Next: Data Driven Discovery --
AM is a program that discovers concepts in elementary mathematics and set theory.
AM has 2 inputs:
- A description of some concepts of set theory (in LISP form). E.g.
set union, intersection, the empty set.
- Information on how to perform mathematics. E.g. functions.
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
- 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:
- A frame based representation of mathematical concepts.
- AM can create new concepts (slots) and fill in their values.
- Heuristic search employed
- 250 heuristics represent hints about activities that might lead to
- How to employ functions, create new concepts, generalisation etc.
- Hypothesis and test based search.
- Agenda control of discovery process.