Quotations by Gottfried Leibniz


[about him:]
It is rare to find learned men who are clean, do not stink and have a sense of humour.
[attributed variously to Charles Louis de Secondat Montesquieu and to the Duchess of Orléans]

Nothing is more important than to see the sources of invention which are, in my opinion more interesting than the inventions themselves.
Quoted in J Koenderink, Solid Shape (Cambridge Mass. 1990).

Musica est exercitium arithmeticae occultum nescientis se numerare animi
The pleasure we obtain from music comes from counting, but counting unconsciously. Music is nothing but unconscious arithmetic.
From a letter to Goldbach, 27 April 1712, quoted in O Sacks, The Man who Mistook his Wife for a Hat

He who understands Archimedes and Apollonius will admire less the achievements of the foremost men of later times.
Quoted in G Simmons Calculus Gems (New York 1992).

In symbols one observes an advantage in discovery which is greatest when they express the exact nature of a thing briefly and, as it were, picture it; then indeed the labor of thought is wonderfully diminished.
Quoted in G Simmons Calculus Gems (New York 1992).

The art of discovering the causes of phenomena, or true hypothesis, is like the art of decyphering, in which an ingenious conjecture greatly shortens the road.
New Essays Concerning Human Understanding

Although the whole of this life were said to be nothing but a dream and the physical world nothing but a phantasm, I should call this dream or phantasm real enough, if, using reason well, we were never deceived by it.
Quoted in J R Newman, The World of Mathematics (New York 1956).

The soul is the mirror of an indestructible universe.
The Monadology.

The imaginary number is a fine and wonderful resource of the human spirit, almost an amphibian between being and not being.
Quoted in A L Mackay, Dictionary of Scientific Quotations (London 1994)

Therefore, I have attacted [the problem of the catenary] which I had hitherto not attempted, and with my key [the differential calculus] happily opened its secret.
Acta eruditorum

Taking mathematics from the beginning of the world to the time of Newton, what he has done is much the better half.
Quoted in C B Boyer, A History of Mathematics (New York 1968)

The art of discovering the causes of phenomena, or true hypothesis, is like the art of decyphering, in which an ingenious conjecture greatly shortens the road.
New Essays Concerning Human Understanding It is unworthy of excellent men to lose hours like slaves in the labour of calculation which could safely be relegated to anyone else if machines were used.

Miracles are not to be multiplied beyond necessity.

The dot was introduced as a symbol for multiplication by Leibniz. On July 29, 1698, he wrote in a letter to Johann Bernoulli: "I do not like X as a symbol for multiplication, as it is easily confounded with x..."
Quoted in F Cajori, A History of Mathematical Notations (1928)

What is is what must be.

It is unworthy of excellent men to lose hours like slaves in the labor of calculation which could be relegated to anyone else if machines were used.


JOC/EFR April 2011

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