, nerves, arteries, veins and all the other parts in the body of every animal. They will think of this body like a machine which, having been made by the hand of God, is incomparably better structured than any machine that could be invented by human beings, and contains many more admirable movements.
— René Descartes
Discourse on Method in Discourse on Method and Related Writings (1637), trans. Desmond M. Clarke, Penguin edition (1999), Part 5, 39-40.
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There is no quantity that is not divisible into an infinity of parts.
— René Descartes
From the original French, “Il n’y a point de quantité qui ne soit divisible en une infinité de parties,” in letter (11 Mar 1640) to Père Marin Mersenne (AT III 36), collected in Lettres de Mr Descartes (1659), Vol. 2, 211-212. English version by Webmaster using online resources. See context in longer quote that begins, “I have no doubt….” on the René Descartes Quotes page of this website.
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We cannot doubt of our existence while we doubt, and that this is the first knowledge we acquire when we philosophize in order. … The knowledge, I think, therefore I am, is the first and most certain that occurs to one who philosophizes orderly.
— René Descartes
From the original Latin: “Non posse à nobis dubitari, quin existamus dum dubitamus; atque quod ordine philosophando cognoscimus. … Ac proinde hæc cognitio, ego cognito, ergo sum, est omnium | prima & certissima, quæ cuilibet ordine philosophanti occurant,” in Principia Philosophiæ (1644), Pars Prima, as collected in Charles Adam and Paul Tannery, Œuvres de Descartes (1905), Vol. 8, Proposition VII, 6-7. English version as given in John Veitch (trans.), The Method, Meditations, and Selections from the Principles of Descartes (1880), 195.
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When first I applied my mind to Mathematics I read straight away most of what is usually given by the mathematical writers, and I paid special attention to Arithmetic and Geometry because they were said to be the simplest and so to speak the way to all the rest. But in neither case did I then meet with authors who fully satisfied me. I did indeed learn in their works many propositions about numbers which I found on calculation to be true. As to figures, they in a sense exhibited to my eyes a great number of truths and drew conclusions from certain consequences. But they did not seem to make it sufficiently plain to the mind itself why these things are so, and how they discovered them. Consequently I was not surprised that many people, even of talent and scholarship, should, after glancing at these sciences, have either given them up as being empty and childish or, taking them to be very difficult and intricate, been deterred at the very outset from learning them. … But when I afterwards bethought myself how it could be that the earliest pioneers of Philosophy in bygone ages refused to admit to the study of wisdom any one who was not versed in Mathematics … I was confirmed in my suspicion that they had knowledge of a species of Mathematics very different from that which passes current in our time.
— René Descartes
In Elizabeth S. Haldane (trans.) and G.R.T. Ross (trans.), 'Rules for the Direction of the Mind', The Philosophical Works of Descartes (1911, 1973), Vol. 1, Rule 4, 11.
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When it is not in our power to determine what is true, we ought to act according to what is most probable.
— René Descartes
In Discours de la Méthode: Troisième partie, collected in Oeuvres Philosophiques de Descartes (1835), 23. As quoted and translated in Joseph William Mellor, Higher Mathematics for Students of Chemistry and Physics (1901), 416. From the original French, “Lorsqu’il n’est pas eu notre pouvoir de discerner les plus vraies opinions, nous devons suivre les plus probables.”
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When someone says “I am thinking, therefore I am, or I exist,” he does not deduce existence from thought by means of a syllogism, but recognises it as something self-evident by a simple intuition of the mind. This is clear from the fact that if he were deducing it by means of a syllogism, he would have to have had previous knowledge of the major premiss 'Everything which thinks is, or exists'; yet in fact he learns it from experiencing in his own case that it is impossible that he should think without existing. It is in the nature of our mind to construct general propositions on the basis of our knowledge of particular ones.
— René Descartes
Author's Replies to the Second set of Objections to Meditations on the First Philosophy (1641), in The Philosophical Writings of Descartes (1985), trans. J. Cottingham, R. Stoothoff and D. Murdoch, Vol. 2, 100.
