Alfred North Whitehead Quotes

One of the strangest features of string theory is that it requires more than the three spatial dimensions that we see directly in the world around us. That sounds like science fiction, but it is an indisputable outcome of the mathematics of string theory.

To the pure geometer the radius of curvature is an incidental characteristic - like the grin of the Cheshire cat. To the physicist it is an indispensable characteristic. It would be going too far to say that to the physicist the cat is merely incidental to the grin. Physics is concerned with interrelatedness such as the interrelatedness of cats and grins. In this case the "cat without a grin" and the "grin without a cat" are equally set aside as purely mathematical phantasies.

Where there is matter, there is geometry.

It's not completely obvious what gravity is, fundamentally, or what dimensions are, fundamentally. One of these days we'll understand better what we mean, what is the fundamental thing that's given us space in the first place and dimensions of space in particular.

Even before string theory, especially as physics developed in the 20th century, it turned out that the equations that really work in describing nature with the most generality and the greatest simplicity are very elegant and subtle.

The field equations and the whole history of general relativity have been complicated.

The book of nature is written in the language of mathematics.

Speaking of ways, pet, by the way, there is such a thing as a tesseract.

Equations are just the boring part of mathematics. I attempt to see things in terms of geometry.

In Einstein's theory of relativity the observer is a man who sets out in quest of truth armed with a measuring-rod. In quantum theory he sets out with a sieve.

There's no answer for my offense, just like the polythagorean theorem.

The best that Gauss has given us was likewise an exclusive production. If he had not created his geometry of surfaces, which served Riemann as a basis, it is scarcely conceivable that anyone else would have discovered it. I do not hesitate to confess that to a certain extent a similar pleasure may be found by absorbing ourselves in questions of pure geometry.

Without space, there is no time.

The application of algebra to geometry ... has immortalized the name of Descartes, and constitutes the greatest single step ever made in the progress of the exact sciences.

There is nothing special in the world. nothing magic. just physics.

In the beginning God said, the four-dimensional divergence of an antisymmetric, second rank tensor equals zero, and there was light, and it was good. And on the seventh day he rested.

The existence of these patterns [fractals] challenges us to study forms that Euclid leaves aside as being formless, to investigate the morphology of the amorphous. Mathematicians have disdained this challenge, however, and have increasingly chosen to flee from nature by devising theories unrelated to anything we can see or feel.

Mathematics has a threefold purpose. It must provide an instrument for the study of nature. But this is not all: it has a philosophical purpose, and, I daresay, an aesthetic purpose.

Symmetrical equations are good in their place, but ' vector ' is a useless survival, or offshoot from quaternions, and has never been of the slightest use to any creature.

Fourier's theorem is not only one of the most beautiful results of modern analysis, but it may be said to furnish an indispensable instrument in the treatment of nearly every recondite question in modern physics.

Fractals, the theory of relativity, the genome: these are magnificently beautiful constructs.

I have an infamously low capacity for visualizing relationships, which made the study of geometry and all subjects derived from it impossible for me.

Ordinary language is totally unsuited for expressing what physics really asserts, since the words of everyday life are not sufficiently abstract. Only mathematics and mathematical logic can say as little as the physicist means to say.

I like to think that Einstein would look at string theory’s journey and smile, enjoying the theory’s remarkable geometrical features while feeling kinship with fellow travelers on the long and winding road toward unification.

As a child it was clear to me that in some sense math was in the world around us. I became fascinated by what this means. When you look at the shape of the sun and the moon, they're circles, so every time you see a circular thing, there's pi embedded in it.