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 are well and good but nature keeps dragging us around by the nose.

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...

In Mathematics the art of proposing a question must be held of higher value than solving it.

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

dialect” are themselves fuzzy.

Real mathematics must be justified as art if it can be justified at all.

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...

Infinite is a meaningless word: except – it states / The mind is capable of performing / an endless process of addition.

Seven.” Switch to eight, and the majority of humanity was lost.

Always preoccupied with his profound researches, the great Newton showed in the ordinary-affairs of life an absence of mind which has become proverbial. It is related that one day, wishing to find the number of...

Mathematics is the music of reason. To do mathematics is to engage in an act of discovery and conjecture, intuition and inspiration; to be in a state of confusion—not because it makes no sense to...

In his school, Bertrand Russell thought it was better if they had the sex, so they could give their undivided attention to mathematics, which was the main thing.

There is no great religion without a great schism. All of them have it. And that’s because you’re dealing with something called faith. And faith is not something you can prove; faith is personal opinion....

I could never have gone far in any science because on the path of every science the lion Mathematics lies in wait for you.

He possesses the minimum sensibility necessary for his intelligence not to be merely mathematical, the minimum a human being needs so that it can be proven with a thermometer that he’s not dead.

More often than not, at the end of the day (or a month, or a year), you realize that your initial idea was wrong, and you have to try something else. These are the moments...

A Puritan twist in our nature makes us think that anything good for us must be twice as good if it’s hard to swallow. Learning Greek and Latin used to play the role of character...

It appears that the solution of the problem of time and space is reserved to philosophers who, like Leibniz, are mathematicians, or to mathematicians who, like Einstein, are philosophers.

If we increase r [in a logistic map] even more, we will eventually force the system into a period-8 limit cycle, then a period-16 cycle, and so on. The amount that we have to increase...

Music is the pleasure the human mind experiences from counting without being aware that it is counting.

Nothing takes place in the world whose meaning is not that of some maximum or minimum.

If there is anything that can bind the mind of man to this dreary exile of our earthly home and can reconcile us with our fate so that one can enjoy living,—then it is verily...

The analytical geometry of Descartes and the calculus of Newton and Leibniz have expanded into the marvelous mathematical method—more daring than anything that the history of philosophy records—of Lobachevsky and Riemann, Gauss and Sylvester. Indeed,...

Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality. Though...

My first feeling was that there was no way to continue. Writing isn’t like math;in math, two plus two always equals four no matter what your mood is like. With writing, the way you feel...

Since the mathematicians have invaded the theory of relativity, I do not understand it myself anymore.

Atheism is the opium of the mathematicians. Atheism is the religion of Mathematics.

PHI is one H of a lot cooler than PI!

… I left Caen, where I was living, to go on a geological excursion under the auspices of the School of Mines. The incidents of the travel made me forget my mathematical work. Having reached...

Mathematics is not a book confined within a cover and bound between brazen clasps, whose contents it needs only patience to ransack; it is not a mine, whose treasures may take long to reduce into...

The full impact of the Lobachevskian method of challenging axioms has probably yet to be felt. It is no exaggeration to call Lobachevsky the Copernicus of Geometry [as did Clifford], for geometry is only a...

One can be enlightened about proofs as well as theorems. Without enlightenment, one is merely reduced to memorizing proofs. With enlightenment about a proof, its flow becomes clear and it can become an item of...

We are not told, or not told early enough so that it sinks in, that mathematics is a language, and that we can learn it like any other, including our own. We have to learn...

Whenever I meet in Laplace with the words ‘Thus it plainly appears’, I am sure that hours and perhaps days, of hard study will alone enable me to discover how it plainly appears.

But then, if if sex were the same thing as math, a lot more people would be lining up to take calculus.

No mathematician in the world would bother making these senseless distinctions: 2 1/2 is a “mixed number ” while 5/2 is an “improper fraction.” They’re EQUAL for crying out loud. They are the exact same...

Patience is my virtue, but only in Math, Daddy,” – Ashley

[Mathematics] is security. Certainty. Truth. Beauty. Insight. Structure. Architecture. I see mathematics, the part of human knowledge that I call mathematics, as one thing—one great, glorious thing. Whether it is differential topology, or functional analysis,...

Nothing comforted Sabine like long division. That was how she had passed time waiting for Phan and then Parsifal to come back from their tests. She figured the square root of the date while other...

I do not think the division of the subject into two parts – into applied mathematics and experimental physics a good one, for natural philosophy without experiment is merely mathematical exercise, while experiment without mathematics...

For other great mathematicians or philosophers, he used the epithets magnus, or clarus, or clarissimus; for Newton alone he kept the prefix summus.

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...

A term meant to convey a person’s inability to make sense of the numbers that run their lives.

Immortality” may be a silly word, but probably a mathematician has the best chance of whatever it may mean.

Lagrange, in one of the later years of his life, imagined that he had overcome the difficulty (of the parallel axiom). He went so far as to write a paper, which he took with him...

I have stressed this distinction because it is an important one. It defines the fundamental difference between probability and statistics: the former concerns predictions based on fixed probabilities; the latter concerns the inference of those...