This is a tricky domain because, unlike simple arithmetic, to solve a calculus problem - and in particular to perform integration - you have to be smart about which integration technique should be used: integration by partial fractions, integration by parts, and so on.

A couple of hundred years from now, maybe [science fiction writers] Isaac Asimov and Fred Pohl will be considered the important philosophers of the twentieth century, and the professional philosophers will almost all be forgotten, because they're just shallow and wrong, and their ideas aren't very powerful.

A computer is like a violin. You can imagine a novice trying first a phonograph and then a violin. The latter, he says, sounds terrible. That is the argument we have heard from our humanists and most of our computer scientists. Computer programs are good, they say, for particular purposes, but they aren’t flexible. Neither is a violin, or a typewriter, until you learn how to use it.

What would a Martian visitor think to see a human being laugh? It must look truly horrible: the sight of furious gestures, flailing limbs, and thorax heaving in frenzied contortions.

Computer languages of the future will be more concerned with goals and less with procedures specified by the programmer.

Imagine what it would be like if TV actually were good. It would be the end of everything we know.

It makes no sense to seek a single best way to represent knowledge-because each particular form of expression also brings its particular limitations. For example, logic-based systems are very precise, but they make it hard to do reasoning with analogies. Similarly, statistical systems are useful for making predictions, but do not serve well to represent the reasons why those predictions are sometimes correct.