No programming/code is required for this question, though you might submit them
for extra credit
Goldbach's conjecture states that every even number greater than two can be
expressed as the sum of two primes. There is a well known program called AM
(Automated Mathematician) that discovered this, but its internal design is
beyond the scope of this course.
Instead, suggest a scheme/some combination of schemes that
could lead us to this conclusion. i.e., you want to data-mine that
For all even x, there exist primes y and z such that x=y+z, if x>2.
Assume that all you know is the notion of numbers,
the notion of ordinal operators (<,>,<=,>= etc.), and concepts such as "even" and
"prime". In particular, you can assume the existence of predicates such as
prime(n) that returns true if the argument is a prime
and false otherwise. Likewise, you can assume the availability of even(n).
(In reality, there are more predicates available to you, like odd(n),
composite(n), and so on; part of the task is to figure out how exactly
you narrow down on even and prime, as potential interesting
concepts.)
You can use anything from ILP, decision trees, nearest neighbor methods, neural networks,
genetic algorithms or a combination of these. You have to make sure that your design is (i)
powerful enough to express the above concept, (ii) can be expected to converge to the same.
