Leopold Kronecker Quotes

After exponential quantities the circular functions, sine and cosine, should be considered because they arise when imaginary quantities are involved in the exponential.

Geometry was the first exciting course I remember.

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

The longer mathematics lives the more abstract - and therefore, possibly also the more practical - it becomes.

I enjoyed like nothing else working in pure math, discovering new formulas.

I can mention many moments that were unforgettable and revelatory. But the most single revelatory three minutes was the first time I put on scuba gear and dived on a coral reef. It's just the unbelievable fact that you can move in three dimensions.

I didn't discover curves; I only uncovered them.

Nature never uses prime numbers. But mathematicians do.

I love that once you know the basic rules of maths, you can do whatever you want with it.

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

In mathematical analysis we call x the undetermined part of line a: the rest we don't call y, as we do in common life, but a-x. Hence mathematical language has great advantages over the common language.

Walking along past the store windows, into which she peers with her usual eagerness, her usual sense that maybe, today, she will discover behind them something that will truly be worth seeing, she feels as if her feet are not on cement at all but on ice. The blade of the skate floats, she knows, on a thin film of water, which it melts by pressure and which freezes behind it. This is the freedom of the present tense, this sliding edge.

The fact that all Mathematics is Symbolic Logic is one of the greatest discoveries of our age; and when this fact has been established, the remainder of the principles of mathematics consists of the analysis of Symbolic Logic itself.

That this subject [of imaginary magnitudes] has hitherto been considered from the wrong point of view and surrounded by a mysterious obscurity, is to be attributed largely to an ill-adapted notation. If, for example, +1, -1, and the square root of -1 had been called direct, inverse and lateral units, instead of positive, negative and imaginary (or even impossible), such an obscurity would have been out of the question.

What good is a Bill of Rights that does not include the right to play, to wander, to explore, the right to stillness and solitude, to discovery and physical freedom?

It is well known that the central problem of the whole of modern mathematics is the study of transcendental functions defined by differential equations.

There is a fine line between seeing something that's lost as missing, and seeing it as something that might be found.

Had Mittag-Leffler had his way, I should have to wait until the year 1984, which to me seemed too great a demand!

From Euclid to Newton there were straight lines. The modern age analyzes the wavers.

Mathematics is an obscure field, an abstruse science, complicated and exact; yet so many have attained perfection in it that we might conclude almost anyone who seriously applied himself would achieve a measure of success.

I travel because I like to move from place to place, I enjoy the sense of freedom it gives me, it pleases me to be rid of ties, responsibilities, duties, I like the unknown; I meet odd people who amuse me for a moment and sometimes suggest a theme for a composition; I am often tired of myself and I have a notion that by travel I can add to my personality and so change myself a little. I do not bring back from the journey quite the same self that I took

Mathematical Analysis is... the true rational basis of the whole system of our positive knowledge.

Walking gets too boring, when you learn how to fly.

Logic leaves us no choice. In that sense, math always involves both invention and discovery: we invent the concepts but discover their consequences. … in mathematics our freedom lies in the questions we ask – and in how we pursue them – but not in the answers awaiting us.

Just by studying mathematics we can hope to make a guess at the kind of mathematics that will come into the physics of the future... If someone can hit on the right lines along which to make this development, it may lead to a future advance in which people will first discover the equations and then, after examining them, gradually learn how to apply them... My own belief is that this is a more likely line of progress than trying to guess at physical pictures.