Archimedes of Syracus (287-212 B. C. E)

Give me a place to stand, and I will move the earth.

Eureka, euraka!

Don't spoil my circles! (or Do not disturb my circles!)

There are things which seem incredible to most men who have not studied Mathematics.

Aristotle (384-322 B. C. E)

Now what is characteristic of any nature is that which is best for it and gives most joy. Such a man is the life according to reason, since it is that which makes him man.

There is nothing strange in the circle being the origin of any and every marvel.

The so-called Pythagoreans, who were the first to take up mathematics, not only advanced this subject, but saturated with it, they fancied that the principles of mathematics were the principles of all things.

To Thales the primary question was not what do we know, but how do we know it.

If this is a straight line [showing his audience a straight line drawn by a ruler], then it necessarily ensues that the sum of the angles of the triangle is equal to two right angles, and conversely, if the sum is not equal to two right angles, then neither is the triangle rectilinear.

It is not once nor twice but times without number that the same ideas make their appearance in the world.

But Nature flies from the infinite, for the infinite is unending or imperfect, and N

nature ever seeks an end.

We cannot ... prove geometrical truths by arithmetic.

The chief forms of beauty are order and symmetry and definiteness, which the mathematical sciences demonstrate in a special degree.

The continuum is that which is divisible into indivisibles that are infinitely divisible. Physics.

Roger Bacon (1214-1294)

In mathematics I can report no deficience, except it be that men do not sufficiently understand the excellent use of the Pure Mathematics.

Mathematics is the door and key to the sciences.

Neglect of mathematics works injury to all knowledge, since he who is ignorant of it cannot know the other sciences or the things of the world.

There are four great sciences ... Of these sciences the gate and key is mathematics, which the saints discovered at the beginning of the world.

... mathematics is absolutely necessary and useful to the other sciences.

Heri Bergson (1859-1941)

One can always reason with reason.

Janos Bolyai (1802-1860)

I have created a new universe from nothing.

One must do not violence to nature, nor model it in conformity to any blindly formed chimaera.

Bernhard Bolzano (1781-1848)

My special pleasure in mathematics rested particularly on its purely speculative part.

Even in the realm of things which do not claim actuality,

and do not even claim possibility, there exist beyond dispute sets which are infinite.

George Boole (1815-1869)

It is not of the essence of mathematics to be occupied with the ideas of number and quantity.

No matter how correct a mathematical theorem may appear to be, one ought never to be satisfied that there was not something imperfect about it until it also gives the impression of being beautiful.

Geoge Cantor (1845-1918)

The essence of mathematics is its freedom.

I see it, but I don't believe it.

Mathematics is entirely free in its development, and its concepts are only linked by the necessity of being consistent, and are co-ordinated with concepts introduced previously by means of precise definitions.

In mathematics the art of proposing a question must be held of higher value than solving it.

Every transfinite consistent multiplicity, that is, every transfinite set, must have a definite aleph as its cardinal number.

Rene Descartes (1596-1650)

I think, therefore I am.

Perfect numbers like perfect men are very rare.

With me everything turns into mathematics.

It is not enough to have a good mind. The main thing is to use it well.

... the two operations of our understanding, intuition and deduction, on wh ich alone we have said we must rely in the acquisition of knowledge.

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In order to seek truth it is necessary once in the course of our life to doubt as far as possible all things.

Give me extension and motion and I will construct the universe.

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There have been only Mathematicians who were able to find some proofs, that is to say some sure and certain reasons.

Take what you need; act as you must, and you will obtain that for which you wish!

Only having one truth about each object, whoever finds it knows as much as can known about it.

Democritus (460-370 B. C)

Found, but not proven.

No one has ever surpassed me in constructing figures by means of proofs, not even the Egyptian ``harpedouaptes''(knotters of ropes or geometry), as they are called.

I would rather discover one scientific fact than become King of Persia.

Everything existing in the Universe is the fruit of chance and necessity.

Nothing exists except atoms and empty space; everything else is opinion.

Albert Einstein (1879-1955)

So far as the theories of mathematics are about reality, they are not certain ; so far as they are certain, they are not about reality.

I don't believe in mathematics.

God does not care about our mathematical difficulties. He integrates empirically.

Nature to him (Newton) was an open book, whose letters he could read without effort.

Since the mathematics

ans have invaded the theory of relativity, I do not understand it myself anymore.

Do not worry about your difficulties in mathematics, I assure you that mine are greater.