Not to shit on all of your middlebrow dismissals but mathematicians are known to steal language from other fields as metaphors for mathematical phenomena. Sometimes these metaphors are very rigorous and precise and sometimes they're fast and loose. Here, look, I found all these papers which use "repulsion" as a mathematical metaphor for distances between zeroes, eigenvalues, and other special values of a geometric object:<p>Random matrices: tail bounds for gaps between eigenvalues<p>Gaps (or spacings) between consecutive eigenvalues are a central topic in random matrix theory. The goal of this paper is to study the tail distribution of these gaps in various random matrix models. We give the first repulsion bound for random matrices with discrete entries and the first super-polynomial bound on the probability that a random graph has simple spectrum, along with several applications."<p><a href="https://arxiv.org/abs/1504.00396" rel="nofollow">https://arxiv.org/abs/1504.00396</a><p>Real roots of random polynomials: expectation and repulsion<p><a href="https://arxiv.org/abs/1409.4128" rel="nofollow">https://arxiv.org/abs/1409.4128</a><p>Zero repulsion in families of elliptic curve L-functions and an observation of Miller<p><a href="https://academic.oup.com/blms/article-abstract/45/1/80/297678" rel="nofollow">https://academic.oup.com/blms/article-abstract/45/1/80/29767...</a><p>Integral Points on Elliptic Curves and the Bombieri-Pila Bounds<p>Let C be an affine, plane, algebraic curve of degree d with integer coefficients. In 1989, Bombieri and Pila showed that if one takes a box with sides of length N then C can obtain no more than O_{d,\epsilon}(N^{1/d+\epsilon}) integer points within the box. Importantly, the implied constant makes no reference to the coefficients of the curve. Examples of certain rational curves show that this bound is tight but it has long been thought that when restricted to non-rational curves an improvement should be possible whilst maintaining the uniformity of the bound. In this paper we consider this problem restricted to elliptic curves and show that for a large family of these curves the Bombieri-Pila bounds can be improved. The techniques involved include repulsion of integer points, the theory of heights and the large sieve. As an application we prove a uniform bound for the number of rational points of bounded height on a general del Pezzo surface of degree 1.<p><a href="https://arxiv.org/abs/1301.4116" rel="nofollow">https://arxiv.org/abs/1301.4116</a>
Wow, this is an absolutely lovely presentation of that result. Huge props to Hartnett for writing this piece! It's a perfect mix of intuitive and well-explained without being too hand-wavy and it's quite an interesting subject, too.<p>Again, big props to Hartnett (and Dimitrov, of course)!
This is an interesting and important result, but framing it in terms of a "repulsive force" is beyond ridiculous. In fact, it's actively harmful. Forces are physical things and this result has nothing to do with anything physical. It's pure number theory.