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[We] can easily distinguish what relates to Mathematics in any question from that which belongs to the other sciences. But as I considered the matter carefully it gradually came to light that all those matters only were referred to Mathematics in which order and measurements are investigated, and that it makes no difference whether it be in numbers, figures, stars, sounds or any other object that the question of measurement arises. I saw consequently that there must be some general science to explain that element as a whole which gives rise to problems about order and measurement, restricted as these are to no special subject matter. This, I perceived was called “Universal Mathematics,” not a far-fetched asignation, but one of long standing which has passed into current use, because in this science is contained everything on account of which the others are called parts of Mathematics.
— René Descartes
Rules for the Direction of the Mind (written 1628). As translated by Elizabeth Sanderson Haldane and George Robert Thomson Ross in The Philosophical Works of Descartes (1911, 1931), 13.
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~~[Orphan]~~ Perfect numbers like perfect men are very rare.
— René Descartes
Appears without citation in Howard W. Eves, Mathematical Circles Squared (1972), 7, and it is noted with the fact that only 12 perfect numbers were known in Descartes’ time. Webmaster regards this as an orphan (better regarded as anonymous), and has so far been unable to trace a primary source in the work of Descartes. Can you help?
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~~[Orphan]~~ When writing about transcendental issues, be transcendentally clear.
— René Descartes
Quoted, without citation, in George F. Simmons, Calculus Gems (1992, 2007), 89. It is a bad sign that other quotes on the same page do have sources footnoted, but not for this subject quote. So, Webmaster regards the quote as an orphan (better attributed to anonymous) having so far being unable to locate a primary source. Can you help?
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Quotes by others about René Descartes (35)

Descartes' immortal conclusion cogito ergo sum was recently subjected to destruction testing by a group of graduate researchers at Princeton led by Professors Montjuic and Lauterbrunnen, and now reads, in the Shorter Harvard Orthodoxy:
(a) I think, therefore I am; or
(b) Perhaps I thought, therefore I was; but
(c) These days, I tend to leave that side of things to my wife.
Tom Holt
Ye Gods! (1992), 223.
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Follow Descartes! Do not give up the religion of your youth until you get a better one.
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The stone that Dr. Johnson once kicked to demonstrate the reality of matter has become dissipated in a diffuse distribution of mathematical probabilities. The ladder that Descartes, Galileo, Newton, and Leibniz erected in order to scale the heavens rests upon a continually shifting, unstable foundation.
Mathematics in Western Culture (1953), 382.
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Break the chains of your prejudices and take up the torch of experience, and you will honour nature in the way she deserves, instead of drawing derogatory conclusions from the ignorance in which she has left you. Simply open your eyes and ignore what you cannot understand, and you will see that a labourer whose mind and knowledge extend no further than the edges of his furrow is no different essentially from the greatest genius, as would have been proved by dissecting the brains of Descartes and Newton; you will be convinced that the imbecile or the idiot are animals in human form, in the same way as the clever ape is a little man in another form; and that, since everything depends absolutely on differences in organisation, a well-constructed animal who has learnt astronomy can predict an eclipse, as he can predict recovery or death when his genius and good eyesight have benefited from some time at the school of Hippocrates and at patients' bedsides.
Machine Man (1747), in Ann Thomson (ed.), Machine Man and Other Writings (1996), 38.
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Laplace would have found it child's-play to fix a ratio of progression in mathematical science between Descartes, Leibnitz, Newton and himself
The Education of Henry Adams: An Autobiography? (1918), 491.
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It is impossible not to feel stirred at the thought of the emotions of man at certain historic moments of adventure and discovery—Columbus when he first saw the Western shore, Pizarro when he stared at the Pacific Ocean, Franklin when the electric spark came from the string of his kite, Galileo when he first turned his telescope to the heavens. Such moments are also granted to students in the abstract regions of thought, and high among them must be placed the morning when Descartes lay in bed and invented the method of co-ordinate geometry.
Quoted in James Roy Newman, The World of Mathematics (2000), Vol. 1, 239.
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There are some men who are counted great because they represent the actuality of their own age, and mirror it as it is. Such an one was Voltaire, of whom it was epigrammatically said: “he expressed everybody's thoughts better than anyone.” But there are other men who attain greatness because they embody the potentiality of their own day and magically reflect the future. They express the thoughts which will be everybody's two or three centuries after them. Such as one was Descartes.
Quoted in James Roy Newman, The World of Mathematics (2000), Vol. 1, 239.
