Constants and computations have inspired many authors. Here is a list of a few quotes.

1  Quotes on the constant p

And he made a molten sea, ten cubits from the one brim to the other; it was round all about ... and a line of thirty cubits did compass it round about.

Praise to Allah who knows the ratio of the diameter to the circumference ... and peace to Muhammad, the Chosen, the center of the circle of prophets. (In his Treatise on the circumference of the Circle, 1424 [1]. At the same time, he also computed p to an impressive 16 decimal places)

I am ashamed to tell you to how many figures I carried these calculations, having no other business at the time. (about a computation of p)

This mysterious 3.141592..., which comes in at every door and window, and down every chimney.

It is easier to square the circle than to get round a mathematician.

Whether any other Mathematician will appear, possessing sufficient leisure, patience, and facility of computation, to calculate the value of p to a still greater extent, remains to be seen: all that the Author can say is, he takes leave of the subject for the present ... (he spent a great part of his life in huge hand calculations of constants [11])

I shall risk nothing on an attempt to prove the transcendence of p. If others undertake this enterprise, no one will be happier than I in their success. But believe me, it will not fail to cost them some effort. (After his successful proof of the transcendence of the number e ; quoted by Maor [8])

Ten decimal places of p are sufficient to give the circumference of the earth to a fraction of an inch, and thirty decimal places would give the circumference of the visible universe to a quantity imperceptible to the most powerful microscope.

The value of p has engaged the attention of many mathematicians and calculators from the time of Archimedes to the present day, and has been computed from so many different formulae, that a complete account of its calculation would almost amount to a history of mathematics. (in his history of Euler's constant [5])

Ludolph's number p cannot be the root of any algebraic equation with (real or complex) rational coefficients. (in the famous article where Lindemann gave, for the first time, the proof of the transcendence of p [7])

It can be of no practical use to know that Pi is irrational, but if we can know, it surely would be intolerable not to know.

The history of pi is a quaint little mirror of the history of man.

2  On other constants

He is unworthy of the name of man who is ignorant of the fact that the diagonal of a square is incommensurable with its side.

... for the sake of brevity, we will always represent this number 2.718281828459... by the letter e. (in his remarkable book [4]) 

The letter e may now no longer be used to denote anything other than this positive universal constant. (quoted in [8])

Euler's constant (...) though of far less celebrity than p or e, has still strong claims to notice ... (also in [5])

There are certainly people who regard Ö2 as something perfectly obvious but jib at Ö[(-1)]. This is because they think they can visualise the former as something in physical space but not the latter. Actually Ö[(-1)] is a much simpler concept.

At the present day it is perhaps somewhat difficult to form an adequate conception of the greatness of Napier's invention ; yet it is beyond all question that the invention of logarithms marks an epoch in the history of science. (During Napier Tercentenary Exhibition)

Apéry's incredible proof appears to be a mixture of miracles and mysteries. (On the proof of the irrationality of z(3) by Roger Apéry in 1978 [10])

Like the existence of odd perfect numbers, the irrationality of g is a fitting challenge for anyone hoping to achieve mathematical immortality. [3].

3  Miscellaneous

3.0.1  Numbers

Defendit numerus. (there is safety in numbers)

I am ill at these numbers. (Hamlet : Act II, Scene 2)

Perfect numbers like perfect men are very rare.

Round numbers are always false. (1750 given in [6])

God does arithmetic.

Mathematics is the queen of sciences and arithmetic is the queen of mathematics.

Numbers are intellectual witnesses that belong only to mankind.

3.0.2  Computation

A good calculator does not need artificial aids. (Tao Te Ching)

He who can properly define and divide is to be considered a god.

Nature laughs at the difficulties of integration.

You have no idea, how much poetry there is in the calculation of a table of logarithms! (to his students [9])

3.0.3  Mathematicians

Euler and Ramanujan are mathematicians of the greatest importance in the history of constants. (and of course in the history of Mathematics ...)

Read Euler, read Euler. He is the master of us all.

Euler calculated without apparent effort, as men breathe, or as eagles sustain themselves in the wind.

I can strongly recommend the applicant. He is a young man of quite exceptional capacity in mathematics and especially in work relating to numbers. He has a natural aptitude for computation and is very quick at figure work. (a recommendation by a professor of Mathematics, the young man is the great Ramanujan)

... they must be true, because if they were not true, no one would have had the imagination to invent them. (about formulas that Ramanujan sent to the British mathematician Hardy [2])


L. Berggren, J. Borwein, P. Borwein, Pi : A Source Book, Springer, (1997)

J.M. Borwein and P.B. Borwein, Ramanujan and Pi, Scientific American, (1988), p. 112-117

W. Dunham, Euler The Master of Us All, The Mathematical Association of America, (1999)

L. Euler, Introduction à l'analyse infinitésimale (french traduction by Labey), Barrois, ainé, Librairie, (original 1748, traduction 1796), vol. 1

J.W.L. Glaisher, History of Euler's constant, Messenger of Math., (1872), vol. 1, p. 25-30

D.E. Knuth, The Art of Computer Programming, Vol. II, Seminumerical Algorithms, Addison Wesley, (1998)

F. Lindemann, Ueber die Zahl p, Mathematische Annalen, (1882), vol. 20, p. 213-225

E. Maor, e: The Story of a Number, Princeton University Press, (1994)

J. Muir, Of Men and Numbers, Dover Publications, New York, (1996, first edition 1961)

A. van der Poorten, A Proof that Euler Missed ..., Apéry's Proof of the Irrationality of z(3), The Mathematical Intelligencer, (1979), vol. 1, p. 195-203

W. Shanks, Contributions to Mathematics Comprising Chiefly the Rectification of the Circle to 607 Places of Decimals, G. Bell, London, (1853)

Related link on quotations

We took one or two quotations from the excellent site of the Furman University and collected by Mark R. Woodard. The site is entirely dedicated to mathematical quotations.