Science Quotes - Page 4

Underneath his sweetness and gentleness was the heat of a volcano. [Michael Faraday] was a man of excitable and fiery nature; but through high self-discipline he had converted the fire into a central glow and motive power of life, instead of permitting it to waste itself in useless passion.

John Tyndall

In the field of Egyptian mathematics Professor Karpinski of the University of Michigan has long insisted that surviving mathematical papyri clearly demonstrate the Egyptians' scientific interest in pure mathematics for its own sake. I have now no doubt that Professor Karpinski is right, for the evidence of interest in pure science, as such, is perfectly conclusive in the Edwin Smith Surgical Papyrus.

James Henry Breasted

The physical method becomes a philosophy when it asserts there is no higher knowledge than the empirical knowledge of scientific phenomena. The mathematical method becomes a philosophy when it asserts that some higher knowledge is needed to explain scientific facts, and that higher knowledge is mathematics.

Fulton J. Sheen

Littlewood, on Hardy's own estimate, is the finest mathematician he has ever known. He was the man most likely to storm and smash a really deep and formidable problem; there was no one else who could command such a combination of insight, technique and power.

Henry Hallett Dale

To the average mathematician who merely wants to know his work is securely based, the most appealing choice is to avoid difficulties by means of Hilbert's program. Here one regards mathematics as a formal game and one is only concerned with the question of consistency ... . The Realist position is probably the one which most mathematicians would prefer to take. It is not until he becomes aware of some of the difficulties in set theory that he would even begin to question it. If these difficulties particularly upset him, he will rush to the shelter of Formalism, while his normal position will be somewhere between the two, trying to enjoy the best of two worlds.

Paul Cohen

[Benjamin Peirce's] lectures were not easy to follow. They were never carefully prepared. The work with which he rapidly covered the blackboard was very illegible, marred with frequent erasures, and not infrequent mistakes (he worked too fast for accuracy). He was always ready to digress from the straight path and explore some sidetrack that had suddenly attracted his attention, but which was likely to have led nowhere when the college bell announced the close of the hour and we filed out, leaving him abstractedly staring at his work, still with chalk and eraser in his hands, entirely oblivious of his departing class.

William Elwood Byerly

Through the judicious employment of symbols, diagrams, and calculations, mathematics enables us to acquire significant facts about extremely significant things (universal laws, even), not by first forging out into the cosmos with teams of scientists, but rather from the comforts and confines of coffee tables in our living rooms! p. 72

G. Arnell Williams

Some mathematics problems look simple, and you try them for a year or so, and then you try them for a hundred years, and it turns out that they're extremely hard to solve. There's no reason why these problems shouldn't be easy, and yet they turn out to be extremely intricate. [Fermat's] Last Theorem is the most beautiful example of this.

Andrew John Wiles

I carried this problem around in my head basically the whole time. I would wake up with it first thing in the morning, I would be thinking about it all day, and I would be thinking about it when I went to sleep. Without distraction I would have the same thing going round and round in my mind.(Recalling the degree of focus and determination that eventually yielded the proof of Fermat's Last Theorem.)

Andrew John Wiles

Mathematics, as much as music or any other art, is one of the means by which we rise to a complete self-consciousness. The significance of mathematics resides precisely in the fact that it is an art; by informing us of the nature of our own minds it informs us of much that depends on our minds.

Antoine Thomson d'Abbadie

Philosophers and psychiatrists should explain why it is that we mathematicians are in the habit of systematically erasing our footsteps. Scientists have always looked askance at this strange habit of mathematicians, which has changed little from Pythagoras to our day.

Gian-Carlo Rota

How did Biot arrive at the partial differential equation? [the heat conduction equation] . . . Perhaps Laplace gave Biot the equation and left him to sink or swim for a few years in trying to derive it. That would have been merely an instance of the way great mathematicians since the very beginnings of mathematical research have effortlessly maintained their superiority over ordinary mortals.

Clifford A. Truesdell

[I was advised] to read Jordan's 'Cours d'analyse'; and I shall never forget the astonishment with which I read that remarkable work, the first inspiration for so many mathematicians of my generation, and learnt for the first time as I read it what mathematics really meant.

G H Hardy

The integrals which we have obtained are not only general expressions which satisfy the differential equation, they represent in the most distinct manner the natural effect which is the object of the phenomenon... when this condition is fulfilled, the integral is, properly speaking, the equation of the phenomenon; it expresses clearly the character and progress of it, in the same manner as the finite equation of a line or curved surface makes known all the properties of those forms.

Joseph Fourier

The teacher manages to get along still with the cumbersome algebraic analysis, in spite of its difficulties and imperfections, and avoids the smooth infinitesimal calculus, although the eighteenth century shyness toward it had long lost all point.

