Quotes by Mathematicians - Page 8

After the discovery of spectral analysis no one trained in physics could doubt the problem of the atom would be solved when physicists had learned to understand the language of spectra. So manifold was the enormous amount of material that has been accumulated in sixty years of spectroscopic research that it seemed at first beyond the possibility of disentanglement. An almost greater enlightenment has resulted from the seven years of Röntgen spectroscopy, inasmuch as it has attacked the problem of the atom at its very root, and illuminates the interior. What we are nowadays hearing of the language of spectra is a true 'music of the spheres' in order and harmony that becomes ever more perfect in spite of the manifold variety. The theory of spectral lines will bear the name of Bohr for all time. But yet another name will be permanently associated with it, that of Planck. All integral laws of spectral lines and of atomic theory spring originally from the quantum theory. It is the mysterious organon on which Nature plays her music of the spectra, and according to the rhythm of which she regulates the structure of the atoms and nuclei.
Arnold Sommerfeld
[Regarding mathematics,] there are now few studies more generally recognized, for good reasons or bad, as profitable and praiseworthy. This may be true; indeed it is probable, since the sensational triumphs of Einstein, that stellar astronomy and atomic physics are the only sciences which stand higher in popular estimation.
G H Hardy
There was yet another disadvantage attaching to the whole of Newton’s physical inquiries, ... the want of an appropriate notation for expressing the conditions of a dynamical problem, and the general principles by which its solution must be obtained. By the labours of LaGrange, the motions of a disturbed planet are reduced with all their complication and variety to a purely mathematical question. It then ceases to be a physical problem; the disturbed and disturbing planet are alike vanished: the ideas of time and force are at an end; the very elements of the orbit have disappeared, or only exist as arbitrary characters in a mathematical formula.
George Boole
All integral laws of spectral lines and of atomic theory spring originally from the quantum theory. It is the mysterious organon on which Nature plays her music of the spectra, and according to the rhythm of which she regulates the structure of the atoms and nuclei.
Arnold Sommerfeld
At his "World of Physics" Web site, Eric W. Weisstein notes that the fine structure constant continues to fascinate numerologists, who have claimed that connections exist between alpha, the Cheops pyramid, and Stonehenge!
Clifford A. Pickover
We have one real candidate for changing the rules; this is string theory. In string theory the one-dimensional trajectory of a particle in spacetime is replaced by a two-dimensional orbit of a string. Such strings can be of any size, but under ordinary circumstances they are quite tiny, ... a value determined by comparing the predictions of the theory for Newton's constant and the fine structure constant to experimental values.
Edward Witten
Physicists believe that the Gaussian law has been proved in mathematics while mathematicians think that it was experimentally established in physics.
Henri Poincaré
Only three constants are significant for star formation: the gravitational constant, the fine structure constant, and a constant that governs nuclear reaction rates.
Ian Stewart
The simple process of eating and breathing weave all of us together into a vast four-dimensional array. No matter how isolated you may sometimes feel, no matter how lonely, you are never really cut off from the whole.
Rudy Rucker
Give me a place to stand, a lever long enough and a fulcrum. and I can move the Earth
Archimedes
...it's really more intelligent to be able to simplify things than to complicate them. Even if some people think it makes you look stupid.
Eugenia Cheng
In Euclid's Elements we meet the concept which later plays a significant role in the development of science. The concept is called the "division of a line in extreme and mean ratio" (DEMR). ...the concept occurs in two forms. The first is formulated in Proposition 11 of Book II. ...why did Euclid introduce different forms... which we can find in Books II, VI and XIII? ...Only three types of regular polygons can be faces of the Platonic solids: the equilateral triangle... the square... and the regular pentagon. In order to construct the Platonic solids... we must build the two-dimensional faces... It is for this purpose that Euclid introduced the golden ratio... (Proposition II.11)... By using the "golden" isosceles triangle...we can construct the regular pentagon... Then only one step remains to construct the dodecahedron... which for Plato is one of the most important regular polyhedra symbolizing the universal harmony in his cosmology.
Alexey Stakhov
In the pentagram, the Pythagoreans found all proportions well-known in antiquity: arithmetic, geometric, harmonic, and also the well-known golden proportion, or the golden ratio. ... Probably owing to the perfect form and the wealth of mathematical forms, the pentagram was chosen by the Pythagoreans as their secret symbol and a symbol of health. - Alexander Voloshinov [As quoted in Stakhov]
Alexey Stakhov
Patriots always talk of dying for their country but never of killing for their country.
Bertrand Russell
Quite often, when an idea that could be helpful presents itself, we do not appreciate it, for it is so inconspicuous. The expert has, perhaps, no more ideas than the inexperienced, but appreciates more what he has and uses it better.
George Pólya
Il n'est pas certain que tout soit incertain.(Translation: It is not certain that everything is uncertain.)
Blaise Pascal
And it certainly did seem a little provoking ('almost as if it happened on purpose,' she thought) that, though she managed to pick plenty of beautiful rushes as the boat glided by, there was always a more lovely one that she couldn't reach."The prettiest are always further!" she said at last, with a sigh at the obstinacy of the rushes in growing so far off.
Lewis Carroll
Being a hero is the easiest way to meet a bullet with your name on it.
David Kendall
Education is not to be viewed as something like filling a vessel with water but, rather, assisting a flower to grow in its own way
Bertrand Russell
am i insane" asked alice"yes, but all the best people are" replied her father
Lewis Carroll
,"I am not crazy, my reality is just different from yours."-Cheshire Cat
Lewis Carroll
String theory is an attempt at a deeper description of nature by thinking of an elementary particle not as a little point but as a little loop of vibrating string.
Edward Witten
Who in the world am I? Ah, that's the great puzzle.
Lewis Carroll
In the year 1456 ... a Comet was seen passing Retrograde between the Earth and the sun... Hence I dare venture to foretell, that it will return again in the year 1758.
Edmond Halley
The orbit of every planet is an ellipse with the sun at one of the two foci.
Johannes Kepler
In the midst of all dwells the Sun. For who could set this luminary in another or better place in this most glorious temple, than whence he can at one and the same time brighten the whole.
Nicolaus Copernicus
Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.
G H Hardy
What Galileo and Newton were to the seventeenth century, Darwin was to the nineteenth.
Bertrand Russell
Einstein created an unstoppable "intellectual chain reaction," an avalanche of pulsing, chattering neurons and memes that will ring for an eternity
Clifford A. Pickover
With the magnificence of eternity before us, let time, with all its fluctuations, dwindle into its own littleness.
Thomas Chalmers
He lived far from the gods, but in his mind he was at home with them.
Pythagoras
Why is it that showers and even storms seem to come by chance, so that many people think it quite natural to pray for rain or fine weather, though they would consider it ridiculous to ask for an eclipse by prayer?
Henri Poincaré
Most people have some appreciation of mathematics, just as most people can enjoy a pleasant tune; and there are probably more people really interested in mathematics than in music. Appearances suggest the contrary, but there are easy explanations. Music can be used to stimulate mass emotion, while mathematics cannot; and musical incapacity is recognized (no doubt rightly) as mildly discreditable, whereas most people are so frightened of the name of mathematics that they are ready, quite unaffectedly, to exaggerate their own mathematical stupidity
G H Hardy
Oh, don't go on like that!" cried the poor Queen, wringing her hands in despair. "Consider what a great girl you are. Consider what a long way you've come today. Consider what o'clock it is. Consider anything, only don't cry!"Alice could not help laughing at this, even in the midst of her tears. "Can you keep from crying by considering things?" she asked."That's that way it's done," the Queen said with great decision: "nobody can do two things at once, you know.
Lewis Carroll
Laughing like crazythe child goes back to the citygives birth to monsterscreates earthquakeshairy women run nakedold folks who look like fetuses laugh and smoke.
Nicanor Parra
To be sure, this is what generally happens when one eats cake; but Alice had got so much into the way of expecting nothing but out-of-the-way things to happen, that it seemed quite dull and stupid for life to go on in the common way.
Lewis Carroll
Now because 18 months ago the first dawn, 3 months ago broad daylight but a very few days ago the full sun of the most highly remarkable spectacle has risen — nothing holds me back. I can give myself up to the sacred frenzy, I can have the insolence to make a full confession to mortal men that I have stolen the golden vessel of the Egyptians to make from them a tabernacle for my God far from the confines of the land of Egypt. If you forgive me I shall rejoice; if you are angry, I shall bear it; I am indeed casting the die and writing the book, either for my contemporaries or for posterity to read, it matters not which: let the book await its reader for a hundred years; God himself has waited six thousand years for his work to be seen.
Johannes Kepler
But the interesting cases are those where the conflict remains obstinately in place however much we ponder the problem. These are the cases where we are tempted to conclude that "intuition cannot be trusted." In these situations we need to improve our intuition, to debug it, but the pressure on us is to abandon intuition and rely on equations instead.
Seymour Papert
Be honest: did you actually read [the above geometric proof]? Of course not. Who would want to? The effect of such a production being made over something so simple is to make people doubt their own intuition. Calling into question the obvious by insisting that it be 'rigorously proved' ... is to say to a student 'Your feelings and ideas are suspect. You need to think and speak our way.
Paul Lockhart
Dull minds are never either intuitive or mathematical.
Blaise Pascal
The virtue of a man ought to be measured not by his extraordinary exertions, but by his every-day conduct.
Blaise Pascal
I do not admire the excess of a virtue like courage unless I see at the same time an excess of the opposite virtue, as in Epaminondas, who possessed extreme courage and extreme kindness. We show greatness not by being at one extreme, but by touching both at once and occupying all the space in between.
