Best 579 quotes in «mathematics quotes» category

The world is continuous, but the mind is discrete.

This book is about physics and its about physics and its relationship with mathematics and how they seem to be intimately related and to what extent can you explore this relationship and trust it.

This branch of mathematics [Probability] is the only one, I believe, in which good writers frequently get results which are entirely erroneous.

This is not mathematics; this is theology.

This method of deduction ... is often called "combinatory". Its usefulness is not exhausted at this stage, but it does even at the outset lead to some valuable conclusions.

This splendid subject [mathematics], queen of all exact sciences, and the ideal and norm of all careful thinking.

Thought, then, is the execution of this computer code.

To be successful, you should concentrate on the world of companies, not arcane accounting mathematics.

To speak algebraically, Mr. M. is execrable, but Mr. G. is (x + 1)- ecrable.

To many, mathematics is a collection of theorems. For me, mathematics is a collection of examples; a theorem is a statement about a collection of examples and the purpose of proving theorems is to classify and explain the examples.

To me, mathematics is like playing the violin. Some people can do it - others can't. If you don't have it, then there's no point in pretending.

Tout ce qu'on invente est vrai, soi-en sure. La poesie est une chose aussi precise que la geometrie.

To those who ask what the infinitely small quantity in mathematics is, we answer that it is actually zero. Hence there are not so many mysteries hidden in this concept as they are usually believed to be.

We can... treat only the geometrical aspects of mathematics and shall be satisfied in having shown that there is no problem of the truth of geometrical axioms and that no special geometrical visualization exists in mathematics.

We know that nature is described by the best of all possible mathematics because God created it.

We have heard much about the poetry of mathematics, but very little of it has yet been sung. The ancients had a juster notion of their poetic value than we.

We know that nature is described by the best of all possible mathematics because God created it. So there is a chance that the best of all possible mathematics will be created out of physicists' attempts to describe nature.

We ourselves are co-called non-linear dynamical systems... I don't feel quite so pathetic when I interrupt a project to check on some obscure web site or newsgroup or derive an iota of cheer by getting rid of pocketful of change.

What has philosophy got to do with measuring anything? It's the mathematicians you have to trust, and they measure the skies like we measure a field.

What exactly is mathematics? Many have tried but nobody has really succeeded in defining mathematics; it is always something else.

What affected me most profoundly was the realization that the sciences of cryptography and mathematics are very elegant, pure sciences. I found that the ends for which these pure sciences are used are less elegant.

What cannot be known is more revealing than what can.

When a branch of mathematics ceases to interest any but the specialists, it is very near its death, or at any rate dangerously close to a paralysis, from which it can be rescued only by being plunged back into the vivifying source of the science.

What Is Mathematics? This question, if asked in earnest, has no answer.

What mathematics are to matter and force, occult science is to life and consciousness.

Without computers we will be stuck only proving theorems that have short proofs.

Wherefore in all great works are Clerks so much desired? Wherefore are Auditors so well-fed? What causeth Geometricians so highly to be enhaunsed? Why are Astronomers so greatly advanced? Because that by number such things they find, which else would farre excell mans minde.

When I give this talk to a physics audience, I remove the quotes from my 'Theorem'.

Wherever Mathematics is mixed up with anything, which is outside its field, you will find attempts to demonstrate these merely conventional propositions a priori, and it will be your task to find out the false deduction in each case.

Why do children dread mathematics? Because of the wrong approach. Because it is looked at as a subject.

With randomness it is very unlikely to be embarrassed, but even if you get embarrassed, you can't replicate it.

You are the mountain and the valley.

4.23..If 'thought' means: instance of the subject in a truth-procedure, then there is no thought of this thought, because it contains no knowledge.

You can not apply mathematics as long as words still becloud reality.

You know, I'm not terribly fast at my times tables, because that's not what I think mathematics is about.

You want to know how to rhyme, then learn how to add. It's mathematics.

4.19. Dedekind's approach is a singular combination of Descartes' Cogito and the idea of the idea in Spinoza. The starting point is the very space of the Cogito, as 'closed' configuration of all possible thoughts, existential point of pure thought. It is claimed (but only the Cogito assures us of this) that something like the set of all my possible thoughts exists. From Spinoza's causal 'serialism' (regardless of whether or not he figured in Dedekind's historical sources) are taken both the existence of a parallelism' which allows us to identify simple ideas by way of their object (Spinoza says: through the body of which the idea is an idea), and the existence of a reflexive redoubling, which secures the existence of 'complex' ideas, whose object is no longer a body, but another idea. For Spinoza, as for Dedekind, this process of reflexive redoubling must go to infinity. An idea of an idea (or the thought of a thought of an object) is an idea. So there exists an idea of the idea of a body, and so on.

