Mathematicians From France

"Let us calculate the motion of bodies, but also consult the plans of the Intelligence that makes them move. It seems that the ancient philosophers made the first attempts at this sort of science, in looking for metaphysical relationships between numbers and material bodies. When they said that God occupies himself with geometry, they surely meant that He unites in that science the works of His power with the perspectives of His wisdom. From the all too few ancient geometers who undertook such studies, we have little that is intelligible or well-founded. The perfection which geometry has acquired since their time puts us in a better position to succeed, and may more than compensate for the advantages that those great minds had over us."

"Having discovered the true principle, I then derived all the laws that govern the motion of light, those concerning its direct propagation, its reflection and its refraction. I reserve for particular members of our Assembly the geometrical demonstration of my theory. I know the distaste that many mathematicians have for final causes applied to physics, a distaste that I share up to some point. I admit, it is risky to introduce such elements; their use is dangerous, as shown by the errors made by Fermat and Leibniz in following them. Nevertheless, it is perhaps not the principle that is dangerous, but rather the hastiness in taking as a basic principle that which is merely a consequence of a basic principle."

"The refraction of light agrees with the grand principle that Nature always uses the simplest means to accomplish its effects. From this principle, can be derived whenever light passes from one medium to another, the ratio of the sine of the angle of refraction to the sine of the angle of refraction equals the inverse ratio of the speeds at which light moves in each medium. But this "budget", this expense of action that Nature minimizes in the refraction of light, is it also minimized in the direct propagation and reflection of light? Yes, it always has the smallest possible value."

"Now I have to define what I mean by "action". When a material body is transported from one point to another, it involves an action that depends on the speed of the body and on the distance it travels. However, the action is neither the speed nor the distance taken separately; rather, it is proportional to the sum of the distances travelled multiplied each by the speed at which they were travelled."

"After meditating deeply on this topic, it occurred to me that light, upon passing from one medium to another, has to make a choice, whether to follow the path of shortest distance (the straight line) or the path of least time. But why should it prefer time over space? Light cannot travel both paths at once, yet how does it decide to take one path over another? Rather than taking either of these paths per se, light takes the path that offers a real advantage: light takes the path that minimizes its action."

"The first law is the same for both light and material bodies; they both move in a straight line, as long as they are not deflected by an outside force. The second law is also the same as that governing the reflection of an elastic ball from an impenetrable surface. Mechanics shows that such a ball is reflected from such a surface so that its angle of reflection equals its angle of incidence, as observed for light. But the third law still requires a plausible explanation. The passage of light from one medium to another exhibits behavior that is totally different from a ball moving through different media."

"The ancient Greeks knew the laws that govern the propagation of light in a uniform medium and upon its reflection. However, the law governing the refraction of light as it passes from one transparent medium to another was unknown until the last century. Snell discovered it, Descartes tried to explain it and Fermat criticized his explanation. Since then, many great geometers have researched the problem, although no one has yet found a way of harmonizing the law of refraction with more fundamental laws that Nature must obey."

"The most beautiful discoveries since the Renaissance, indeed since the beginnings of all science, are the laws governing light, whether moving through a uniform medium, or being reflected from an opaque surface, or changing direction upon entering another transparent medium."

"May we not say that, in the fortuitous combination of the productions of Nature, since only those creatures could survive in whose organizations a certain degree of adaptation was present, there is nothing extraordinary in the fact that such adaptation is actually found in all these species which now exist? Chance, one might say, turned out a vast number of individuals; a small proportion of these were organized in such a manner that the animals' organs could satisfy their needs. A much greater number showed neither adaptation nor order; these last have all perished.... Thus the species which we see today are but a small part of all those that a blind destiny has produced."

"We cannot doubt that all things are regulated by a supreme Being, who, while he has imprinted on matter forces which show his power, has destined it to execute effects which mark his wisdom... Let us calculate the motion of bodies, but let us also consult the designs of the Intelligence which makes them move."

"Nature always uses the simplest means to accomplish its effects."

"I must now explain what I mean by the quantity of action. A certain action is necessary for the carrying of a body from one point to another: this action depends on the velocity which the body has and the space which it describes; but it is neither the velocity nor the space taken separately. The quantity of action varies directly as the velocity and the length of path described; it is proportional to the sum of the spaces, each being multiplied by the velocity with which the body describes it. It is this quantity of action which is here the true expense (dépense) of nature, and which she economizes as much as possible in the motion of light."

"Everything is so arranged that the blind logic of mathematics executes the will of the most enlightened and free Mind."

"The supreme Being is everywhere; but He is not equally visible everywhere. Let us seek Him in the simplest things, in the most fundamental laws of Nature, in the universal rules by which movement is conserved, distributed or destroyed; and let us not seek Him in phenomena that are merely complex consequences of these laws."

"La vie n'est bonne qu'à deux choses : à faire des mathématiques et à les professer. (The only two good things in life are doing mathematics and teaching it.)"

"In many different fields, empirical phenomena appear to obey a certain general law, which can be called the Law of Large Numbers. This law states that the ratios of numbers derived from the observation of a very large number of similar events remain practically constant, provided that these events are governed partly by constant factors and partly by variable factors whose variations are irregular and do not cause a systematic change in a definite direction."

"That which can affect our senses in any manner whatever, is termed matter."

"A mathematician, then, will be defined in what follows as someone who has published the proof of at least one non-trivial theorem."

"« La Logique peut être patiente, car elle est éternelle. » ("Logic can be patient because it is eternal.") ibid. p. 150"

"Agreement with experiment is the sole criteria of truth for a physical theory."

"A physical theory reputed to be satisfactory by the sectarians of one metaphysical school will be rejected by the partisans of another school."

