Johannes Kepler Quotes

The composer opens the cage door for arithmetic, the draftsman gives geometry its freedom.

As a child it was clear to me that in some sense math was in the world around us. I became fascinated by what this means. When you look at the shape of the sun and the moon, they're circles, so every time you see a circular thing, there's pi embedded in it.

There are no sects in geometry.

Geometry enlightlens the intellect and sets one's mind right

Projective geometry is all geometry.

I use trigonometry all the time.

... preliminary accounting, banking and surveying (known as arithmetic, algebra and geometry).

Math is the only place where truth and beauty mean the same thing.

Geometry, like arithmetic, requires for its logical development only a small number of simple, fundamental principles. These fundamental principles are called the axioms of geometry.

Geometry is the foundation of all painting.

Experience proves that anyone who has studied geometry is infinitely quicker to grasp difficult subjects than one who has not.

Mathematics would certainly have not come into existence if one had known from the beginning that there was in nature no exactly straight line, no actual circle, no absolute magnitude.

The only royal road to elementary geometry is ingenuity.

If equations are trains threading the landscape of numbers, then no train stops at pi.

Geometry is the only science that it hath pleased God hitherto to bestow on mankind.

Inspiration is needed in geometry, just as much as in poetry.

Ordinary language is totally unsuited for expressing what physics really asserts, since the words of everyday life are not sufficiently abstract. Only mathematics and mathematical logic can say as little as the physicist means to say.

No employment can be managed without arithmetic, no mechanical invention without geometry.

... being perpetually charmed by his familiar siren, that is, by his geometry, he neglected to eat and drink and took no care of his person; that he was often carried by force to the baths, and when there he would trace geometrical figures in the ashes of the fire, and with his finger draws lines upon his body when it was anointed with oil, being in a state of great ecstasy and divinely possessed by his science.

Nature does not count nor do integers occur in nature. Man made them all, integers and all the rest, Kronecker to the contrary notwithstanding.

Mathematics is the key and door to the sciences.

[A mathematician is a] scientist who can figure out anything except such simple things as squaring the circle and trisecting an angle.

The analytical geometry of Descartes and the calculus of Newton and Leibniz have expanded into the marvelous mathematical method

By keenly confronting the enigmas that surround us, and by considering and analyzing the observations that I had made, I ended up in the domain of mathematics. Although I am absolutely without training in the exact sciences, I often seem to have more in common with mathematicians than with my fellow artists.

We cannot ... prove geometrical truths by arithmetic.