Gregory Benford Quotes

The most vitally characteristic fact about mathematics is, in my opinion, its quite peculiar relationship to the natural sciences, or more generally, to any science which interprets experience on a higher than purely descriptive level.

It is almost as hard to define mathematics as it is to define economics, and one is tempted to fall back on the famous old definition attributed to Jacob Viner, "Economics is what economists do," and say that mathematics is what mathematicians do. A large part of mathematics deals with the formal relations of quantities or numbers.

Science begins with the world we have to live in, accepting its data and trying to explain its laws. From there, it moves toward the imagination: it becomes a mental construct, a model of a possible way of interpreting experience. The further it goes in this direction, the more it tends to speak the language of mathematics, which is really one of the languages of the imagination, along with literature and music. Art, on the other hand, begins with the world we construct, not with the world we see. It starts with the imagination, and then works toward ordinary experience.

Lies are infinite in number, and the truth so small and singular.

Neither concepts nor mathematical formulae can explain the infinite.

All things were together, infinite both in number and in smallness; for the small too was infinite.

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.

It took me 1057 pages to describe the hundreds of mathematical equations, algorithms and programming techniques that I invented and used.

The Ludolphian number is fixed in eternity— not a digit out of place, all characters in their proper order, an endless sentence written to the end of the world by the division of the circle’s diameter into its circumference.

Algebra is the intellectual instrument which has been created for rendering clear the quantitative aspects of the world.

Mathematics is not something that you find lying around in your back yard. It's produced by the human mind. Yet if we ask where mathematics works best, it is in areas like particle physics and astrophysics, areas of fundamental science that are very, very far removed from everyday affairs.

Euclid avoids it [the treatment of the infinite]; in modern mathematics it is systematically introduced, for only then is generality obtained.

Everything that occupies space has form. The formless can only be infinite.

[On Cantor's work:] The finest product of mathematical genius and one of the supreme achievements of purely intellectual human activity.

Mathematics is the abstract key which turns the lock of the physical universe.

Mathematics is a more powerful instrument of knowledge than any other that has been bequeathed to us by human agency.

Every relationship of man to the infinite is religion, namely of a man in the full abundance of his humanity. Whenever a mathematician calculates infinity, that, to be sure, is not religion. Infinity conceived in this abundance is the Godhead.

I didn't want to become a pure mathematician, as a matter of fact, my uncle was one, so I knew what the pure mathematician was and I did not want to be a pure - I wanted to do something different.

On all levels primary, and secondary and undergraduate - mathematics is taught as an isolated subject with few, if any, ties to the real world. To students, mathematics appears to deal almost entirely with things whlch are of no concern at all to man.

Mathematics may be defined as the economy of counting. There is no problem in the whole of mathematics which cannot be solved by direct counting.

But let us remember that we are dealing with infinities and indivisibles both of which transcend our finite understanding, the former on account of their magnitude, the latter because of their smallness.

All science requires mathematics.

Mathematics is the key and door to the sciences.

Infinity is a dreadfully poor place. They can never manage to make ends meet.

The infinite we shall do right away. The finite may take a little longer.