Knowledge is power.
For whatever deserves to exist deserves also to be known, for knowledge is the image of existance.
E. T. Bell
Obvious is the most dangerous word in mathematics.
The essense of mathematics resides in its freedom.
Algebra is generous; she often gives more than is asked of her.
I think, therefore I am
M. C. Escher
He who wonders, discovers that this in itself is a wonder.
Everything should be made as simple as possible, but not simpler.
Pure mathematics is, in its way, the poetry of logical ideas.
Do not worry too much about your difficulties in mathematics, I can assure you that mine are still greater.
If we knew what it was we were doing, it would not be called research, would it?
In questions of science the authority of a thousand is not worth the humble reasoning of an individual.
The Universe is a grand book which cannot be read until one first learns to comprehend the language and become familiar with the characters in which it is composed. That language is mathematics.
You cannot teach a man anything, you can only help him find it within himself.
Mathematics is the queen of the sciences, and number theory is the queen of mathematics.
Omar Khayyam(Early Persian Mathematician and poet)
The Moving Hand writes, and having writ,
Moves on; not all thy Piety nor Wit
Shall lure it back to cancel half a line,
Nor all thy Tears wash out a Word of it.
I think that modern physics has definitely decided in favor of Plato. In fact the smallest units of matter are not physical objects in the ordinary sense; they are forms, ideas which can be expressed unambiguously only in mathematical language.
The infinite! No other question has ever moved so profoundly the spirit of man.
Logic is the anatomy of thought.
I tell them if they will occupy themselves with the study of mathematics they will find in it the best remedy against the sins of the flesh. (Commentary: Well, not quite!)
I do not know what I may appear to the world, but to myself I seem to have been only a boy playing on the sea shore, and diverting myself now and then finding a smoother pebble or a prettier sea shell than ordinary whilst the great ocean of truth lay all undiscovered before me.
If I have seen farther than others, it is because I have stood on the shoulders of giants.
Geometry existed before creation.
He is unworthy of the name of man who is ignorant that the diagonal of a square is incommensurate with its side.
Jules Henri Poincare(Father of Algebraic Topology)
To doubt everything or to believe everything are two equally convenient solutions; both dispense with the necessity of reflection.
Science is built with facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house.
It is far better to foresee even without certainty than not to foresee at all.
The scientist does not study Nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful. If Nature were not beautiful, it would not be worth knowing, and if Nature were not worth knowing, life would not be worth living.
There is geometry in the humming of the strings.
Mathematics takes us still further from what is human into the region of absolute necessity, to which not only the actual world, but every possible world, must conform.
A mathematician who is not also something of a poet will never be a complete mathematician.
A. N. Whitehead
The pursuit of mathematics is a divine madness of the human spirit.