Mathematical Quotations

Let no one ignorant of geometry enter here.
Plato (429-347 BC). Inscription written over the entrance to his Academy.

It is impossible to calculate accurately events that are determined by chance.
Thucydides (c. 400 BC).

Quod erat demonstrandum.
[Which was to be proved.]

Euclid (c.300 BC). Elements, I:5

Eureka!
Archimedes (c.287-212 BC).

All science requires mathematics.
Roger Bacon (c.1214-c.1292). Opus Maius, Pt. IV

When it is not in our power to follow what is true, we ought to follow what is most probable.
Rene Descartes (1596-1650).

Rules for demonstration:
1. Do not attempt to demonstrate any of those things so self evident that we have nothing clearer to prove them by.

Blaise Pascal (1623-1662).

Life is good for only two things, discovering mathematics and teaching mathematics.
Siméon Poisson (1781-1840).

There are three kinds of lies: lies, damned lies, and statistics.
Benjamin Disraeli (1804-1881).

A mathematician may say anything he pleases, but a physicist must be at least partially sane.
Josiah Willard Gibbs (1839-1903).

Mathematics ... would certainly have not come into existence if one had known from the beginning that there was in nature no exactly straight line, no actual circle, no absolute magnitude.
Friedrich Nietzsche (1844-1900). Human, All Too Human.

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.
Bertrand Russell (1872-1970). Mysticism and Logic, Ch. 4

Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is, of which it is supposed to be true.
Bertrand Russell (1872-1970). Mysticism and Logic, Ch. 5

Beauty is the first test: there is no permanent place in the world for ugly mathematics.
Godfrey H. Hardy (1877-1947). A Mathematician's Apology p.25

As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.
Albert Einstein (1879-1955). The Tao of Physics, Ch. 2

It is now quite lawful for a Catholic woman to avoid pregnancy by a resort to mathematics, though she is still forbidden to resort to physics and chemistry.
H.L. Mencken (1880-1956). Notebooks, 'Minority Report'.

Proof is an idol, before which the mathematician tortures himself.
Sir Arthur Eddington (1882-1944).

We must believe in luck. Otherwise, how can we explain the success of those we don't like?
Jean Cocteau (1889-1963).

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.
Paul Dirac (1902-1984) The Mathematical Experience.

Statistician: a man who can go straight from an unwarranted assumption to a preconceived conclusion.
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