When we are young, we spend much time and pains in filling our note-books with all definitions of Religion, Love, Poetry, Politics, Art, in the hope that, in the course of a few years, we...

Humans are like Variables in mathematics, some Dependent, some Independent. Variables are in relationship but remain Variable. Of course, there are some Constants too both in mathematics and humans. Constants help define precisely the relationship...

The algebraic sum of all the transformations occurring in a cyclical process can only be positive, or, as an extreme case, equal to nothing.[Statement of the second law of thermodynamics, 1862]

There was, I think, a feeling that the best science was that done in the simplest way. In experimental work, as in mathematics, there was ‘style’ and a result obtained with simple equipment was more...

Mathematics is a terrible calling. It’s as merciless as gravity. It swallows the soul. There’s a point near a black hole called the last stable orbit. Once you drop below that radius, no force in...

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...

Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing. It is essential not...

Mathematicians deal with large numbers sometimes, but never in their income.

…and his analysis proved him to be the first of theoretical astronomers no less than the greatest of ‘arithmeticians.

I started studying law, but this I could stand just for one semester. I couldn’t stand more. Then I studied languages and literature for two years. After two years I passed an examination with the...

Ideas that require people to reorganize their picture of the world provoke hostility.

Mathematics began to seem too much like puzzle solving. Physics is puzzle solving, too, but of puzzles created by nature, not by the mind of man.

I had a polynomial once. My doctor removed it.

Poincaré was a vigorous opponent of the theory that all mathematics can be rewritten in terms of the most elementary notions of classical logic; something more than logic, he believed, makes mathematics what it is.

Logic, it is often said, is the study of valid arguments. It is a systematic attempt to distinguish valid arguments from invalid arguments.

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...

Soon after I began working for the Professor, I realized that he talked about numbers whenever he was unsure of what to say or do. Numbers were also his way of reaching out to the...

The mere formulation of a problem is far more essential than its solution, which may be merely a matter of mathematical or experimental skills. To raise new questions, new possibilities, to regard old problems from...

A mathematician says that an electromagnetic wave travels from Andromeda to your eye and that it also extends from Andromeda to your eye.

The manner of Demoivre’s death has a certain interest for psychologists. Shortly before it, he declared that it was necessary for him to sleep some ten minutes or a quarter of an hour longer each...

In the judgment of the most competent living mathematicians, Fraulein Noether was the most significant mathematical genius thus far produced since the higher education of women began.

I know that two and two make four – and should be glad to prove it too if I could – though I must say if by any sort of process I could convert 2...

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,...

It’s a simple matter of mathematics.

Mathematics is much more than a language for dealing with the physical world. It is a source of models and abstractions which will enable us to obtain amazing new insights into the way in which...

Facts are stubborn things, but statistics are more pliable.

In any case, do you really think kids even want something that is relevant to their daily lives? You think something practical like compound interest is going to get them excited? People enjoy fantasy, and...

Before an experiment can be performed, it must be planned—the question to nature must be formulated before being posed. Before the result of a measurement can be used, it must be interpreted—nature’s answer must be...

The ingenious method of expressing every possible number using a set of ten symbols (each symbol having a place value and an absolute value) emerged in India. The idea seems so simple nowadays that its...

The study of mathematics is apt to commence in disappointment… We are told that by its aid the stars are weighed and the billions of molecules in a drop of water are counted. Yet, like...

It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important...

Mathematics has the inhuman quality of starlight, brilliant and sharp, but cold.

Making mathematics accessible to the educated layman, while keeping high scientific standards, has always been considered a treacherous navigation between the Scylla of professional contempt and the Charybdis of public misunderstanding.

As is well known the principle of virtual velocities transforms all statics into a mathematical assignment, and by D’Alembert’s principle for dynamics, the latter is again reduced to statics. Although it is is very much...

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...

Children must be taught mathematics well in anywhere under every condition at every age and so we can have more rational, more logical societies!

Only dead mathematics can be taught where competition prevails: living mathematics must always be a communal possession.

You’re probably better at math than I am, because pretty much everyone’s better at math than I am, but it’s okay, I’m fine with it. See, I excel at other, more important things—guitar, sex, and...

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...

. . . we come astonishingly close to the mystical beliefs of Pythagoras and his followers who attempted to submit all of life to the sovereignty of numbers. Many of our psychologists, sociologists, economists and...

And I’ll go even further and say that mathematics, this art of abstract pattern-making — even more than storytelling, painting, or music – is our most quintessentially human art form. This is what our brains...

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

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...

As for methods I have sought to give them all the rigour that one requires in geometry, so as never to have recourse to the reasons drawn from the generality of algebra.

[As a young teenager] Galois read Legendre]’s geometry from cover to cover as easily as other boys read a pirate yarn.

I have been able to solve a few problems of mathematical physics on which the greatest mathematicians since Euler have struggled in vain … But the pride I might have held in my conclusions was...

There was a seminar for advanced students in Zürich that I was teaching and von Neumann was in the class. I came to a certain theorem, and I said it is not proved and it...

There cannot be a language more universal and more simple, more free from errors and obscurities…more worthy to express the invariable relations of all natural things [than mathematics]. [It interprets] all phenomena by the same...

Every formula which expresses a law of nature is a hymn of praise to God.

I think we need more math majors who don’t become mathematicians. More math major doctors, more math major high school teachers, more math major CEOs, more math major senators. But we won’t get there unless...