The most interesting project that I read about in AI: The Tumultuous History of the Search for Artificial Intelligence by Daniel Crevier was called Automated Mathematician (AM) and was developed by Douglas Lenat. The idea was to have the program learn and discover math principles and laws by playing around with different concepts on its own. Lenat wanted the program to learn by discovery, to learn about the world by playing with things it found interesting.

The program was had three principle components. First it had 115 initial ideas such as the concepts of sets, intersections of sets, etc. Next it had a set of 184 rules for manipulating these basic concepts. Basically heuristics like looking for inverses and extreme cases of things. Finally the program was given a metric to determine how good and interesting a discovery is so it would know which ones to follow or report.

The program rediscovered over 200 mathematic concepts including some that have not yet been proven or thoroughly researched. One of the most interesting was the programs interest in numbers that have many factors, sort of the opposite of prime numbers. This as something that was mentioned by a mathematician a while ago but never really followed up on.

Eventually the program slowed down and stopped discovering new concepts. This was likely because the program was limited by the manipulation rules and metrics that it was programmed with. The program would not be able to add new discoveries to its manipulation rules or change the metrics for what it finds interesting so it was unable to build on what it discovered. Lenat wrote a new program that could revise its discovery heuristics and used it both for computer chip design and for a contest called Traveller TCS. His new program bears a lot of similarities to the genetic algorithms now in use as the heuristics evolved through generations in a similar way.

More recently genetic algorithms have been used in the design of circuits and other areas, following up on AM’s initial success.