Felix Klein

…numerical precision is the very soul of science, and its attainment affords the best, perhaps the only criterion of the truth of theories and the correctness of experiments.

D'Arcy Wentworth Thompson

So they rolled up their sleeves and sat down to experiment -- by simulation, that is mathematically and all on paper. And the mathematical models of King Krool and the beast did such fierce battle across the equation-covered table, that the constructors' pencils kept snapping. Furious, the beast writhed and wriggled its iterated integrals beneath the King's polynomial blows, collapsed into an infinite series of indeterminate terms, then got back up by raising itself to the nth power, but the King so belabored it with differentials and partial derivatives that its Fourier coefficients all canceled out (see Riemann's Lemma), and in the ensuing confusion the constructors completely lost sight of both King and beast. So they took a break, stretched their legs, had a swig from the Leyden jug to bolster their strength, then went back to work and tried it again from the beginning, this time unleashing their entire arsenal of tensor matrices and grand canonical ensembles, attacking the problem with such fervor that the very paper began to smoke. The King rushed forward with all his cruel coordinates and mean values, stumbled into a dark forest of roots and logarithms, had to backtrack, then encountered the beast on a field of irrational numbers (F_1) and smote it so grievously that it fell two decimal places and lost an epsilon, but the beast slid around an asymptote and hid in an n-dimensional orthogonal phase space, underwent expansion and came out fuming factorially, and fell upon the King and hurt him passing sore. But the King, nothing daunted, put on his Markov chain mail and all his impervious parameters, took his increment Δk to infinity and dealt the beast a truly Boolean blow, sent it reeling through an x-axis and several brackets—but the beast, prepared for this, lowered its horns and—wham!!—the pencils flew like mad through transcendental functions and double eigentransformations, and when at last the beast closed in and the King was down and out for the count, the constructors jumped up, danced a jig, laughed and sang as they tore all their papers to shreds, much to the amazement of the spies perched in the chandelier—perched in vain, for they were uninitiated into the niceties of higher mathematics and consequently had no idea why Trurl and Klapaucius were now shouting, over and over, "Hurrah! Victory!!

Stanisław Lem

This skipping is another important point. It should be done whenever a proof seems too hard or whenever a theorem or a whole paragraph does not appeal to the reader. In most cases he will be able to go on and later he may return to the parts which he skipped.

Emil Artin

For we may remark generally of our mathematical researches, that these auxiliary quantities, these long and difficult calculations into which we are often drawn, are almost always proofs that we have not in the beginning considered the objects themselves so thoroughly and directly as their nature requires, since all is abridged and simplified, as soon as we place ourselves in a right point of view.

Louis Poinsot

The first successes were such that one might suppose all the difficulties of science overcome in advance, and believe that the mathematician, without being longer occupied in the elaboration of pure mathematics, could turn his thoughts exclusively to the study of natural laws.

Joseph Louis François Bertrand

Mathematics is the science which draws necessary conclusions.

Benjamin Peirce

Everything can be summed up into an equation.

Alexei Maxim Russell

...in pure mathematics the mind deal only with its own creations and imaginations. The concepts of number and form have not been derived from any source other than the world of reality. The ten fingers on which men learned to count, that is, to carry out the first arithmetical operation, may be anything else, but they are certainly not only objects that can be counted, but also the ability to exclude all properties of the objects considered other than their number-and this ability is the product of a long historical evolution based on experience. Like the idea of number, so the idea of form is derived exclusively from the external world, and does not arise in the mind as a product of pure thought.

Friedrich Engels

What is it, in fact, that we are supposed to abstract from, in order to get, for example, from the moon to the number 1? By abstraction we do indeed get certain concepts, viz. satellite of the Earth, satellite of a planet, non-self-luminous heavenly body, heavenly body, body, object. But in this series 1 is not to be met with; for it is no concept that the moon could fall under. In the case of 0, we have simply no object at all from which to start our process of abstracting. It is no good objecting that 0 and 1 are not numbers in the same sense as 2 and 3. What answers the question How many? is number, and if we ask, for example, "How many moons has this planet?", we are quite as much prepared for the answer 0 or 1 as for 2 or 3, and that without having to understand the question differently. No doubt there is something unique about 0, and about 1000; but the same is true in principle of every whole number, only the bigger the number the less obvious it is. To make out of this a difference in kind is utterly arbitrary. What will not work with 0 and 1 cannot be essential to the concept of number.

Gottlob Frege

Mathematical knowledge is unlike any other knowledge. While our perception of the physical world can always be distorted, our perception of mathematical truths can’t be. They are objective, persistent, necessary truths. A mathematical formula or theorem means the same thing to anyone anywhere – no matter what gender, religion, or skin color; it will mean the same thing to anyone a thousand years from now. And what’s also amazing is that we own all of them. No one can patent a mathematical formula, it’s ours to share. There is nothing in this world that is so deep and exquisite and yet so readily available to all. That such a reservoir of knowledge really exists is nearly unbelievable. It’s too precious to be given away to the “initiated few.” It belongs to all of us.

Edward Frenkel

In these days of conflict between ancient and modern studies, there must surely be something to be said for a study which did not begin with Pythagoras, and will not end with Einstein, but is the oldest and the youngest of all.

G H Hardy

My dream is that all of us will be able to see, appreciate, and marvel at the magic beauty and exquisite harmony of these ideas, formulas, and equations, for this will give so much more meaning to our love for this world and for each other.

Frenkel writes

And, believe me, if I were again beginning my studies, I should follow the advice of Plato and start with mathematics.

Galileo Galilei

The algebraic sum of all the transformations occurring in a cyclical process can only be positive, or, as an extreme case, equal to no

Rudolf Clausius

Scientists have invented a new strain of cannabis without the high. They celebrated with non-alcoholic beer and furious dry-humping.

Stephen Colbert

There was something ghost-like and insubstantial about gases to these early chemists. They called liquids that turned into gases easily, "spirits." Methyl alcohol, they called "wood spirit"; ethyl alcohol, "wine spirit." Even today, alcoholic beverages are frequently referred to as "spirits." (Modern Arabs, from whose language the word "alcohol" was taken, call ethyl alcohol "spirit" from the English. This is a queer exchange.)

Isaac Asimov

If I can't have your babies, I'll damn sure deliver them!

Frouwkje Denoo

In the Bible, a woman was made from a man. In real life, a man is made from a woman.

Mokokoma Mokhonoana

Science is a form of arrogance control.

Carol Tavris

Random search for data on ... off-chance is hardly scientific. A questionnaire on 'Intellectual Immoralities' was circulated by a well-known institution. 'Intellectual Immorality No. 4' read: 'Generalizing beyond one's data'. [Wilder Dwight] Bancroft asked whether it would not be more correct to word question no. 4 'Not generalizing beyond one's data.

Hans Selye

In science, the credit goes to the man who convinces the world, not to the man to whom the idea first occurs.

William Osler

The wild gas, the fixed air is plainly broke loose: but we ought to suspend our judgments until the first effervescence is a little subsided, till the liquor is cleared, and until we see something deeper than the agitation of the troubled and frothy surface.[Alluding to Joseph Priestley's Observations on Air]

Edmund Burke

All the truths of mathematics are linked to each other, and all means of discovering them are equally admissible.

Adrien-Marie Legendre

The deep study of nature is the most fruitful source of mathematical discoveries. By offering to research a definite end, this study has the advantage of excluding vague questions and useless calculations; besides it is a sure means of forming analysis itself and of discovering the elements which it most concerns us to know, and which natural science ought always to conserve.

Joseph Fourier

At my urgent request the Curie laboratory, in which radium was discovered a short time ago, was shown to me. The Curies themselves were away travelling. It was a cross between a stable and a potato-cellar, and, if I had not seen the worktable with the chemical apparatus, I would have thought it a practical joke.(Wilhelm Ostwald on seeing the Curie's laboratory facilities.)

Wilhelm

A demonstrative and convincing proof that an acid does consist of pointed parts is, that not only all acid salts do Crystallize into edges, but all Dissolutions of different things, caused by acid liquors, do assume this figure in their Crystallization; these Crystalls consist of points differing both in length and bigness from one another, and this diversity must be attributed to the keener or blunter edges of the different sorts of acids.

Nicolas Lemery

Facts, and facts alone, are the foundation of science... When one devotes oneself to experimental research it is in order to augment the sum of known facts, or to discover their mutual relations.

François Magendie

We can distinguish three groups of scientific men. In the first and very small group we have the men who discover fundamental relations. Among these are van't Hoff, Arrhenius and Nernst. In the second group we have the men who do not make the great discovery but who see the importance and bearing of it, and who preach the gospel to the heathen. Ostwald stands absolutely at the head of this group. The last group contains the rest of us, the men who have to have things explained to us.

Wilder Dwight Bancroft

This theory [the oxygen theory] is not as I have heard it described, that of the French chemists, it is mine (elle est la mienne); it is a property which I claim from my contemporaries and from posterity.

Antoine Lavoisier

Children discover and verify their theories in quite the same way that scientists do: through experimentation. They manipulate the world and discover regularities of causation from those manipulations. Why do they do it? The discovery of regularities comes with a pleasurable burst of insight, which all of us, but especially children and scientists, continuously long for like bonbons or opium.

Matthew M. Hurley

Discovery consists of seeing what everybody has seen and thinking what nobody else has thought.

