eight plus nine is congruent to five, modulo twelve.

Physics depends on a universe infinitely centred on an equals sign.

Luck is the grand equalizer.

E per tutto il giorno mi riempivano la testa di stronzate che volevano farmi tenere a mente, come ad esempio le equazioni per calcolare la distanza fra il posto dove ci trovavamo e quelle in...

{Replying to G. H. Hardy’s suggestion that the number of a taxi (1729) was ‘dull’, showing off his spontaneous mathematical genius}No, it is a very interesting number; it is the smallest number expressible as a...

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...

In adolescence, I hated life and was continually on the verge of suicide, from which, however, I was restrained by the desire to know more mathematics.

Mr Baley”, said Quemot, “you can’t treat human emotions as though they were built about a positronic brain”.”I’m not saying you can. Robotics is a deductive science and sociology an inductive one. But mathematics can...

The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and...

Questions that pertain to the foundations of mathematics, although treated by many in recent times, still lack a satisfactory solution. Ambiguity of language is philosophy’s main source of problems. That is why it is of...

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...

Magic is like a lot of other disciplines that people have recently begun developing, in historic terms. Working with magic is a way of understanding the universe and how it functions. You can approach it...

Women have a passion for mathematics. They divide their age in half, double the price of their clothes, and always add at least five years to the age of their best friend.

With me, everything turns into mathematics.

By simple mathematics giving is key to the world you seek to live in. If I take I alone gain. If I give or share then two at least are enriched.

[The Old Astronomer to His Pupil]Reach me down my Tycho Brahe, I would know him when we meet,When I share my later science, sitting humbly at his feet;He may know the law of all things,...

Programmers are not mathematicians, no matter how much we wish and wish for it.

Yes, we have to divide up our time like that, between our politics and our equations. But to me our equations are far more important, for politics are only a matter of present concern. A...

A mathematician is a magician who converts adjectives into nouns: continuous into continuum, infinite into infinity, infinitesimal into location, 0D into point, 1D into line, curved into geodesic…

I lose faith in mathematics, logical and rigid. What with those that even zero doesn’t accept?

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...

Mathematics is the music of reason.

In every department of physical science there is only so much science, properly so-called, as there is mathematics.

Of course, reading novels was just another form of escape. As soon as he closed their pages he had to come back to the real world. But at some point Tengo noticed that returning to...

But that can never be,” said Milo, jumping to his feet.”Don’t be too sure,” said the child patiently, “for one of the nicest things about mathematics, or anything else you might care to learn, is...

Mathemata mathematicis scribuntur.

The issue, then, is not, What is the best way to teach? but, What is mathematics really all about?… Controversies about…teaching cannot be resolved without confronting problems about the nature of mathematics.

The thing I want you especially to understand is this feeling of divine revelation. I feel that this structure was “out there” all along I just couldn’t see it. And now I can! This is...

Adaptability to change is itself a hallmark of successful education.

But there is another reason for the high repute of mathematics: it is mathematics that offers the exact natural sciences a certain measure of security which, without mathematics, they could not attain.

I studied mathematics which is the madness of reason.

The calculative exactness of practical life which the money economy has brought about corresponds to the ideal of natural science: to transform the world by mathematical formulas. Only money economy has filled the days of...

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...

Réduites à des théories générales, les mathématiques seraient une belle forme sans contenu.Reduced to general theories, mathematics would be a beautiful form without content.

[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...

I think a strong claim can be made that the process of scientific discovery may be regarded as a form of art. This is best seen in the theoretical aspects of Physical Science. The mathematical...

Jack had wondered how geometers could be so inventive as to produce so many types and families of curves. Later he had come to perceive that of curves there was no end, and the true...

Increasingly, the mathematics will demand the courage to face its implications.

the theorem of incompleteness . . . [shows] there is nothing on this level of existence that can fully explain this level of existence.

Proofs are to mathematics what spelling (or even calligraphy) is to poetry. Mathematical works do consist of proofs, just as poems do consist of words.

Its a mathematical fact that two negatives make a positive so even under adverse circumstances think positively.

Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music,...

Mathematics education is much more complicated than you expected, even though you expected it to be more complicated than you expected.

What, after all, is mathematics but the poetry of the mind, and what is poetry but the mathematics of the heart?

In short, if we adhere to the standard of perfection in all our endeavors, we are left with nothing but mathematics and the White Album.

Mathematics has always shown a curious ability to be applicable to nature, and this may express a deep link between our minds and nature. We are the Universe speaking out, a part of nature. So...

Mathematics, which most of us see as the most factual of all sciences, constitutes the most colossal metaphor imaginable, and must be judged, aesthetically as well as intellectually in terms of the success of this...

I am no friend of probability theory, I have hated it from the first moment when our dear friend Max Born gave it birth. For it could be seen how easy and simple it made...

Poincaré [was] the last man to take practically all mathematics, pure and applied, as his province. … Few mathematicians have had the breadth of philosophic vision that Poincaré had, and none in his superior in...

The ‘Muse’ is not an artistic mystery, but a mathematical equation. The gift are those ideas you think of as you drift to sleep. The giver is that one you think of when you first...