"[U]n symbole n'est, à proprement parler, ni vrai, ni faux; il est plus ou moins bien choisi pour signifier la réalité qu'il représente, il la figure d'une manière plus ou moins précise, plus ou moins détaillée..."

"The first question we should face is: What is the aim of a physical theory? To this question diverse answers have been made, but all of them may be reduced to two main principles: "A physical theory," certain logicians have replied, "has for its object the explanation of a group of laws experimentally established." "A physical theory," other thinkers have said, "is an abstract system whose aim is to summarize and classify logically a group of experimental laws without claiming to explain these laws... Now these two questions — Does there exist a material reality distinct from sensible appearances? and What is the nature of reality? — do not have their source in experimental method, which is acquainted only with sensible appearances and can discover nothing beyond them. The resolution of these questions transcends the methods used by physics; it is the object of metaphysics. Therefore, if the aim of physical theories is to explain experimental laws, theoretical physics is not an autonomous science; it is subordinate to metaphysics... Now, to make physical theories depend on metaphysics is surely not the way to let them enjoy the privilege of universal consent."

"There you have, then, a theoretical physics which is neither the theory of a believer nor that of a nonbeliever, but merely and simply a theory of a physicist; admirably suited to classify the laws studied by the experimenter, it is incapable of opposing any assertion whatever of metaphysics or of religious dogma, and is equally incapable of lending effective support to any such assertion."

"Every time people cite a principle of theoretical physics in support of a metaphysical doctrine or physical dogma, they commit a mistake, for they attribute to this principle a meaning not its own, an import not belonging to it."

"The one who contributed most to break down the barrier between physical method and metaphysical method, and to confound their domains, so clearly distinguished in the Aristotelian philosophy, was surely Descartes."

"Les esprits partagés, s'égarant dans des routes différentes, perdent l'immense avantage qui résulterait de leurs forces réunies."

"The first step to be taken, is to study carefully the fundamental phenomenon above described, and to examine all the various circumstances under which it presents itself."

"It would be easier to endow a fool with intellect than to persuade him that he had none."

"Ce qui est familier aux savants de profession a grand besoin d'être mis dans le domaine commun."

"There is no let up! No end to it! Accursed problems! Innumerable calculations. Endless fighting. Signs. Formulas. Theorems besetting me from dawn to dusk!"

"I am a sincere Catholic as it were Corneille, Racine, La Bruyère, Bossnet, Bourdaloue, Fènelon, as were and still are so many of the most of the honor of out science, philosophy and literature, and have conferred such brilliant ustre on our Academies. I share the deep conviction openly manifested in words, deeds and writings by so many savants of the first rank, by a Ruffini, a Haüy, a Laënnec, an Ampere, a Pelletier, a Freycinet, a Coriolis and I avoid naming any of those living, for fear of paining their podesty. I may at least be allowed to say that I loved to recognize all the noble generosity of the Christian Faith in my illustrious friends the creator of Crystallography (Haüy), the introducers of quinine and stethoscope (Pelletier and Laënnec), the famous voyager on board of the 'Urania', and the immortal founders of the theory of Dynamic Electricity (Frencinet and Ampère)."

"As translated by Julio Antonio Gonzalo (2008). The Intelligible Universe: An Overview of the Last Thirteen Billion Years. World Scientific. p. 301."

"I am a Christian, that is, I believe in the divinity of Christ, as did Tycho Brahe, Copernicus, Descartes, Newton, Fermat, Leibniz, Pascal, Grimaldi, Euler, Guldin; Boscovich, Gerdil, as did all the great astronomers, physicist and geometricians of past ages."

"... très souvent les lois particulières déduites par les physiciens d'un grand nombre d'observations ne sont pas rigoureuses, mais approchées."

"Residues arise … naturally in several branches of analysis … . Their consideration provides simple and easy-to-use methods, which are applicable to a large number of diverse questions, and some new results … ."

"Trying to solve the worlds problems by making things 5% more efficient is like trying to play the violin with gardening gloves. Not much good will come out of it. We must invent new ways!"

"There is no greater goal than to truly improve Mr and Ms Everyone's health, as an innovator that is where I want to spend my energy."

"Camera-phones are like nuclear power plants: bad people will turn them into evil, good people will put them to good use."

"Camera-Phones are at the root of the Citizen-Journalism revolution."

"I'd gone to the Lamaze classes, and the second time I said, 'Breathe!' Sonia said, 'Shut up!' So I said, 'OK, I'll sit at this desk and find something to do."

"I build things that I think are exciting from a technology standpoint and will help make life easier, simpler and better for people."

"Accelerometrics is a cool new discipline. Newton and Galileo would love it."

"Great fit and synergism for both companies and excellent outcome for employees, customers and shareholders."

"If a sleep monitor has electrodes and wires that look like something from Frankenstein's lab, you might not wear it consistently, and the information it gathers and reports may be compromised."

"We were trying to monitor the sailboat, trying to help us keep it upright and optimized, and it turned out that sailing became an incredible practical laboratory."

"Sitting outside a cafe people watching would be no fun if everyone looks the same. It would be an Orwellian world where everyone wears the same thing and uses the same phone. Wearable tech is diversity."

"We're trying to change the Kleenex mentality of technology - you buy a smartband or an Android Wear watch and next year you'll throw it away. This is a horrible world we're preparing for the next generation. We have to get away from that crazy approach, as we look at the resources left on this planet. We need to be able to create objects that are worth keeping and upgrading."

"A watch is much more than a list of functionality and features... the bottom line is this is fashion, this is image, this something that is on our skin that we want to wear, and it’s not just another electronic gadget that becomes obsolete…. there is an emotional character to it."

"We’re operating a huge sleep experiment, worldwide, unlike anything anyone has ever done. We have 250 million nights of sleep in our database, and we’re using all the latest technologies to make sense of it."