Galileo Galilei

View the biography of Galileo Galilei

[The universe] cannot be read until we have learnt the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word.
Opere Il Saggiatore p. 171.
Measure what is measurable, and make measurable what is not so.
Quoted in I Gordonand and S Sorkin, The Armchair Science Reader (New York 1959).
And who can doubt that it will lead to the worst disorders when minds created free by God are compelled to submit slavishly to an outside will? When we are told to deny our senses and subject them to the whim of others? When people devoid of whatsoever competence are made judges over experts and are granted authority to treat them as they please? These are the novelties which are apt to bring about the ruin of commonwealths and the subversion of the state.
On the margin of his own copy of Dialogue on the Great World Systems.
Quoted in J R Newman, The World of Mathematics (New York 1956)
In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual.
Quoted in Arago, Eulogy of Galileo (1874)
Take note, theologians, that in your desire to make matters of faith out of propositions relating to the fixity of sun and earth you run the risk of eventually having to condemn as heretics those who would declare the earth to stand still and the sun to change position -- eventually, I say, at such a time as it might be proved that the earth moves and the sun stands still.
Epur si muove

[And yet it does move.]
Apocryphal words to himself after making his abjuration of heliocentricity.
I wish, my dear Kepler, that we could have a good laugh together at the extraordinary stupidity of the mob. What do you think of the foremost philosophers of this University? In spite of my oft-repeated efforts and invitations, they have refused, with the obstinacy of a glutted adder, to look at the planets or Moon or my telescope.
I mentally conceive of some movable projected on a horizontal plane all impediments being put aside. Now it is evident ... that the equable motion on this plane would be perpetual if the plane were of infinite extent; but if we assume it to be ended, and [situated] on high, the movable ... , driven to the end of the plane and going on further, adds on to its previous equable and indelible motion that downward tendency which it has from its own heaviness. Thus there emerges a certain motion, compounded from equable horizontal and from naturally accelerated downward [motion], which I call projection.
Two New Sciences 1638
Infinities and indivisibles transcend our finite understanding, the former on account of their magnitude, the latter because of their smallness; Imagine what they are when combined.
Two New Sciences 1638
Among the great men who have philosophized about [the action of the tides], the one who surprised me most is Kepler. He was a person of independent genius, [but he] became interested in the action of the moon on the water, and in other occult phenomena, and similar childishness.
It is very pious to say and prudent to affirm that the holy Bible can never speak untruth -- whenever its true meaning is understood. But I believe nobody will deny that it is often very abstruse, and may say things which are quite different from what its bare words signify.
Infinities and indivisibles transcend our finite understanding, the former on account of their magnitude, the latter because of their smallness; Imagine what they are when combined.
Quoted in E Maor, To infinity and beyond (Princeton 1991)
To excite in us tastes, odors, and sounds I believe that nothing is required in external bodies except shapes, numbers, and slow or rapid movements. ... if ears, tongues, and noses were removed, shapes and numbers and motions would remain, but not odors or tastes or sounds.
The Divine intellect indeed knows infinitely more propositions [than we can ever know]. But with regard to those few which the human intellect does understand, I believe that its knowledge equals the Divine in objective certainty.
Dialogue on the Great World Systems
The laws of Nature are written in the language of mathematics ... the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word.
Quoted in M Kline, Mathematical thought from ancient to modern times
[The difficulties in the study of the infinite arise because] we attempt, with our finite minds, to discuss the infinite, assigning to it those properties which we give to the finite and limited; but this ... is wrong, for we cannot speak of infinite quantities as being the one greater or less than or equal to another.
Two New Sciences 1638
I do not feel obliged to believe that the same God who endowed us with sense, reason, and intellect intended us to forgo their use.
Quoted in Des MacHale, Wisdom (London, 2002).
I have never met a man so ignorant that I couldn't learn something from him.
All truths are easy to understand once they are discovered; the point is to discover them.
Mathematics is the key and door to the sciences.