Mathematical Elegance Quotes

A physical law must possess mathematical beauty.

Through algebra you easily arrive at equations, but always to pass therefrom to the elegant constructions and demonstrations which usually result by means of the method of porisms is not so easy, nor is one's ingenuity and power of invention so greatly exercised and refined in this analysis.

When I am working on a problem, I never think about beauty but when I have finished, if the solution is not beautiful, I know it is wrong.

The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic. It has engaged the industry and wisdom of ancient and modern geometers to such an extent that it would be superfluous to discuss the problem at length. ... Further, the dignity of the science itself seems to require that every possible means be explored for the solution of a problem so elegant and so celebrated.

What is especially striking and remarkable is that in fundamental physics, a beautiful or elegant theory is more likely to be right than a theory that is inelegant. A theory appears to be beautiful or elegant (or simple, if you prefer) when it can be expressed concisely in terms of mathematics we already have. Symmetry exhibits the simplicity. The Foundamental Law is such that the different skins of the onion resemble one another and therefore the math for one skin allows you to express beautifully and simply the phenomenon of the next skin.

Euclid alone Has looked on Beauty bare. Fortunate they Who, though once only and then but far away, Have heard her massive sandal set on stone.

Theoretical physicists accept the need for mathematical beauty as an act of faith... For example, the main reason why the theory of relativity is so universally accepted is its mathematical beauty.

It is more important to have beauty in one's equations than to have them fit experiment.

When something is beautiful in math, everything is just perfectly lined up, and you see through sheer thought that something really beautiful can take place.

No matter how correct a mathematical theorem may appear to be, one ought never to be satisfied that there was not something imperfect about it until it also gives the impression of being beautiful.

I am very seldom interested in applications. I am more interested in the elegance of a problem. Is it a good problem, an interesting problem?

Perhaps we see equations as simple because they are easily expressed in terms of mathematical notation already invented at an earlier stage of development of the science, and thus what appears to us as elegance of description really reflects the interconnectedness of Nature's laws at different levels.

My colleagues in elementary particle theory in many lands [and I] are driven by the usual insatiable curiosity of the scientist, and our work is a delightful game. I am frequently astonished that it so often results in correct predictions of experimental results. How can it be that writing down a few simple and elegant formulae, like short poems governed by strict rules such as those of the sonnet or the waka, can predict universal regularities of Nature?

This has been done elegantly by Minkowski; but chalk is cheaper than grey matter, and we will do it as it comes.

Science should have no less lofty a goal. My ambition is to live to see all of physics reduced to a formula so elegant and simple that it will fit easily on the front of a T-shirt.

Phyllis explained to him, trying to give of her deeper self, 'Don't you find it so beautiful, math? Like an endless sheet of gold chains, each link locked into the one before it, the theorems and functions, one thing making the next inevitable. It's music, hanging there in the middle of space, meaning nothing but itself, and so moving...'

The traditional mathematician recognizes and appreciates mathematical elegance when he sees it. I propose to go one step further, and to consider elegance an essential ingredient of mathematics: if it is clumsy, it is not mathematics.

I have the vagary of taking a lively interest in mathematical subjects only where I may anticipate ingenious association of ideas and results recommending themselves by elegance or generality.

A great part of its theories derives an additional charm from the peculiarity that important propositions, with the impress of simplicity on them, are often easily discovered by induction, and yet are of so profound a character that we cannot find the demonstrations till after many vain attempts; and even then, when we do succeed, it is often by some tedious and artificial process, while the simple methods may long remain concealed.

The Besicovitch style is architectural. He builds out of simply elements a delicate and complicated architectural structure, usually with a hierarchical plan, and then, when the building is finished, the completed structure leads by simple arguments to an unexpected conclusion. Every Besicovitch proof is a work of art, as carefully constructed as a Bach fugue.

The pursuit of pretty formulas and neat theorems can no doubt quickly degenerate into a silly vice, but so can the quest for austere generalities which are so very general indeed that they are incapable of application to any particular.

The essential point is that, although coordinates are a powerful, and sometimes essential, tool in many calculations, the fundamental laws of physics can be expressed without the aid of coordinates; and, indeed, their coordinate-free expressions are generally elegant and exceedingly powerful.

There's a beauty to math. Math is so simple. It's just one step after the next.

As for everything else, so for a mathematical theory: beauty can be perceived but not explained.

It is not so much whether a theorem is useful that matters, but how elegant it is.