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CARTESIAN, adj. Relating to Descartes, a famous philosopher, author of the celebrated dictum, Cogito, ergo sum—whereby he was pleased to suppose he demonstrated the reality of human existence. The dictum might be improved, however, thus: Cogito ergo cogito sum—'I think that I think, therefore I think that I am;' as close an approach to certainty as any philosopher has yet made.
The Collected Works of Ambrose Bierce (1911), Vol. 7, The Devil's Dictionary,  46-47.
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The analytical geometry of Descartes and the calculus of Newton and Leibniz have expanded into the marvelous mathematical method—more daring than anything that the history of philosophy records—of Lobachevsky and Riemann, Gauss and Sylvester. Indeed, mathematics, the indispensable tool of the sciences, defying the senses to follow its splendid flights, is demonstrating today, as it never has been demonstrated before, the supremacy of the pure reason.
In 'What Knowledge is of Most Worth?', Presidential address to the National Education Association, Denver, Colorado (9 Jul 1895). In Educational Review (Sep 1895), 10, 109.
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The difference between myth and science is the difference between divine inspiration of “unaided reason” (as Bertrand Russell put it) on the one hand and theories developed in observational contact with the real world on the other. It is the difference between the belief in prophets and critical thinking, between Credo quia absurdum (I believe because it is absurd–Tertullian) and De omnibus est dubitandum (Everything should be questioned–Descartes). To try to write a grand cosmical drama leads necessarily to myth. To try to let knowledge substitute ignorance in increasingly large regions of space and time is science.
In 'Cosmology: Myth or Science?' Journal of Astrophysics and Astronomy (1984), 5, 79-98.
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Descartes constructed as noble a road of science, from the point at which he found geometry to that to which he carried it, as Newton himself did after him. ... He carried this spirit of geometry and invention into optics, which under him became a completely new art.
A Philosophical Dictionary: from the French? (2nd Ed.,1824), Vol. 5, 110.
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Very few of us can now place ourselves in the mental condition in which even such philosophers as the great Descartes were involved in the days before Newton had announced the true laws of the motion of bodies.
'Introductory Lecture on Experimental Physics', 1871. In W. D. Niven (ed.), The Scientific Papers of James Clerk Maxwell (1890), Vol. 2, 241.
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Putting together the mysteries of nature with the laws of mathematics, he dared to hope to be able to unlock the secrets of both with the same key.
Epitaph of René Descartes
Epitaph
In Peter Pešic, Labyrinth: A Search for the Hidden Meaning of Science (2001), 73.
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Kepler’s discovery would not have been possible without the doctrine of conics. Now contemporaries of Kepler—such penetrating minds as Descartes and Pascal—were abandoning the study of geometry ... because they said it was so UTTERLY USELESS. There was the future of the human race almost trembling in the balance; for had not the geometry of conic sections already been worked out in large measure, and had their opinion that only sciences apparently useful ought to be pursued, the nineteenth century would have had none of those characters which distinguish it from the ancien régime.
From 'Lessons from the History of Science: The Scientific Attitude' (c.1896), in Collected Papers (1931), Vol. 1, 32.
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Descartes, the father of modern philosophy … would never—so he assures us—have been led to construct his philosophy if he had had only one teacher, for then he would have believed what he had been told; but, finding that his professors disagreed with each other, he was forced to conclude that no existing doctrine was certain.
From 'Philosophy For Laymen', collected in Unpopular Essays (1950, 1996), 57.
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Descartes said, “I think; therefore I am.” The philosophic evolutionist reverses and negatives the epigram. He says, “I am not; therefore I cannot think.”
In Orthodoxy (1918, 2008), 25.
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It appears … [Descartes] has inverted the order of philosophising, … it seemed good to him not to learn from things, but to impose his own laws on things.… First he collected … truths which he thought suitable …; and then gradually advanced to particulars explicable from principles which … he had framed without consulting Nature.
As quoted in B.J.T. Dobbs, The Foundations of Newton's Alchemy (1983), 101. Cited as Osmond’s translation in Percy Herbert Osmond, Isaac Barrow, His Life and Times (1944), 30-31.
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To complete a PhD[,] I took courses in the history of philosophy. … As a result of my studies, I concluded that the traditional philosophy of science had little if anything to do with biology. … I had no use for a philosophy based on such an occult force as the vis vitalis. … But I was equally disappointed by the traditional philosophy of science, which was all based on logic, mathematics, and the physical sciences, and had adopted Descartes’ conclusion that an organism was nothing but a machine. This Cartesianism left me completely dissatisfied.
