Mathematics is written for mathematicians.

Near the sun is the center of the universe.

Therefore I would not have it unknown to Your Holiness, the the only thing which induced me to look for another way of reckoning the movements of the heavenly bodies was that I knew that mathematicians by no means agree in their investigation thereof.

I shall now recall to mind that the motion of the heavenly bodies is circular, since the motion appropriate to a sphere is rotation in a circle.

Although all the good arts serve to draw man's mind away from vices and lead it toward better things, this function can be more fully performed by this art, which also provides extraordinary intellectual pleasure.

Moreover, since the sun remains stationary, whatever appears as a motion of the sun is really due rather to the motion of the earth.

First of all, we must note that the universe is spherical.

So far as hypotheses are concerned, let no one expect anything certain from astronomy, which cannot furnish it, lest he accept as the truth ideas conceived for another purpose, and depart from this study a greater fool than when he entered it.

We regard it as a certainty that the earth, enclosed between poles, is bounded by a spherical surface.

At rest, however, in the middle of everything is the sun.

To know that we know what we know, and to know that we do not know what we do not know, that is true knowledge.

Therefore, when I considered this carefully, the contempt which I had to fear because of the novelty and apparent absurdity of my view, nearly induced me to abandon utterly the work I had begun.

Mathematics is written for mathematicians.

More stars in the north are seen not to set, while in the south certain stars are no longer seen to rise.

I can easily conceive, most Holy Father, that as soon as some people learn that in this book which I have written concerning the revolutions of the heavenly bodies, I ascribe certain motions to the Earth, they will cry out at once that I and my theory should be rejected.

Those things which I am saying now may be obscure, yet they will be made clearer in their proper place.

Finally we shall place the Sun himself at the center of the Universe.

Not a few other very eminent and scholarly men made the same request, urging that I should no longer through fear refuse to give out my work for the common benefit of students of Mathematics.

In so many and such important ways, then, do the planets bear witness to the earth's mobility.

Therefore, in the course of the work I have followed this plan: I describe in the first book all the positions of the orbits together with the movements which I ascribe to the Earth, in order that this book might contain, as it were, the general scheme of the universe.

The earth also is spherical, since it presses upon its center from every direction.

Therefore, having obtained the opportunity from these sources, I too began to consider the mobility of the earth.

Those who know that the consensus of many centuries has sanctioned the conception that the earth remains at rest in the middle of the heavens as its center, would, I reflected, regard it as an insane pronouncement if I made the opposite assertion that the earth moves.

So, influenced by these advisors and this hope, I have at length allowed my friends to publish the work, as they had long besought me to do.

I am aware that a philosopher's ideas are not subject to the judgment of ordinary persons, because it is his endeavour to seek the truth in all things, to the extent permitted to human reason by God.

The massive bulk of the earth does indeed shrink to insignificance in comparison with the size of the heavens.

Accordingly, since nothing prevents the earth from moving, I suggest that we should now consider also whether several motions suit it, so that it can be regarded as one of the planets. For, it is not the center of all the revolutions.

Yet if anyone believes that the earth rotates, surely he will hold that its motion is natural, not violent.

Pouring forth its seas everywhere, then, the ocean envelops the earth and fills its deeper chasms.

For I am not so enamoured of my own opinions that I disregard what others may think of them.

The earth together with its surrounding waters must in fact have such a shape as its shadow reveals, for it eclipses the moon with the arc of a perfect circle.

Of all things visible, the highest is the heaven of the fixed stars.

For it is the duty of an astronomer to compose the history of the celestial motions through careful and expert study.

For a traveler going from any place toward the north, that pole of the daily rotation gradually climbs higher, while the opposite pole drops down an equal amount.

Of all things visible the highest is the heaven of the fixed stars.

Every light has its shadow, and every shadow hath a succeeding morning.

As I say, there was this movement to try to bring philosophers and mathematicians together into an organization where they would talk to each other. An organization wasn't effective unless you had a journal. That's about all I know.

Mathematicians are born, not made.

As far as I know, only a small minority of mathematicians, even of those with Platonist views, accept the idea that there may be mathematical facts which are true but unknowable.

Therefore I would not have it unknown to Your Holiness, the the only thing which induced me to look for another way of reckoning the movements of the heavenly bodies was that I knew that mathematicians by no means agree in their investigation thereof.

Mathematicians may flatter themselves that they possess new ideas which mere human language is as yet unable to express.

It may be true, that men, who are mere mathematicians, have certain specific shortcomings, but that is not the fault of mathematics, for it is equally true of every other exclusive occupation.

Mathematicians aren't satisfied because they know there are no solutions up to four million or four billion, they really want to know that there are no solutions up to infinity.

The greatest mathematicians, as Archimedes, Newton, and Gauss, always united theory and applications in equal measure.

Pure mathematicians just love to try unsolved problems - they love a challenge.

The greatest problem for mathematicians now is probably the Riemann Hypothesis.

Mathematics is written for mathematicians.

First rate mathematicians choose first rate people, but second rate mathematicians choose third rate people.

Abel has left mathematicians enough to keep them busy for 500 years.