... the most essential characteristic of mind is memory, using this word in its broadest sense to include every influence of past experience on present reactions...

Although this may seem a paradox, all exact science is dominated by the idea of approximation. When a man tells you that he knows the exact truth about anything, you are safe in infering that he is an inexact man. Every careful measurement in science is always given with the probable error... every observer admits that he is likely wrong, and knows about how much wrong he is likely to be.

Aristotle maintained that women have fewer teeth than men; although he was twice married, it never occurred to him to verify this statement by examining his wives' mouths.

At the age of eleven, I began Euclid, with my brother as my tutor.... I had not imagined that there was anything so delicious in the world. After I had learned the fifth proposition, my brother told me that it was generally considered difficult, but I had found no difficulty whatsoever. This was the first time it had dawned on me that I might have some intelligence.

Broadly speaking, we are in the middle of a race between human skill as a means and human folly as an end.

But it is just this characteristic of simplicity in the laws of nature hitherto discovered which it would be fallacious to generalize, for it is obvious that simplicity has been a part cause of their discovery, and can, therefore, give no ground for the supposition that other undiscovered laws are equally simple

Can a society in which thought and technique are scientific persist for a long period, as, for example, ancient Egypt persisted, or does it necessarily contain within itself forces which must bring either decay or explosion?

Even if the open windows of science at first make us shiver after the cozy indoor warmth of traditional humanizing myths, in the end the fresh air brings vigor, and the great spaces have a splendor of their own.

In attempting to understand the elements out of which mental phenomena are compounded, it is of the greatest importance to remember that from the protozoa to man there is nowhere a very wide gap either in structure or in behaviour. From this fact it is a highly probable inference that there is also nowhere a very wide mental gap..

John Locke invented common sense, and only Englishmen have had it ever since!

Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.

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 georgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. (1902)

Of these austerer virtues the love of truth is the chief, and in mathematics, more than elsewhere, the love of truth may find encouragement for waning faith. Every great study is not only an end in itself, but also a means of creating and sustaining a lofty habit of mind; and this purpose should be kept always in view throughout the teaching and learning of mathematics.

One must expect a war between U.S.A. and U.S.S.R. which will begin with the total destruction of London. I think the war will last 30 years, and leave a world without civilised people, from which everything will have to build afresh—a process taking (say) 500 years.
Stated just one month after the Hiroshima atomic explosion. Russell became one of the best-known antinuclear activists of his era.

One of the chiefest triumphs of modern mathematics consists in having discovered what mathematics really is.

One of the symptoms of approaching nervous breakdown is the belief that one's work is terribly important.

Only mathematics and mathematical logic can say as little as the physicist means to say. (1931)

Organic life, we are told, has developed gradually from the protozoan to the philosopher, and this development, we are assured, is indubitably an advance. Unfortunately it is the philosopher, not the protozoon, who gives us this assurance.

People are born ignorant, not stupid; they are made stupid by education.

Philosophy is that part of science which at present people chose to have opinions about, but which they have no knowledge about. Therefore every advance in knowledge robs philosophy of some problems which formerly it had …and will belong to science.

Physics, owing to the simplicity of its subject matter, has reached a higher state of devlopment than any other science. (1931)

Remote from human passions, remote even from the pitiful facts of nature, the generations have gradually created an ordered cosmos [mathematics], where pure thought can dwell in its natural home...

Science is what you more or less know and philosophy is what you do not know.

Scientific method, although in its more refined forms it may seem complicated, is in essence remarkably simply. It consists in observing such facts as will enable the observer to discover general laws governing facts of the kind in question. The two stages, first of observation, and second of inference to a law, are both essential, and each is susceptible of almost indefinite refinement. (1931)

The examination system, and the fact that instruction is treated mainly as a training for a livelihood, leads the young to regard knowledge from a purely utilitarian point of view as the road to money, not as the gateway to wisdom.

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 first man who said 'fire burns' was employing scientific method, at any rate if he had allowed himself to b e burnt several times. This man had already passed through the two stages of observation and generalization. He had not, however, what scientific technique demands—a careful choice of significant facts on the one hand, and, on the other hand, various means of arriving at laws otherwise than my mere generalization. (1931)

The human race may well become extinct before the end of the century. Speaking as a mathematician, I should say the odds are about three to one against survival.

The more we realize our minuteness and our impotence in the face of cosmic forces, the more amazing becomes what human beings have achieved.

The most savage controversies are those about matters as to which there is no good evidence either way. Persecution is used in theology, not in arithmetic.

The scientific attitude of mind involves a sweeping away of all other desires in the interest of the desire to know.

The trouble with the world is that the stupid are cocksure and the intelligent full of doubt.

The true spirit of delight, the exaltation, the sense of being more than man, which is the touchstone of highest excellence, is to be found in mathematics as surely as in poetry.

The universe may have a purpose, but nothing we know suggests that, if so, this purpose has any similarity to ours.

There are infinite possibilities of error, and more cranks take up fashionable untruths than unfashionable truths.

Three passions, simple but overwhelmingly strong, have governed my life: the longing for love, the search for knowledge, and unbearable pity for the suffering of mankind.

To a mind of sufficient intellectual power, the whole of mathematics would appear trivial, as trivial as the statement that a four-footed animal is an animal. (1959)

To be able to fill leisure intelligently is the last product of civilization.

What Galileo and Newton were to the seventeenth century, Darwin was to the nineteenth.

What is best in mathematics deserves not merely to be learnt as a task, but to assimilated as a part of daily thought, and brought again and again before the mind with ever-renewed encouragement.

William James used to preach the 'will to believe'. For my part, I should wish to preach the 'will to doubt.' … What is wanted is not the will to believe, but the wish to find out, which is the exact opposite.

William James used to preach the 'will to believe.' For my part, I should wish to preach the 'will to doubt' ... what is wanted is not the will to believe, but the wish to find out, which is the exact opposite.

Work is of two kinds: first, altering the position of matter at or near the earth's surface relative to other such matter; second, telling other people to do so. The first kind is unpleasant and ill paid; the second is pleasant and highly paid.

[Man] ... his origin, his growth, his hopes and fears, his loves and his beliefs are but the outcome of accidental collocations of atoms; that no fire, no heroism, no intensity of thought and feeling can preserve an individual life beyond the grave; that all the labour of the ages, all the devotion, all the inspiration, all the noonday brightness of human genius are destined to extinction in the vast death of the solar system, and that the whole temple of Man's achievement must inevitably be buried beneath the debris of a universe in ruins...