Daniel Kleitman, a combinatorialist at MIT (not a consultant), is famous for having solved more than a handful of problems proposed by Erdos(*), and in the process acquired an Erdos number 1. He also consulted for "Good Will Hunting", which gave him a Bacon number 2 via Minnie Driver.

http://en.wikipedia.org/wiki/Daniel_KleitmanIt is a bit sad that the only substantial paragraph in his Wikipedia page is devoted to this fact, instead of his work. For example, he settled the following fascinating conjecture from combinatorial geometry, which stood open for a good 25 years:

(*) Let N be a normed vector space (think of it as the plane, or 3-space, or R^n if you want), and let v_1,...,v_n be vectors of N, each with norm greater than 1. Form the 2^n sums Σ (e_i * v_i), where each of e_1,...,e_n is either -1 or +1. For example, for n=2 one would form the 4 sums v1+v2, v1-v2, -v1+v2, -v1-v2. Now the question is: at most how many of these sums can lie on any single closed ball of radius 1? The conjecture is: n choose n/2, the middle binomial coefficient at level n (coefficients if n is odd).

This is nontrivial already in 1 dimension, but doable (basically Sperner's theorem on antichains in the power set of {1,...,n}). Erdos proved a small generalization of the 1-d case, and used that to provide a partial solution to the 2-d case, in his 1945 paper "On a Lemma of Littlewood and Offord", where he also posed the general problem. Kleitman solved it in 1970 with a beautiful one-page argument. (In 1966, Katona had solved the 2-d case in full by a completely different, but, I daresay, even more beautiful argument.)

I always wondered about the meaning of life. So I looked it up in the dictionary under "L" and there it was --- the meaning of life. It was not what I expected. (Dogbert)