WikiFindings

Scientists struggle with mathematical details

Background

Most research in biology involves observation or experiments with animals or humans, but this research usually tests the predictions of mathematical or computational theories. However, many experimental papers only refer to other experimental papers; ignoring the relevant theory. This suggests a failure of communication between experimentalists and theoreticians. The spread of an idea in science can be measured by the number of citations to a paper containing the idea.

Findings

We counted the density of equations (equations per page) in all the articles in 3 leading journals in a particular year. Scientific articles presenting many equations on each page are seldom referred to by other scientists. Every time the density of equations went up by 1, the number of citations dropped by 28%. The most maths-heavy articles are referenced 50 per cent less often than those with little or no maths. Long equation-dense papers are cited a lot only by other theory papers. Equations presented in appendices do not have any effect.

Implications

Scientists would like to believe that the popularity of new theories depends entirely on their scientific value, in terms of novelty, importance and technical correctness. However, scientists pay less attention to theories that are crammed with mathematical details. This is an important issue because nearly all areas of science rely on close links between mathematical theory and experimental work. If new theories are presented in a way that is off-putting to other scientists, then no one will perform the crucial experiments needed to test those theories. Scientists need to think more carefully about how they present the mathematical details of their work. The ideal solution is not to hide the maths away, but to add more explanatory text to take the reader carefully through the assumptions and implications of the theory.