In 'Introduction', What Makes Biology Unique?: Considerations on the Autonomy of a Scientific Discipline (2007), 2.
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The mechanical world view is a testimonial to three men: Francis Bacon, Rene Descartes, and Isaac Newton. After 300 years we are still living off their ideas.
In Jeremy Rifkin and Ted Howard, Entropy: Into the Greenhouse World (1980), 19.
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I am a Christian which means that I believe in the deity of Christ, like Tycho de Brahe, Copernicus, Descartes, Newton, Leibnitz, Pascal ... like all great astronomers mathematicians of the past.
…...
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The vortices of Descartes, gave way to the gravitation of Newton... One generation blows bubbles, and the next breaks them.
From Letter (29 Sep 1783) to Rev. William Unwin, collected in William Cowper and William Hayley (ed.), The Life, and Posthumous Writings, of William Cowper (1803), Vol. 3, 196.
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In the index to the six hundred odd pages of Arnold Toynbee’s A Study of History, abridged version, the names of Copernicus, Galileo, Descartes and Newton do not occur … yet their cosmic quest destroyed the mediaeval vision of an immutable social order in a walled-in universe and transformed the European landscape, society, culture, habits and general outlook, as thoroughly as if a new species had arisen on this planet.
First lines of 'Preface', in The Sleepwalkers: A History of Man’s Changing Vision of the Universe (1959), 13.
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In a famous passage, René Descartes tells us that he considered himself to be placed in three simultaneous domiciles, patiently recognizing his loyalties to the social past, fervidly believing in a final solution of nature’s secrets and in the meantime consecrated to the pursuit of scientific doubt. Here we have the half way house of the scientific laboratory, of the scientific mind in the midst of its campaign.
In 'The Three Dimensions of Time', Part I, 'The Classic of Science', A Classic and a Founder (1937), collected in Rosenstock-Huessy Papers (1981), Vol. 1, 14.
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Descartes … commanded the future from his study more than Napoleon from his throne.
Paraphrased from Oliver Wendell Holmes, Montesquieu: A Critical and Biographical Introduction to “The Spirit of the Laws” (1900), xiv. The context referred to “Montesquieu … a lonely scholar sitting in a library. Like Descartes or Kant, he commanded the future from his study more than Napoléon from his throne.”
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In the index to the six hundred odd pages of Arnold Toynbee’s A Study of History, abridged version, the names of Copernicus, Galileo, Descartes and Newton do not occur yet their cosmic quest destroyed the medieval vision of an immutable social order in a walled-in universe and transformed the European landscape, society, culture, habits and general outlook, as thoroughly as if a new species had arisen on this planet.
In The Sleepwalkers: A History of Man's Changing Vision of the Universe (1959), Preface, 13.
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The union of philosophical and mathematical productivity, which besides in Plato we find only in Pythagoras, Descartes and Leibnitz, has always yielded the choicest fruits to mathematics; To the first we owe scientific mathematics in general, Plato discovered the analytic method, by means of which mathematics was elevated above the view-point of the elements, Descartes created the analytical geometry, our own illustrious countryman discovered the infinitesimal calculus—and just these are the four greatest steps in the development of mathematics.
In Geschichte der Mathematik im Altertum und im Mittelalter (1874), 149-150. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 210. From the original German, “Die Verbindung philosophischer und mathematischer Productivität, wie wir sie ausser in Platon wohl nur noch in Pythagoras, Descartes, Leibnitz vorfinden, hat der Mathematik immer die schönsten Früchte gebracht: Ersterem verdanken wir die wissenschaftliche Mathematik überhaupt, Platon erfand die analytische Methode, durch welche sich die Mathematik über den Standpunct der Elemente erhob, Descartes schuf die analytische Geometrie, unser berühmter Landsmann den Infinitesimalcalcül—und eben daß sind die vier grössten Stufen in der Entwickelung der Mathematik.”
