Math is hard: the use of complex equations decreases the chance a paper will be cited

Figure 1- math is hard

How many of you asked “when am I ever going to need to know this” in math class? While basic mathematical literacy is essential for life in the modern world, most people can achieve success in their careers if they can’t remember the difference between pi and apple pie.

One of the exceptions to this comes from my own career path- scientists absolutely, positively need to have strong quantitative skills in order to perform research. However, many scientists struggle with math.  I can’t even count how many conference presentations I’ve attended that included a statement along the lines of “don’t worry about all the complicated equations here”, or how many students or journal club attendees have told me that they just skipped over the section of a paper focusing on models and equations.  See what I did there? Can’t even count? Anyway, while math may be more directly relevant to our jobs than it is to some of yours, we still find it hard.

British scientists Tim Fawcett and Andrew Higginson attempted to determine the extent of this problem by calculating the impact of using complex math in a scientific paper on the number of citations that paper gets. In a recent paper entitled “Heavy use of equations impedes communication among biologists”, they analyzed hundreds scientific articles from top ecology and evolution journals from 1998, which allowed them to assess the long-term impact of each article. Their conclusion is clear- and startling! According to Tim Fawcett,

“Biological articles with lots of mathematical equations per page have a lower impact on their field, as measured by the number of times those articles are cited by other scientists. This suggests that some biologists are reluctant to read, or have difficulty understanding, heavily mathematical papers. We were not surprised by the existence of this effect, but we were surprised by how large it was: for each extra equation per page, an article gets 35% fewer citations in non-theoretical work. That’s a big effect!”


Figure 2 from Fawcett and Higginson 2012. “Equations presented in the main text reduce citations from nontheoretical articles, whereas equations presented in an appendix do not. The graphs show the mean (±SEM) number of citations by nontheoretical papers for cited articles of differing length and number of equations per page, when those equations are presented in the main text”

This paper clearly got the attention of the theoretical ecology community- one of the most recent issues of PNAS contained not one, but FOUR separate responses to it! That’s almost five times as many as one! See? Unlike some scientists, I can do math.

One response claimed that Fawcett and Higginson had misinterpreted their results, and that the lack of citations was attributable to a decline in the scientific community’s interest in math-based theoretical ecology in general.  One called for an overhaul in science education with more of a focus on math skills (instead of asking current scientists to explain their equations more clearly). Another points to a few examples of highly-cited math-heavy works as evidence contradicting these conclusions- which is ironic because it relies on anecdotal evidence instead of mathematically rigorous analysis.

“Judging by the responses we’ve received, some scientists appear reluctant to change the way they present their theoretical work, instead placing the blame at the door of the readers and calling for greater mathematical literacy among biologists,” Dr. Fawcett and Dr. Higginson said of the responses in PNAS.  “While we wholeheartedly agree that biologists should become more mathematically literate, it is a mistake to view this as an alternative to improving the communication of theoretical work. The two goals are complementary, and neglecting either risks slowing scientific progress.”

The backlash against these conclusions is unsurprising. Even if the situation isn’t as severe as indicated by this analysis, it certainly exists. To those who recognize that this is a problem, fear not- Dr. Fawcett and Dr. Higginson have suggestions on how to fix it.

“Mathematical theory is indispensable to most, if not all, areas of science. So there is a real conflict here with our finding that heavy use of mathematics appears to be off-putting to many biologists: we cannot simply omit the equations. There are two complementary solutions to this problem: one is to enhance the mathematical training of biology graduates so that they are less fazed by heavily mathematical articles; the other is to make those articles more accessible, to communicate the theory more clearly to non-specialists. To achieve the latter goal, we do not recommend that scientists start removing equations from their work. Instead, they should either add more explanatory text to take the reader carefully through the assumptions and implications of the mathematics, or else move some of the less fundamental equations to an appendix, where there is more room for explaining them in detail. There might also be other ways to help communicate a mathematical model more effectively, for example perhaps by making better use of figures and tables.  Important theory deserves careful explanation, otherwise it won’t get the recognition it deserves. Scientists should think about how to communicate the essence of those equations in the most effective way.”

This analysis quantifies what we’ve known is a problem for a long time, and it will be fascinating to watch how the scientific community responds. I really hope that scientists work to improve our mathematical literacy as well as our ability to explain the equations so essential to our work. If we continue to ignore the problem, it could multiply- and before you know it, our number will be up.

Fawcett, T., & Higginson, A. (2012). Heavy use of equations impedes communication among biologists Proceedings of the National Academy of Sciences, 109 (29), 11735-11739 DOI: 10.1073/pnas.1205259109
Gibbons, J. (2012). Do not throw equations out with the theory bathwater Proceedings of the National Academy of Sciences, 109 (45) DOI: 10.1073/pnas.1212498109
Chitnis, N., & Smith, T. (2012). Mathematical illiteracy impedes progress in biology Proceedings of the National Academy of Sciences, 109 (45) DOI: 10.1073/pnas.1213115109
Kane, A. (2012). A suggestion on improving mathematically heavy papers Proceedings of the National Academy of Sciences, 109 (45) DOI: 10.1073/pnas.1212310109
Fernandes, A. (2012). No evidence that equations cause impeded communication among biologists Proceedings of the National Academy of Sciences, 109 (45) DOI: 10.1073/pnas.1211892109
Fawcett, T., & Higginson, A. (2012). Reply to Chitnis and Smith, Fernandes, Gibbons, and Kane: Communicating theory effectively requires more explanation, not fewer equations Proceedings of the National Academy of Sciences, 109 (45) DOI: 10.1073/pnas.1213721109

November 16, 2012 • 8:38 am