Automated Mathematician
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The Automated Mathematician is one of the earliest successful discovery systems developed. It was created by Doug Lenat in Lisp, and in 1977 led to Lenat being awarded the IJCAI Computers and Thought Award.
AM worked by generating and modifying short Lisp programs which were then interpreted as defining various mathematical concepts; for example, a program that tested equality between the length of two lists was considered to represent the concept of numerical equality, while a program that produced a list whose length was the product of the lengths of two other lists was interpreted as representing the concept of multiplication. The system had elaborate heuristics for choosing which programs to extend and modify, based on the experiences of working mathematicians in solving mathematical problems.
Lenat claimed that the system had rediscovered both Goldbach's conjecture and the Unique Prime Factorization Theorem. Later critics accused Lenat of over-interpreting the output of AM, and argued that any system that generated enough short Lisp programs would generate ones that could be interpreted by an external observer as representing equally sophisticated mathematical concepts. In his paper Why AM appears to work, Lenat conceded the point but argued that this property was in itself interesting—and that a promising direction for further research would be to look for other languages in which short random strings were likely to be useful.
This intuition was the basis of AM's successor Eurisko, which attempted to generalize the search for mathematical concepts to the search for useful heuristics.