Logic is invincible because in order to combat logic it is necessary to use logic.
Physicists have come to realize that mathematics, when used with sufficient care, is a proven pathway to truth.
Outside observers often assume that the more complicated a piece of mathematics is, the more mathematicians admire it. Nothing could be further from the truth. Mathematicians admire elegance and simplicity above all else, and the ultimate goal in solving a problem is to find the method that does the job in the most efficient manner.
Geometry is one and eternal shining in the mind of God.
This is a mathematical universe. We are surrounded by equations and summations. Your life: the current state of your life and life itself is a direct summation of the equation you have created.
In many cases, mathematics is an escape from reality. The mathematician finds his own monastic niche and happiness in pursuits that are disconnected from external affairs. Some practice it as if using a drug.
There is no smallest among the small and no largest among the large; but always something still smaller and something still larger.
In the company of friends, writers can discuss their books, economists the state of the economy, lawyers their latest cases, and businessmen their latest acquisitions, but mathematicians cannot discuss their mathematics at all. And the more profound their work, the less understandable it is.
A set is a Many that allows itself to be thought of as a One.
Mathematics is not a deductive science - that`s a cliche. When you try to prove a theorem, you don`t just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork.
Life is good for only two things, discovering mathematics and teaching mathematics.
I like mathematics because it is not human and has nothing particular to do with this planet or with the whole accidental universe - because, like Spinoza`s God, it won`t love us in return.
One of the chief triumphs of modern mathematics consists in having discovered what mathematics really is.
The mathematician has reached the highest rung on the ladder of human thought.