Mathematics is the language with which God has written the universe.
All truths are easy to understand once they are discovered; the point is to discover them.
In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual.
I would beg the wise and learned fathers of the church to consider with all diligence the difference which exists between matters of mere opinion and matters of demonstration.
Nothing physical which sense-experience sets before our eyes, or which necessary demonstrations prove to us, ought to be called in question (much less condemned) upon the testimony of biblical passages.
The Universe is a grand book which cannot be read until one first learns to comprehend the language and become familiar with the characters in which it is composed. It is written in the language of mathematics.
See now the power of truth; the same experiment which at first glance seemed to show one thing, when more carefully examined, assures us of the contrary.
But some, besides allegiance to their original error, possess I know not what fanciful interest in remaining hostile not so much toward the things in question as toward their discoverer.
But, because my private lectures and domestic pupils are a great hinderance and intteruption of my studies, I wish to live entirely exempt from the former, and in great measure from the latter. ... in short, I should wish to gain my bread from my writings.
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.
That sculpture is more admirable than painting for the reason that it contains relief and painting does not is completely false. ... Rather, how much more admirable the painting must be considered, if having no relief at all, it appears to have as much as sculpture!
If experiments are performed thousands of times at all seasons and in every place without once producing the effects mentioned by your philosophers, poets, and historians, this will mean nothing and we must believe their words rather than our own eyes?
Well, since paradoxes are at hand, let us see how it might be demonstrated that in a finite continuous extension it is not impossible for infinitely many voids to be found.
Names and attributes must be accommodated to the essence of things, and not the essence to the names, since things come first and names afterwards.
For my part I consider the earth very noble and admirable precisely because of the diverse alterations, changes, generations, etc. that occur in it incessantly.
The doctrine that the earth is neither the center of the universe nor immovable, but moves even with a daily rotation, is absurd, and both philosophically and theologically false, and at the least an error of faith.
The prohibition of science would be contrary to the Bible, which in hundreds of places teaches us how the greatness and the glory of God shine forth marvelously in all His works, and is to be read above all in the open book of the heavens.
With regard to matters requiring thought: the less people know and understand about them, the more positively they attempt to argue concerning them.
But let us remember that we are dealing with infinities and indivisibles both of which transcend our finite understanding, the former on account of their magnitude, the latter because of their smallness.
Philosophy is written in that great book which ever lies before our eyes -- I mean the universe -- but we cannot understand it if we do not first learn the language and grasp the symbols, in which it is written.
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.
I abjure with a sincere heart and unfeigned faith, I curse and detest the said errors and heresies, and generally all and every error and sect contrary to the Holy Catholic Church.
I am inclined to think that the authority of Holy Scripture is intended to convince men of those truths which are necessary for their salvation, which, being far above man's understanding, can not be made credible by any learning, or any other means than revelation by the Holy Spirit.
Being infinitely amazed, so do I give thanks to God, Who has been pleased to make me the first observer of marvelous things, unrevealed to bygone ages.
It reveals to me the causes of many natural phenomena that are entirely incomprehensible in the light of the generally accepted hypotheses. To refute the latter I collected many proofs, but I do not publish them ... I would dare to publish my speculations if there were people men like you.
The surface of the Moon is not smooth, uniform, and precisely spherical as a great number of philosophers believe it to be, but is uneven, rough, and full of cavities and prominences, being not unlike the face of the Earth, relieved by chains of mountains and deep valleys.
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 wha.
To apply oneself to great inventions, starting from the smallest beginnings, is no task for ordinary minds; to divine that wonderful arts lie hid behind trivial and childish things is a conception for superhuman talents.
I therefore concluded, and decided unhesitatingly, that there are three stars in the heavens moving about Jupiter, as Venus and Mercury about the Sun; which at length was established as clear as daylight by numerous other observations.
And, believe me, if I were again beginning my studies, I should follow the advice of Plato and start with mathematics.
And believe me, if I were again beginning my studies, I should follow the advice of Plato and start with the mathematical sciences, which proceed very cautiously and admit nothing as established until it has been rigorously demonstrated.
If you could see the earth illuminated when you were in a place as dark as night, it would look to you more splendid than the moon.
In my studies of astronomy and philosophy I hold this opinion about the universe, that the Sun remains fixed in the centre of the circle of heavenly bodies, without changing its place; and the Earth, turning upon itself, moves round the Sun.
He who looks the higher is the more highly distinguished, and turning over the great book of nature (which is the proper object of philosophy) is the way to elevate one's gaze.
The sun, with all those planets revolving around it and dependent on it, can still ripen a bunch of grapes as if it had nothing else in the universe to do.
If I were again beginning my studies, I would follow the advice of Plato and start with mathematics.
I do not feel obliged to believe that the same God who has endowed us with sense, reason, and intellect has intended us to forgo their use.
It vexes me when they would constrain science by the authority of the Scriptures, and yet do not consider themselves bound to answer reason and experiment.
Facts which at first seem improbable will, even on scant explanation, drop the cloak which has hidden them and stand forth in naked and simple beauty.