At the 1978 International Congress of Mathematicians at Helsinki, André Weil delivered an address entitled "History of Mathematics: Why and How". His answer was that he was glad to find a way allowing to dodge the answer.

In 1991 the US House Committee on Science , Space and Technology called upon AMS  to answer the question "What are the main goals in the mathematical sciences?"

The  answer was summarized as : “The most important long-term goals for the mathematical sciences are: provision of fundamental tools for science and technology, improvement of mathematics education, discovery of new mathematics, facilitation of technology transfer, and support of efficient computation.”

All these facts are found in the paper of Michael Harris: "Why Mathematics?"You May Ask" (in The Princeton Companion to Mathematics, T. Gowers et al, eds. pp. 966-977, 2003).

What are the goals of integrating AI and symbolic computation? From the above quotations, a possible answer is "to do mathematics".

We build our answer on a joint paper with John Campbell when we started the AISC conference series. We show that among the goals we had, are a few successes, a few misses. In any case these goals were an illustration of the relationship of mathematical symbolic computation and AI at that time. This view is updated to account for the new capabilities of AI and information technology.