Quotes About Computation

If equations are trains threading the landscape of numbers, then no train stops at pi.

Mathematics doesn't care about those beyond the numbers.

Calculators can only calculate - they cannot do mathematics.

uncomputable numbers

I've always enjoyed mathematics. It is the most precise and concise way of expressing any idea.

We want to build systems that can generalize to a new task. Being able to do things with much less data and with much less computation is going to be interesting and important.

Without mathematics, there's nothing you can do. Everything around you is mathematics. Everything around you is numbers.

If we suppose that many natural phenomena are in effect computations, the study of computer science can tell us about the kinds of natural phenomena that can occur.

Artificial intelligence is the science of making machines do things that would require intelligence if done by men.

Nowadays we can do computer experiments using Mathematica, and even solve a system of 42 equations. This offers another route to knowledge, rather than mere ideas.

The Analytical Engine is an embodying of the science of operations, constructed with peculiar reference to abstract number as the subject of those operations.

With thought comprising a non-computational element, computers can never do what we human beings can.

But biology and computer science - life and computation - are related. I am confident that at their interface great discoveries await those who seek them.

Understanding is, after all, what science is all about — and science is a great deal more than mindless computation.

Without computers we will be stuck only proving theorems that have short proofs.

Computer assisted proofs are getting better and better and computers will play a bigger and bigger role in the future.

In order to figure out how to make atoms compute, you have to learn how to speak their language and to understand how they process information under normal circumstances.

In subjects that physicists think of as purely quantum, classical ideas and classical computational techniques can often be powerful.

terminal into compute mode, and made a quick calculation. "Seventy-seven microradians per second comes out to

Mathematics ... is indispensable as an intellectual technique. In many subjects, to think at all is to think like a mathematician.

Perhaps it is conceivable that, in the future, some different kind of 'computer' might be introduced, that makes critical use of continuous physical parameters-albeit within the standard theoretical framework of today's physics-enabling it to behave in a way that is essentially different from a digital computer.

Any complicated activity, which may be mathematical calculations, or playing a game of chess, or commonplace actions-if they have been understood in terms of clear-cut computational rules-are the things that modern computers are good at; but the very understanding that underlies these computational rules is something that is itself beyond computation.

is not easy to ascertain what an algorithm actually is, simply by examining its output.

It is possible to invent a single machine which can be used to compute any computable sequence.