Albert Szent-Györgyi

In chemistry, our theories are crutches; to show that they are valid, they must be used to walk... A theory established with the help of twenty facts must explain thirty, and lead to the discovery of ten more.

Jean-Baptiste Dumas

Will fluorine ever have practical applications?It is very difficult to answer this question. I may, however, say in all sincerity that I gave this subject little thought when I undertook my researches, and I believe that all the chemists whose attempts preceded mine gave it no more consideration.A scientific research is a search after truth, and it is only after discovery that the question of applicability can be usefully considered.

Henri Moissan

[In the case of research director, Willis R. Whitney, whose style was to give talented investigators as much freedom as possible, you may define 'serendipity' as] the art of profiting from unexpected occurrences. When you do things in that way you get unexpected results. Then you do something else and you get unexpected results in another line, and you do that on a third line and then all of a sudden you see that one of these lines has something to do with the other. Then you make a discovery that you never could have made by going on a direct road.

Irving Langmuir

Do experimental work but keep in mind that other investigators in the same field will consider your discoveries as less than one fourth as important as they seem to you.

Charles Manning Child

The discovery of an interaction among the four hemes made it obvious that they must be touching, but in science what is obvious is not necessarily true. When the structure of hemoglobin was finally solved, the hemes were found to lie in isolated pockets on the surface of the subunits. Without contact between them how could one of them sense whether the others had combined with oxygen? And how could as heterogeneous a collection of chemical agents as protons, chloride ions, carbon dioxide, and diphosphoglycerate influence the oxygen equilibrium curve in a similar way? It did not seem plausible that any of them could bind directly to the hemes or that all of them could bind at any other common site, although there again it turned out we were wrong. To add to the mystery, none of these agents affected the oxygen equilibrium of myoglobin or of isolated subunits of hemoglobin. We now know that all the cooperative effects disappear if the hemoglobin molecule is merely split in half, but this vital clue was missed. Like Agatha Christie, Nature kept it to the last to make the story more exciting. There are two ways out of an impasse in science: to experiment or to think. By temperament, perhaps, I experimented, whereas Jacques Monod thought.

Max F. Perutz

... the irregularities of the motion of Uranus...in order to find out whether they may be attributed to the action of an undiscovered planet beyond it.[John Couch Adams on how he began to discover Neptune.]

John Couch Adams

I do not think that G. H. Hardy was talking nonsense when he insisted that the mathematician was discovering rather than creating... The world for me is a necessary system, and in the degree to which the thinker can surrender his thought to that system and follow it, he is in a sense participating in that which is timeless or eternal.

Brand Blanshard

Think of a "discovery" as an act that moves the arrival of information from a later point in time to an earlier time. The discovery's value does not equal the value of the information discovered but rather the value of having the information available earlier than it otherwise would have been. A scientist or a mathematician may show great skill by being the first to find a solution that has eluded many others; yet if the problem would soon have been solved anyway, then the work probably has not much benefited the world [unless having a solution even slightly sooner is immensely valuable or enables further important and urgent work].

Nick Bostrom

The trouble with science geeks, as you call them, is that hey put discovery before anything else. It was a science geek who discovered the atom bomb. He didn't intend to cause mass murder, but he did nonetheless.

Gemma Malley

The scientist is a lover of truth for the very love of truth itself, wherever it may lead.

Luther Burbank

Steve's throat swelled with tension as the intimacy of the moment became more tangible. He moved his eyes from the dark, reflective river, to the dark, reflective pupils in Diane's eyes. They seemed to quiver with tenderness - but then they would grow distant. He found himself continually surprised at the "aliveness" of the person standing just a foot away from him now. She wasn't inanimate: she would flinch if he pinched her, and answer if he asked her. And she was beautiful." -- From "The Grand Unified Story" -- a short story in Zack Love's Stories and Scripts: an Anthology

Zack Love

A famous name has this peculiarity that it becomes gradually smaller especially in natural sciences where each succeeding discovery invariably overshadows what precedes.

Jacobus Henricus van 't Hoff

Fact: Cells are constantly dying and new ones are taking their placeFact: After seven years have gone by, every cell in my body has died and a new one has taken its place.Do the math. That means that every seven years, I'm a totally new me. not one of the old cells remains. Twice, I've had a total makeover

Jill Wolfson

There are always more questions. Science as a process is never complete. It is not a foot race, with a finish line.... People will always be waiting at a particular finish line: journalists with their cameras, impatient crowds eager to call the race, astounded to see the scientists approach, pass the mark, and keep running. It's a common misunderstanding, he said. They conclude there was no race. As long as we won't commit to knowing everything, the presumption is we know nothing.

Barbara Kingsolver

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Science Quotes - Page 4

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