>> “You can think of the roots of a polynomial as negatively charged particles that repel each other with a force that decays when the distance increases,” Breuillard said.

> No, you can't.

Well, yes, you can, and a professional mathematician just said so, yet it seems you insist that mathematics is all about dotting the i's and crossing the t's. Thinking of the roots in the way described is exactly what Dmitrov did: he explored this analogy, worked with a formalized version of it, and used it to prove a significant theorem.

I agree that the article writer's intro takes the analogy much too far, to the point of being just false — mathematicians don't look at the number line and see "forces" at work maintaining the distances between the integers.