The Polynomial Ham Sandwich Theorem!
The ham sandwich theorem, states that given n measurable "objects" in n-dimensional space, it is possible to divide all of them in half (according to volume) with a single (n - 1)-dimensional hyperplane.

The ham sandwich theorem takes its name from the case when n = 3 and the three objects of any shape are a chunk of ham, a hunk of cheese, and a piece of bread -- notionally, a sandwich -- which can then each be bisected with a single cut (i.e., a plane). The theorem then states that it is possible to slice the sandwich in half such that each half contains the same amount of bread, cheese, and ham.
              -- paraphrased from Wikipedia
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Basically, given a bunch of objects (N) in an N-dimensional space, you can divide it into two halves both containing the same amount of stuff in both halves using a single cut (an N-1object).

Definitely beyond my mathematics skills nowadays to use it, but I hope the explanation helps.

I'm not a PhD, but I did get the opportunity to help recruit for a Fortune 500 company for several years. We had a number of PhD grads talk to us, and not one made it past the screening interview, because their interests didn't match our needs. PhD's gave the impression of desire in research and more esoteric computing activities - very valid, but not what most companies need. Combine that with the fact that most wanted more money than their backgrounds appeared to merit, and it was no-go. Most companies need someone who have a good understanding of the basics, an area or two of focused knowledge, and the ability to execute, all at a reasonable price. PhD's often don't fit that bill.

That said, I have to agree with a few posts above - you should go with what you love. If you want to do the research and high end computing - do it. But do it because you love it, not as a career advancing step, because it may not help.