Nature is relentless and unchangeable, and it is indifferent as to whether its hidden reasons and actions are understandable to man or not.
Measure what is measurable, and make measurable what is not so.
Long experience has taught me this about the status of mankind with regard to matters requiring thought: the less people know and understand about them, the more positively they attempt to argue concerning them, while on the other hand to know and understand a multitude of things renders men cautious in passing judgment upon anything new.
By denying scientific principles, one may maintain any paradox.
We must say that there are as many squares as there are numbers.
The fear of infinity is a form of myopia that destroys the possibility of seeing the actual infinite, even though it in its highest form has created and sustains us.
In time you may discover everything that can be discovered, and still your progress will only be progress away from humanity. The distance between you and them can one day become so great that your joyous cry over some new gain could be answered by an universal shriek of horror.
The Bible shows the way to go to heaven, not the way the heavens go.
I entertain no doubts as to the truth of the transfinites, which I have recognized with God's help.
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.
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.
Who indeed will set bounds to human ingenuity? Who will assert that everything in the universe capable of being perceived is already discovered and known?
I have never met a man so ignorant that I couldn't learn something from him.
It is surely harmful to souls to make it a heresy to believe what is proved.
To our natural and human reason, I say that these terms ‘large,' ‘small,' ‘immense,' ‘minute,' etc. are not absolute but relative; the same thing in comparison with various others may be called at one time ‘immense' and at another ‘imperceptible.
I notice that young men go to the universities in order to become doctors or philosophers or anything, so long as it is a title, and that many go in for those professions who are utterly unfit for them, while others who would be very competent are prevented by business or their daily cares, which keep them away from letters.
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 the planets around it, and depending on it, can still ripen a bunch of grapes as though 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.
In the sciences, the authority of thousands of opinions is not worth as much as one tiny spark of reason in an individual man.
Who would set a limit to the mind of man? Who would dare assert that we know all there is to be known?
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.
Mathematics is the language with which God has written the universe.
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.
There are those who reason well, but they are greatly outnumbered by those who reason badly.
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.
You cannot teach a man anything, you can only help him find it within himself.
To me, a great ineptitude exists on the part of those who would have it that God made the universe more in proportion to the small capacity of their reason than to His immense, His infinite, power.
The sun, with all those plants revolving around it and dependent upon it, can still ripen a bunch of grapes as if it had nothing else in the universe to do.
We cannot teach people anything; we can only help them discover it within themselves.
With regard to matters requiring thought: the less people know and understand about them, the more positively they attempt to argue concerning them.
And, believe me, if I were again beginning my studies, I should follow the advice of Plato and start with mathematics.
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.
I give infinite thanks to God, who has been pleased to make me the first observer of marvelous things.
All truths are easy to understand once they are discovered; the point is to discover them.
The Milky Way is nothing else but a mass of innumerable stars planted together in clusters.
It is a beautiful and delightful sight to behold the body of the Moon.
In the future, there will be opened a gateway and a road to a large and excellent science into which minds more piercing than mine shall penetrate to recesses still deeper.
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.
Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the letters in which it is composed.
Surely it is a great thing to increase the numerous host of fixed stars previously visible to the unaided vision, adding countless more which have never before been seen, exposing these plainly to the eye in numbers ten times exceeding the old and familiar stars.
They seemed to forget that the increase of known truths stimulates the investigation, establishment and growth of the arts; not their dimination or destruction.
In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual.
The nature of the human mind is such that unless it is stimulated by images of things acting upon it from without, all remembrance of them passes easily away.