I was under the impression that the results of Schwartz and Zippel go a little bit beyond the fundamental theorem of algebra. Otherwise they wouldn’t have been published as research papers not so long ago, would they? And no, not everybody has to be familiar with them.

If those results do get carefully reexamined, then what would be wrong with that? That’s what should happen, as far as I’m concerned. In fact I’d be reading those papers right now if I weren’t sick. Because that’s what many of us do when a big result in our area gets proved. We examine the proof, including the results that it relies on where possible – not just to check for correctness, but also to understand the argument better.

A new application of an old theorem can put that theorem in a new light and lead to questions that wouldn’t have been thought of otherwise. We will want to know how far the argument extends, or whether similar ideas can be used in other settings, and for that we will need to know how the Schwartz-Zippel theorem works. Even if there turn out to be no such extensions, at least we will have learned something that we didn’t know before. Which is always a good thing.