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It is not only a decided preference for synthesis and a complete denial of general methods which characterizes the ancient mathematics as against our newer Science [modern mathematics]: besides this extemal formal difference there is another real, more deeply seated, contrast, which arises from the different attitudes which the two assumed relative to the use of the concept of variability. For while the ancients, on account of considerations which had been transmitted to them from the Philosophie school of the Eleatics, never employed the concept of motion, the spatial expression for variability, in their rigorous system, and made incidental use of it only in the treatment of phonoromically generated curves, modern geometry dates from the instant that Descartes left the purely algebraic treatment of equations and proceeded to investigate the variations which an algebraic expression undergoes when one of its variables assumes a continuous succession of values.
In 'Untersuchungen über die unendlich oft oszillierenden und unstetigen Functionen', Ostwald’s Klassiker der exacten Wissenschaften (1905), No. 153, 44-45. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 115. From the original German, “Nicht allein entschiedene Vorliebe für die Synthese und gänzliche Verleugnung allgemeiner Methoden charakterisiert die antike Mathematik gegenüber unserer neueren Wissenschaft; es gibt neben diesem mehr äußeren, formalen, noch einen tiefliegenden realen Gegensatz, welcher aus der verschiedenen Stellung entspringt, in welche sich beide zu der wissenschaftlichen Verwendung des Begriffes der Veränderlichkeit gesetzt haben. Denn während die Alten den Begriff der Bewegung, des räumlichen Ausdruckes der Veränderlichkeit, aus Bedenken, die aus der philosophischen Schule der Eleaten auf sie übergegangen waren, in ihrem strengen Systeme niemals und auch in der Behandlung phoronomisch erzeugter Kurven nur vorübergehend verwenden, so datiert die neuere Mathematik von dem Augenblicke, als Descartes von der rein algebraischen Behandlung der Gleichungen dazu fortschritt, die Größenveränderungen zu untersuchen, welche ein algebraischer Ausdruck erleidet, indem eine in ihm allgemein bezeichnete Größe eine stetige Folge von Werten durchläuft.”
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The bones of Descartes were returned to France (all except those of the right hand, which were retained by the French Treasurer-General as a souvenir for his skill in engineering the transaction) and were re-entombed in what is now the Pantheon. There was to have been a public oration, but this was hastily forbidden by order of the crown, as the doctrines of Descartes were deemed to be still too hot for handling before the people.
In Men of Mathematics (1937), 51-52. The remains of Descartes were returned to his native France, seventeen years after he died in Stockholm, Sweden.
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The biologist can push it back to the original protist, and the chemist can push it back to the crystal, but none of them touch the real question of why or how the thing began at all. The astronomer goes back untold million of years and ends in gas and emptiness, and then the mathematician sweeps the whole cosmos into unreality and leaves one with mind as the only thing of which we have any immediate apprehension. Cogito ergo sum, ergo omnia esse videntur. All this bother, and we are no further than Descartes. Have you noticed that the astronomers and mathematicians are much the most cheerful people of the lot? I suppose that perpetually contemplating things on so vast a scale makes them feel either that it doesn’t matter a hoot anyway, or that anything so large and elaborate must have some sense in it somewhere.
As co-author with Robert Eustace, The Documents in the Case (1930), 72.
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To Descartes, the great philosopher of the 17th century, is due the undying credit of having removed the bann which until then rested upon geometry. The analytical geometry, as Descartes’ method was called, soon led to an abundance of new theorems and principles, which far transcended everything that ever could have been reached upon the path pursued by the ancients.
In Die Entwickelung der Mathematik in den letzten Jahrhunderten (1884), 10.
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There is something sublime in the secrecy in which the really great deeds of the mathematician are done. No popular applause follows the act; neither contemporary nor succeeding generations of the people understand it. The geometer must be tried by his peers, and those who truly deserve the title of geometer or analyst have usually been unable to find so many as twelve living peers to form a jury. Archimedes so far outstripped his competitors in the race, that more than a thousand years elapsed before any man appeared, able to sit in judgment on his work, and to say how far he had really gone. And in judging of those men whose names are worthy of being mentioned in connection with his,—Galileo, Descartes, Leibnitz, Newton, and the mathematicians created by Leibnitz and Newton’s calculus,—we are forced to depend upon their testimony of one another. They are too far above our reach for us to judge of them.
In 'Imagination in Mathematics', North American Review, 86, 223.
