We wanted to solve robot problems and needed some vision, action, reasoning, planning, and so forth. We even used some structural learning, such as was being explored by Patrick Winston.

There are three basic approaches to AI: Case-based, rule-based, and connectionist reasoning.

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.

Kubrick's vision seemed to be that humans are doomed, whereas Clarke's is that humans are moving on to a better stage of evolution.

Around 1967 Dan Bobrow wrote a program to do algebra problems based on symbols rather than numbers.

If you just have a single problem to solve, then fine, go ahead and use a neural network. But if you want to do science and understand how to choose architectures, or how to go to a new problem, you have to understand what different architectures can and cannot do.