99 percent of all statistics only tell 49 percent of the story.

A distinguished writer [Siméon Denis Poisson] has thus stated the fundamental definitions of the science: 'The probability of an event is the reason we have to believe that it has taken place, or that it will take place.' 'The measure of the probability of an event is the ratio of the number of cases favourable to that event, to the total number of cases favourable or contrary, and all equally possible' (equally like to happen). From these definitions it follows that the word probability, in its mathematical acceptation, has reference to the state of our knowledge of the circumstances under which an event may happen or fail. With the degree of information which we possess concerning the circumstances of an event, the reason we have to think that it will occur, or, to use a single term, our expectation of it, will vary. Probability is expectation founded upon partial knowledge. A perfect acquaintance with all the circumstances affecting the occurrence of an event would change expectation into certainty, and leave neither room nor demand for a theory of probabilities.

A brick can be used to represent the zero probability of this book being any good.

Add Snow White and her seven dwarfs, 2 droids for Luke Skywalker, of course. 1 true ring to rule them all. A decimal is a place to stall. Snow White's gone, the dwarfs alone. This system your next clue has shown. Now you might ask, this little key, Just what does it mean for me? Hold on tight and you will see, Someday it will set clues free.

Euclid's Elements has been for nearly twenty-two centuries the encouragement and guide of that scientific thought which is one thing with the progress of man from a worse to a better state. The encouragement; for it contained a body of knowledge that was really known and could be relied on, and that moreover was growing in extent and application. For even at the time this book was written—shortly after the foundation of the Alexandrian Museum—Mathematics was no longer the merely ideal science of the Platonic school, but had started on her career of conquest over the whole world of Phenomena. The guide; for the aim of every scientific student of every subject was to bring his knowledge of that subject into a form as perfect as that which geometry had attained. Far up on the great mountain of Truth, which all the sciences hope to scale, the foremost of that sacred sisterhood was seen, beckoning for the rest to follow her.

… Fourier's great mathematical poem ... {Referring to Joseph Fourier's mathematical theory of the conduction of heat, one of the precursors to thermodynamics.}

Ohm found that the results could be summed up in such a simple law that he who runs may read it, and a schoolboy now can predict what a Faraday then could only guess at roughly. By Ohm's discovery a large part of the domain of electricity became annexed by Coulomb's discovery of the law of inverse squares, and completely annexed by Green's investigations. Poisson attacked the difficult problem of induced magnetisation, and his results, though differently expressed, are still the theory, as a most important first approximation. Ampere brought a multitude of phenomena into theory by his investigations of the mechanical forces between conductors supporting currents and magnets. Then there were the remarkable researches of Faraday, the prince of experimentalists, on electrostatics and electrodynamics and the induction of currents. These were rather long in being brought from the crude experimental state to a compact system, expressing the real essence. Unfortunately, in my opinion, Faraday was not a mathematician. It can scarcely be doubted that had he been one, he would have anticipated much later work. He would, for instance, knowing Ampere's theory, by his own results have readily been led to Neumann's theory, and the connected work of Helmholtz and Thomson. But it is perhaps too much to expect a man to be both the prince of experimentalists and a competent mathematician.

Abel has left mathematicians enough to keep them busy for five hundred years.

Srinivasa Ramanujan was the strangest man in all of mathematics, probably in the entire history of science. He has been compared to a bursting supernova, illuminating the darkest, most profound corners of mathematics, before being tragically struck down by tuberculosis at the age of 33... Working in total isolation from the main currents of his field, he was able to rederive 100 years’ worth of Western mathematics on his own. The tragedy of his life is that much of his work was wasted rediscovering known mathematics.

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.

He is like the fox, who effaces his tracks in the sand with his tail. {Describing the writing style of famous mathematician Carl Friedrich Gauss}

A key ingredient in appreciating what mathematics is about is to realize that it is concerned with ideas, understanding, and communication more than it is with any specific brand of symbols....It is almost as if ideas set in mathematical form melt and become liquid and just as rivers can, from the most humble beginnings, flow for thousands of miles, through the most varied topography bringing nourishment and life with them wherever they go, so too can ideas cast in mathematical form flow far from their original sources, along well-defined paths, electrifying and dramatically affecting much of what they touch. pp. xii - xiii.

All of these video games are rotting my brain. I'm gonna go watch T.V. instead