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If a mathematician of the past, an Archimedes or even a Descartes, could view the field of geometry in its present condition, the first feature to impress him would be its lack of concreteness. There are whole classes of geometric theories which proceed not only without models and diagrams, but without the slightest (apparent) use of spatial intuition. In the main this is due, to the power of the analytic instruments of investigations as compared with the purely geometric.
In 'The Present Problems in Geometry', Bulletin American Mathematical Society (1906), 286.
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It is not surprising, in view of the polydynamic constitution of the genuinely mathematical mind, that many of the major heros of the science, men like Desargues and Pascal, Descartes and Leibnitz, Newton, Gauss and Bolzano, Helmholtz and Clifford, Riemann and Salmon and Plücker and Poincaré, have attained to high distinction in other fields not only of science but of philosophy and letters too. And when we reflect that the very greatest mathematical achievements have been due, not alone to the peering, microscopic, histologic vision of men like Weierstrass, illuminating the hidden recesses, the minute and intimate structure of logical reality, but to the larger vision also of men like Klein who survey the kingdoms of geometry and analysis for the endless variety of things that flourish there, as the eye of Darwin ranged over the flora and fauna of the world, or as a commercial monarch contemplates its industry, or as a statesman beholds an empire; when we reflect not only that the Calculus of Probability is a creation of mathematics but that the master mathematician is constantly required to exercise judgment—judgment, that is, in matters not admitting of certainty—balancing probabilities not yet reduced nor even reducible perhaps to calculation; when we reflect that he is called upon to exercise a function analogous to that of the comparative anatomist like Cuvier, comparing theories and doctrines of every degree of similarity and dissimilarity of structure; when, finally, we reflect that he seldom deals with a single idea at a tune, but is for the most part engaged in wielding organized hosts of them, as a general wields at once the division of an army or as a great civil administrator directs from his central office diverse and scattered but related groups of interests and operations; then, I say, the current opinion that devotion to mathematics unfits the devotee for practical affairs should be known for false on a priori grounds. And one should be thus prepared to find that as a fact Gaspard Monge, creator of descriptive geometry, author of the classic Applications de l’analyse à la géométrie; Lazare Carnot, author of the celebrated works, Géométrie de position, and Réflections sur la Métaphysique du Calcul infinitesimal; Fourier, immortal creator of the Théorie analytique de la chaleur; Arago, rightful inheritor of Monge’s chair of geometry; Poncelet, creator of pure projective geometry; one should not be surprised, I say, to find that these and other mathematicians in a land sagacious enough to invoke their aid, rendered, alike in peace and in war, eminent public service.
In Lectures on Science, Philosophy and Art (1908), 32-33.
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That mathematics “do not cultivate the power of generalization,”; … will be admitted by no person of competent knowledge, except in a very qualified sense. The generalizations of mathematics, are, no doubt, a different thing from the generalizations of physical science; but in the difficulty of seizing them, and the mental tension they require, they are no contemptible preparation for the most arduous efforts of the scientific mind. Even the fundamental notions of the higher mathematics, from those of the differential calculus upwards are products of a very high abstraction. … To perceive the mathematical laws common to the results of many mathematical operations, even in so simple a case as that of the binomial theorem, involves a vigorous exercise of the same faculty which gave us Kepler’s laws, and rose through those laws to the theory of universal gravitation. Every process of what has been called Universal Geometry—the great creation of Descartes and his successors, in which a single train of reasoning solves whole classes of problems at once, and others common to large groups of them—is a practical lesson in the management of wide generalizations, and abstraction of the points of agreement from those of difference among objects of great and confusing diversity, to which the purely inductive sciences cannot furnish many superior. Even so elementary an operation as that of abstracting from the particular configuration of the triangles or other figures, and the relative situation of the particular lines or points, in the diagram which aids the apprehension of a common geometrical demonstration, is a very useful, and far from being always an easy, exercise of the faculty of generalization so strangely imagined to have no place or part in the processes of mathematics.
In An Examination of Sir William Hamilton’s Philosophy (1878), 612-13.
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Descartes is the completest type which history presents of the purely mathematical type of mind—that in which the tendencies produced by mathematical cultivation reign unbalanced and supreme.
In An Examination of Sir William Hamilton’s Philosophy (1878), 626.
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See also:
  • 31 Mar - short biography, births, deaths and events on date of Descartes's birth.
  • Descartes: A Biography, by Desmond M. Clarke. - book suggestion.
  • Booklist for René Descartes.

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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