Hermann Weyl Quotes

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.

Do not imagine that mathematics is hard and crabbed, and repulsive to common sense. It is merely the etherealization of common sense.

I am interested in mathematics only as a creative art.

The essence of mathematics lies precisely in its freedom.

In the future, as in the past, the great ideas [of mathematics] must be simplifying ideas, the creator must always be one who clarifies, for himself, and for others, the most complicated issues of formulas and concepts.

It is here [in mathematics] that the artist has the fullest scope of his imagination.

I think some people need the assurance of people around them and ideas worked out in advance. I think it keeps me an edge that to be creative on the spot. You have to think of things to do when you meet people. You limit your choices from the beginning. So I don't bring a lot of lenses, cameras, all these elements that can help the picture to a shooting. You confine yourself to, say, one room and you just make it work. You become very creative in that little space. You have left a lot of other options out of the game.

Arithmetic is a kind of knowledge in which the best natures should be trained, and which must not be given up.

Mathematics is a more powerful instrument of knowledge than any other that has been bequeathed to us by human agency.

The only royal road to elementary geometry is ingenuity.

Mathematicians create by acts of insights and intuition. Logic then sanctions the conquests of intuition.

Another characteristic of mathematical thought is that it can have no success where it cannot generalize.

Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity. The activity of the intuition consists in making spontaneous judgements which are not the result of conscious trains of reasoning. The exercise of ingenuity in mathematics consists in aiding the intuition through suitable arrangements of propositions, and perhaps geometrical figures or drawings.

Many who have had an opportunity of knowing any more about mathematics confuse it with arithmetic, and consider it an arid science. In reality, however, it is a science which requires a great amount of imagination.

I don't care much for equations myself. This is partly because it is difficult for me to write them down, but mainly because I don't have an intuitive feeling for equations.

I've always enjoyed mathematics. It is the most precise and concise way of expressing any idea.

Limitations are inspiring: they lead to thinking, so I don't mind them.

There's always some room for improvisation.

Mathematics seems to endow one with something like a new sense.

You have to spend some energy and effort to see the beauty of math.

As the prerogative of Natural Science is to cultivate a taste for observation, so that of Mathematics is, almost from the starting point, to stimulate the faculty of invention.

When I was in school, my favorite subject was math. I took algebra and calculus. At an early age I grasped it and understood it quickly. I just enjoyed breaking the codes and solving problems.

A rigid America is also weak and vulnerable, because it sacrifices its unique strength: the energy of people who think they can always make something new of their lives.

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

The true spirit of delight...is to be found in mathematics as surely as in poetry.