Blaise Pascal
The appearance of Professor Benjamin Peirce, whose long gray hair, straggling grizzled beard and unusually bright eyes sparkling under a soft felt hat, as he walked briskly but rather ungracefully across the college yard, fitted very well with the opinion current among us that we were looking upon a real live genius, who had a touch of the prophet in his make-up.
William Elwood Byerly
I am myself a dissenter from all known religions, and I hope that every kind of religious belief will die out. I do not believe that, on the balance, religious belief has been a force for good. Although I am prepared to admit that in certain times and places it has had some good effects, I regard it as belonging to the infancy of human reason, and to a stage of development which we are now outgrowing.
Bertrand Russell
It is clear that thought is not free if the profession of certain opinions makes it impossible to earn a living. It is clear also that thought is not free if all the arguments on one side of a controversy are perpetually presented as attractively as possible, while the arguments on the other side can only be discovered by diligent search.
Bertrand Russell
I should like to preface my remarks with a personal statement in order that my later remarks will not be misunderstood. I consider myself an atheist.
Subrahmanijan Chandrasekhar
People almost invariably arrive at their beliefs not on the basis of proof but on the basis of what they find attractive.
Blaise Pascal
If a man has any genuine talent he should be ready to make almost any sacrifice in order to cultivate it to the full.
G H Hardy
The secret of architectural excellence is to translate the proportions of a dachshund into bricks, mortar and marble.
Christopher Wren
Plato is my friend, Aristotle is my friend, but my greatest friend is truth.
Isaac Newton
If a mathematician wishes to disparage the work of one of his colleagues, say, A, the most effective method he finds for doing this is to ask where the results can be applied. The hard pressed man, with his back against the wall, finally unearths the researches of another mathematician B as the locus of the application of his own results. If next B is plagued with a similar question, he will refer to another mathematician C. After a few steps of this kind we find ourselves referred back to the researches of A, and in this way the chain closes.
Alfred Tarski
Ever since Plato most philosophers have considered it part of their business to produce ‘proofs’ of immortality and the existence of God. They have found fault with the proofs of their predecessors — Saint Thomas rejected Saint Anselm's proofs, and Kant rejected Descartes' — but they have supplied new ones of their own. In order to make their proofs seem valid, they have had to falsify logic, to make mathematics mystical, and to pretend that deepseated prejudices were heaven-sent intuitions.
Bertrand Russell
Mathematics is not arithmetic. Though mathematics may have arisen from the practices of counting and measuring it really deals with logical reasoning in which theorems—general and specific statements—can be deduced from the starting assumptions. It is, perhaps, the purest and most rigorous of intellectual activities, and is often thought of as queen of the sciences.
Christopher Zeeman
Mathematics had never had more than a secondary interest for him [her husband, George Boole]; and even logic he cared for chiefly as a means of clearing the ground of doctrines imagined to be proved, by showing that the evidence on which they were supposed to give rest had no tendency to prove them.
Mary Everest Boole
Nothing is necessitated whose opposite is possible.
Gottfried Wilhelm Leibniz
Some persons fancy that bias and counter-bias are favorable to the extraction of truth–that hot and partisan debate is the way to investigate. This is the theory of our atrocious legal procedure. But Logic puts its heel upon this suggestion. It irrefragably demonstrates that knowledge can only be furthered by the real desire for it, and that the methods of obstinacy, of authority and every mode of trying to reach a foregone conclusion, are absolutely of no value. These things are proved. The reader is at liberty to think so or not as long as the proof is not set forth, or as long as he refrains from examining it. Just so, he can preserve, if he likes, his freedom of opinion in regard to the propositions of geometry; only, in that case, if he takes a fancy to read Euclid, he will do well to skip whatever he finds with A, B, C, etc., for, if he reads attentively that disagreeable matter, the freedom of his opinion about geometry may unhappily be lost forever.
Charles Sanders Peirce
The world of being is unchangeable, rigid, exact, delightful to the mathematician, the logician, the builder of metaphysical systems, and all who love perfection more than life. The world of existence is fleeting, vague, without sharp boundaries, without any clear plan or arrangement, but it contains all thoughts and feelings, all the data of sense, and all physical objects, everything that can do either good or harm, everything that makes any difference to the value of life and the world. According to our temperaments, we shall prefer the contemplation of the one or of the other.
Bertrand Russell
It is obvious that [leftists] are not cool-headed logicians systematically analyzing the foundations of knowledge. They are deeply involved emotionally in their attack on truth and reality.
Theodore J. Kaczynski
Contrariwise,' continued Tweedledee, 'if it was so, it might be; and if it were so, it would be; but as it isn't, it ain't. That's logic.
Lewis Carroll
Ordinary people who live their lives peacefully, whose days gently resemble each other, may happen one day to stop and wonder why and what for do they do the things they do and have been doing for so many years?
Haim Shapira