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Theory Driven Discovery - AM (1976)

AM is a program that discovers concepts in elementary mathematics and set theory.

AM has 2 inputs:

Given the above information AM discovered:

-- it is possible to count the elements of this set and this is an the image of this counting function -- the integers -- interesting set in its own right.
-- The union of two disjoint sets and their counting function.
-- Having discovered addition and multiplication as laborious set-theoretic operations more effective descriptions were supplied by hand.
Prime Numbers
-- factorisation of numbers and numbers with only one factor were discovered.

Golbach's Conjecture
-- Even numbers can be written as the sum of 2 primes. E.g. 28 = 17 + 11.
Maximally Divisible Numbers
-- numbers with as many factors as possible. A number k is maximally divisible is k has more factors than any integer less than k. E.g. 12 has six divisors 1,2,3,4,6,12.

How does AM work?

AM employs many general-purpose AI techniques: