Morris Kline Quotes

Science is the Differential Calculus of the mind. Art the Integral Calculus; they may be beautiful when apart, but are greatest only when combined.

Without the concepts, methods and results found and developed by previous generations right down to Greek antiquity one cannot understand either the aims or achievements of mathematics in the last 50 years. [Said in 1950]

Mathematicians didn't invent infinity until 1877. So they thought it was impossible that Africans could be using fractal geometry.

I have found a very great number of exceedingly beautiful theorems.

It's such a diversion to be constantly thinking of better ways I can teach people math that my hunger is for that really, for new ways of translating the beauty of it.

The Theory of Groups is a branch of mathematics in which one does something to something and then compares the result with the result obtained from doing the same thing to something else, or something else to the same thing.

The story of pi has been extensively told, no doubt because its history goes back to ancient times, but also because much of it can be grasped without a knowledge of advanced mathematics.

Art and creativity are crucial, whether you're a mathematician, a scientist, or an artist.

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.

Mathematics commands all my respect, but I have no use for engines.

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

Mathematics is the queen of science, and arithmetic the queen of mathematics.

The creative principle [of science] resides in mathematics.

It is almost as hard to define mathematics as it is to define economics, and one is tempted to fall back on the famous old definition attributed to Jacob Viner, "Economics is what economists do," and say that mathematics is what mathematicians do. A large part of mathematics deals with the formal relations of quantities or numbers.

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

The only royal road to elementary geometry is ingenuity.

I didn't want to become a pure mathematician, as a matter of fact, my uncle was one, so I knew what the pure mathematician was and I did not want to be a pure - I wanted to do something different.

No one for a moment can pretend that printing is so great a discovery as writing, or algebra as a language.

The full impact of the Lobachevskian method of challenging axioms has probably yet to be felt. It is no exaggeration to call Lobachevsky the Copernicus of Geometry [as did Clifford], for geometry is only a part of the vaster domain which he renovated; it might even be just to designate him as a Copernicus of all thought.

We may as well cut out group theory. That is a subject that will never be of any use in physics.

I am not interested in what today's mathematicians find interesting.

With an absurd oversimplification, the 'invention' of the calculus is sometimes ascribed to two men, Newton and Leibniz. In reality, the calculus is the product of a long evolution that was neither initiated nor terminated by Newton and Leibniz, but in which both played a decisive part.

The introduction of the cipher 0 or the group concept was general nonsense too, and mathematics was more or less stagnating for thousands of years because nobody was around to take such childish steps.

There still remain three studies suitable for free man. Arithmetic is one of them.