Bertrand Russell Quotes

There exists, if I am not mistaken, an entire world which is the totality of mathematical truths, to which we have access only with our mind, just as a world of physical reality exists, the one like the other independent of ourselves, both of divine creation.

The enchanting charms of this sublime science reveal only to those who have the courage to go deeply into it.

I have found a very great number of exceedingly beautiful theorems.

I enjoyed like nothing else working in pure math, discovering new formulas.

Mathematicians aren't motivated by money and material gain, or even by practical applications of their work. For us it's the glory of solving one of the great unsolved problems that have outwitted previous generations of mathematicians. …. Despite all the things we've discovered over the last 7 millennia, there are still many things we don't understand.

Math research is more like a marathon.

You have to spend some energy and effort to see the beauty of math.

God made the integers, man made the rest.

I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our "creations," are simply the notes of our observations.

317 is a prime, not because we think so, or because our minds are shaped in one way rather than another, but because it is so, because mathematical reality is built that way.

That was the wonderful thing about Ramanujan. He discovered so much, and yet he left so much more in his garden for other people to discover.

The kind of knowledge which is supported only by observations and is not yet proved must be carefully distinguished from the truth; it is gained by induction, as we usually say. Yet we have seen cases in which mere induction led to error. Therefore, we should take great care not to accept as true such properties of the numbers which we have discovered by observation and which are supported by induction alone. Indeed, we should use such a discovery as an opportunity to investigate more exactly the properties discovered and to prove or disprove them; in both cases we may learn something useful.

We are on the verge: Today our program proved Fermat's next-to-last theorem.

The trouble with integers is that we have examined only the very small ones. Maybe all the exciting stuff happens at really big numbers, ones we can't even begin to think about in any very definite way. Our brains have evolved to get us out of the rain, find where the berries are, and keep us from getting killed. Our brains did not evolve to help us grasp really large numbers or to look at things in a hundred thousand dimensions.

The true spirit of delight...is to be found in mathematics as surely as in poetry.

A great deal of my work is just playing with equations and seeing what they give.

The fact that all Mathematics is Symbolic Logic is one of the greatest discoveries of our age; and when this fact has been established, the remainder of the principles of mathematics consists of the analysis of Symbolic Logic itself.

The pretence that numbers are not the humble creation of man, but are the exacting language of the Universe and therefore possess the secret of all things, is comforting, terrifying and mesmeric.

Physicists have come to realize that mathematics, when used with sufficient care, is a proven pathway to truth.

If you are receptive and humble, mathematics will lead you by the hand. Again and again, when I have been at a loss how to proceed, I have just had to wait until I have felt the mathematics led me by the hand. It has led me along an unexpected path, a path where new vistas open up, a path leading to new territory, where one can set up a base of operations, from which one can survey the surroundings and plan future progress.

He that gives a portion of his time and talent to the investigation of mathematical truth, will come to all other questions with a decided advantage over his opponents.

Mathematics is not a contemplative but a creative subject.

Mathematics is the surest way to immortality. If you make a big discovery in mathematics, you will be remembered after everyone else will be forgotten

I had made an empirical discovery and it carried all the weight of a mathematical proof.

Regarding the fundamental investigations of mathematics, there is no final ending ... no first beginning.