Mathematical Structure Quotes

If there is one thing in mathematics that fascinates me more than anything else (and doubtless always has), it is neither "number" nor "size", but always form. And among the thousand-and-one faces whereby form chooses to reveal itself to us, the one that fascinates me more than any other and continues to fascinate me, is the structure hidden in mathematical things.

Where there is matter, there is geometry.

The mathematics is not there till we put it there.

Einstein's theory of General Relativity has a mathematical structure very similar to Yang-Mills theory.

Mathematics is not only real, but it is the only reality. That is that entire universe is made of matter, obviously. And matter is made of particles. It's made of electrons and neutrons and protons. So the entire universe is made out of particles. Now what are the particles made out of They're not made out of anything. The only thing you can say about the reality of an electron is to cite its mathematical properties. So there's a sense in which matter has completely dissolved and what is left is just a mathematical structure.

Music is the arithmetic of sounds as optics is the geometry of light.

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.

Mathematicians do not study objects, but relations among objects; they are indifferent to the replacement of objects by others as long the relations don't change. Matter is not important, only form interests them.

Music is made up out of these building blocks. Studying how these blocks go together and what they consist of and the math of how it works - it's all the same stuff; it's just different aesthetics that we're talking about.

But in spite of the obvious effectiveness of mathematics in physics, I have never heard of a good a prioriargument that the world must be organised to mathematical principles.

The essence of mathematics lies precisely in its freedom.

If I were asked to name, in one word, the pole star round which the mathematical firmament revolves, the central idea which pervades the whole corpus of mathematical doctrine, I should point to Continuity as contained in our notions of space, and say, it is this, it is this!

Among the thousand-and-one faces whereby form chooses to reveal itself to us, the one that fascinates me more than any other, and continues to fascinate me, is the structure hidden in mathematical things.

Science attempts to find logic and simplicity in nature. Mathematics attempts to establish order and simplicity in human thought.

I see a certain order in the universe and math is one way of making it visible.

The theory of ramification is one of pure colligation, for it takes no account of magnitude or position; geometrical lines are used, but these have no more real bearing on the matter than those employed in genealogical tables have in explaining the laws of procreation.

Music is the pleasure the human mind experiences from counting without being aware that it is counting.

Our external physical reality is a mathematical structure.

In my paper the fact the XY was not equal to YX was very disagreeable to me. I felt this was the only point of difficulty in the whole scheme...and I was not able to solve it.

The infinite in mathematics is alway unruly unless it is properly treated.

I just think too many nice things have happened in string theory for it to be all wrong. Humans do not understand it very well, but I just don't believe there is a big cosmic conspiracy that created this incredible thing that has nothing to do with the real world.

I write in a mathematical manner. For some of my songs, I rhyme every syllable. It's a science.

Algebra is the metaphysics of arithmetic.

I can see that, without being excited, mathematics can look pointless and cold.

The seven white notes on the piano - each section of the piece (there are 12 sections) is five of those seven white notes. If you calculate it, there are 21 groups of five notes in any group of seven notes. And although there are 12 sections, this piece actually uses nine of those groups because some of the sections repeat earlier ones. So that's the formula. It's very simple as a way of generating something. It's my inner minimalist.