Felix Klein Quotes

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

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.

The enchanting charms of this sublime science reveal only to those who have the courage to go deeply into it.

It seems that if one is working from the point of view of getting beauty in one's equations, and if one has really a sound insight, one is on a sure line of progress.

Even the greatest mathematicians, the ones that we would put into our mythology of great mathematicians, had to do a great deal of leg work in order to get to the solution in the end.

You don't have to be a mathematician to have a feel for numbers.

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

Creating a body of mathematics is about intellectual labor, not some kind of transcendental revelation. There are plenty of important components of European fractal geometry that are missing from the African version.

Mathematical discoveries, small or great are never born of spontaneous generation.

It is impossible to be a mathematician without being a poet in soul.

Pure mathematics is, in its way, the poetry of logical ideas.

It's fine to work on any problem, so long as it generates interesting mathematics along the way - even if you don't solve it at the end of the day.

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.

For my part, it is difficult for me to say what I owe to Ramanujan - his originality has been a constant source of suggestion to me ever since I knew him, and his death is one of the worst blows I have ever had.

Gauss replied, when asked how soon he expected to reach certain mathematical conclusions, that he had them long ago, all he was worrying about was how to reach them!

Mathematics is not a contemplative but a creative subject.

I am persuaded that this method [for calculating the volume of a sphere] will be of no little service to mathematics. For I foresee that once it is understood and established, it will be used to discover other theorems which have not yet occurred to me, by other mathematicians, now living or yet unborn.

Mathematics is not the rigid and rigidity-producing schema that the layman thinks it is; rather, in it we find ourselves at that meeting point of constraint and freedom that is the very essence of human nature.

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

I have deeply regretted that I did not proceed far enough at least to understand something of the great leading principles of mathematics, for men thus endowed seem to have an extra sense.

It's strange how few of the world's great problems are solved by people who remember their algebra.

If you are receptive and humble, mathematics will lead you by the hand. Again and again, when I have been at a loss how to proceed, I have just had to wait until I have felt the mathematics led me by the hand. It has led me along an unexpected path, a path where new vistas open up, a path leading to new territory, where one can set up a base of operations, from which one can survey the surroundings and plan future progress.

Dull minds are never either intuitive or mathematical.

I had a feeling once about mathematics - that I saw it all... but it was after dinner and I let it go.