Quotes on Mathematics

There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world.

Questions that pertain to the foundations of mathematics, although treated by many in recent times, still lack a satisfactory solution. Ambiguity of language is philosophy's main source of problems. That is why it is of the utmost importance to examine attentively the very words we use.

Many who have never had an opportunity of knowing any more about mathematics confound it with arithmetic, and consider it an arid science. In reality, however, it is a science which requires a great amount of imagination.

I am ever more intrigued by the correspondence between mathematics and physical facts. The adaptability of mathematics to the description of physical phenomena is uncanny.

The unreasonable efficiency of mathematics in science is a gift we neither understand nor deserve.

A lack of seriousness has led to all sorts of wonderful insights.

You know that I write slowly. This is chiefly because I am never satisfied until I have said as much as possible in a few words, and writing briefly takes far more time than writing at length.

Consequently he who wishes to attain to human perfection, must therefore first study Logic, next the various branches of Mathematics in their proper order, then Physics, and lastly Metaphysics.

Pure mathematics is on the whole distinctly more useful than applied... For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics.

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.

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.

Some persons have contended that mathematics ought to be taught by making the illustrations obvious to the senses. Nothing can be more absurd or injurious: it ought to be our never-ceasing effort to make people think, not feel.

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

Taking mathematics from the beginning of the world to the time when Newton lived, what he had done was much the better half.

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.

Men can construct a science with very few instruments, or with very plain instruments; but no one on earth could construct a science with unreliable instruments. A man might work out the whole of mathematics with a handful of pebbles, but not with a handful of clay which was always falling apart into new fragments, and falling together into new combinations. A man might measure heaven and earth with a reed, but not with a growing reed.

Mathematics may be compared to a mill of exquisite workmanship, which grinds you stuff of any degree of fineness; but, nevertheless, what you get out depends upon what you put in; and as the grandest mill in the world will not extract wheat-flour from peascods, so pages of formulae will not get a definite result out of loose data.

Mathematics is the tool specially suited for dealing with abstract concepts of any kind and there is no limit to its power in this field.

Mathematics is the only true metaphysics.

Mathematics is the science which draws necessary conclusions.

It is always noteworthy that all those who seriously study this science [the theory of numbers] conceive a sort of passion for it.