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Mathematics Quotes

The top contributors are mostly people who wrote about mathematics: Jane Frances McDonnell, G. F. J. Temple, Stanislaw Ulam, Bertrand Russell and Morris Kline. The best-sourced lines, though, are by William Blake, filed here for the word infinity. They include “To see a World in a Grain of Sand” from Auguries of Innocence (1803) and the cleansing of the doors of perception in The Marriage of Heaven and Hell (1790).

Three entries are flagged. “Mathematics is the key and door to the sciences” is credited to Galileo and marked misattributed. A line saying the highest form of pure thought is in mathematics is credited to Plato and disputed. So is the claim that the ultimate goal of mathematics is to eliminate any need for intelligent thought, credited to Alfred North Whitehead.

Random quote on Mathematics

Most quoted on mathematics:

The infinite turns out to be the contrary of what it is said to be. It is not what has nothing outside it that is infinite, but what always has something outside it.

Aristotle

If in other sciences we should arrive at certainty without doubt and truth without error, it behooves us to place the foundations of knowledge in mathematics...

Roger Bacon

Aristotle had considered the question of whether space is infinite and gave six nonmathematical arguments to prove that it is finite; he foresaw that this question would be troublesome.

Morris Kline Mathematical Thought from Ancient to Modern Times (1972)

Ruth felt that math was like sex—get all you can, but best not done in public.

Gregory Benford The Sigma Structure Symphony (2012)

The historical approach introduces us personally to the great mathematicians and infuses a humane and genial spirit into what can be the most arid and abstract study.

George Frederick James Temple

Ordinary language is totally unsuited for expressing what physics really asserts, since the words of everyday life are not sufficiently abstract. Only mathematics and mathematical logic can say as little as the physicist means to say.

Bertrand Russell The Scientific Outlook (1931)

The fear of infinity is a form of myopia that destroys the possibility of seeing the actual infinite, even though it in its highest form has created and sustains us, and in its secondary transfinite forms occurs all around us and even inhabits our minds.

Georg Cantor Infinity and the Mind (1995)

Mathematics takes us still further from what is human, into the region of absolute necessity, to which not only the world, but every possible world, must conform.

Bertrand Russell The Study of Mathematics (1907)

Mathematics as an Element in the History of Thought.

Alfred North Whitehead Science and the Modern World (1925)

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 in the analysis of Symbolic Logic itself.

Bertrand Russell Principles of Mathematics (1903)

I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of science, whatever the matter may be.

William Thomson

The potential infinite means nothing other than an undetermined, variable quantity, always remaining finite, which has to assume values that either become smaller than any finite limit no matter how small, or greater than any finite limit no matter how great.

Georg Cantor

Where there is life there is a pattern, and where there is a pattern there is mathematics. Once that germ of rationality and order exists to turn a chaos into a cosmos, then so does mathematics. There could not be a non-mathematical Universe containing living observers.

John D. Barrow The Artful Universe (1995)

As to the query whether the finite parts of a limited continuum [continuo terminato] are finite infinite in number I will... answer that they are neither finite or infinite.

Galileo Galilei

What does infinity mean to you? Are you not infinity and yourself?

Dejan Stojanovic

There are no absolutes... in mathematics or in its history.

Eric Temple Bell The Development of Mathematics (1940)

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.

Bertrand Russell

[A]ll things which can be known have number; for it is not possible that without number anything can either be conceived or known.

Philolaus

Mathematics ought properly to be a model of logical clarity. In actual fact there are perhaps no scientific works where you will find more wrong expressions, and consequently wrong thoughts, than in mathematical ones.

Gottlob Frege What is a Function? (1904)

It’s really beautiful to observe, as you progress in your mathematical maturity, how everything is somehow connected.

Sylvia Serfaty

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