Nov 202016

During the last week, two interesting news items on physics appeared and their juxtaposition may contain a message for mathematical crystallography.

First, Quanta Magazine, “illuminating science,” ran a feature article on how An unexpected connection has emerged between the results of physics experiments and an important, seemingly unrelated set of numbers in pure mathematics. The point of the article is the explosion in the size of Feynman Diagrams used to analyze particle interactions as the number of particles increases. (Crystal structure prediction encounters a similar problem in surveying new structures as the number of “kinds” of components increase.) The point of the article is that it appears that some of the results correspond to parameters generated in algebraic geometry.

Algebraic geometry is concerned with surfaces that can be defined by polynomial equations. For example, a sphere of radius 3 can be defined by the equation x2 + y2 + z2 = 32 = 9. (Algebraic geometry can work in arbitrary dimensions, and a surface-like structure in a higher-dimensional space is called a manifold. Algebraic geometry is concerned with manifolds defined by polynomial equations.)

This heads up suggests that mathematical crystallography might also benefit from using other bits of mathematics that we normally don’t think of. But there is a problem.

Andrew Higginson and Tim Fawcett are back. Four years ago, they published a study on how Heavy use of equations impedes communication among biologists. That paper asserted that empirical biology did not seem to rely much on theoretical biology, and that formal mathematics in theoretical biology papers negatively impacted their citation rates. Last year, three physicists claimed that statistical observations about biologists could also be made about physicists, and suggested that there might be other reasons for what Higginson and Fawcett observed. (The physicists observed that, “much anxiety and pain also seems to be related to doing math,” although the paper that they cited claimed that the anxiety and pain was associated with the anticipation of doing math – and not the actual doing math.) Higginson and Fawcett have just conducted a study of physicists and concluded that “equation density” negatively affected the impact of physics papers as well.

No doubt the food fight will continue, but realistically, whether one reads or scans or drops a paper could depend on whether flipping through the paper it does not look like much fun to read. It would not be surprising if Higginson and Fawcett were on to something. For mathematical crystallographers, the question is how much it affects our field; a rough guess would be somewhere between biology and physics.

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