Mathematical detail puts scientists off

Researchers from the University of Bristol have found that scientists pay less attention to theories that are laden with mathematical formulae. Although one might assume that the popularity of new research varies according to its academic merit, the study, published in the journal Proceedings of the National Academy of Sciences, shows that maths-heavy articles are referenced 50 per cent less frequently than those containing little to no maths.

I spoke to Dr Tim Fawcett, Research Fellow at Bristol’s School of Biological Sciences, to find out why maths appears to be turning scientists off, and to ask what he believes can be done to rectify this situation…

Were you surprised to find that the likelihood of a paper being referenced by another scientist is influenced by the amount of mathematics that it contains?
I wasn’t massively surprised. In fact, that is why we decided to investigate this issue in the first place. We suspected that papers containing lots mathematics would tend to be avoided by many scientists, or at least not cited in their work. We therefore decided to examine articles to see whether this was really the case, and it turned out that it was.

Do you have any idea as to why it is that scientists are paying less attention to maths-heavy articles?
I think that these papers can sometimes be heavily technical. If the maths is not explained in the clearest possible manner, it can require a lot of effort on behalf of the reader to really grasp what the article is talking about. Often, because scientists are under considerable pressure to write concisely, you end up with articles that are densely packed with mathematics. Such articles can be difficult for people, including scientists, to understand.

Did you question scientists directly or did you analyse other data that were available?
We analysed other data that were available. We looked at how often papers were cited by other scientists. This type of information is readily available, and provides a measure of how influential a paper has been within its particular field. Authors hope that the number of citations that their work receives reflects the scientific quality of that work, but in fact, our analysis reveals that the number of equations contained within a paper also has a strong impact.

Is there is a danger that this tendency could lead to scientifically significant work being overlooked?
Absolutely. I think that it is certainly the case that some very important theoretical papers are not getting the recognition that they deserve because their mathematical content is not being explained in the most user-friendly way.

Could you explain more about how maths-heavy theories might be better presented in order to gain the attention of their audience?
I think that the best solution is for authors to spend more time, and to use more words, outlining the details of their mathematical equations. It is important to explain how equations are derived and how the scientific implications of the mathematics are employed. You cannot simply cram a paper with equations. There need to be verbal explanations alongside these equations in order to take the reader through all of the assumptions and implications involved in the theory.

You have said that the limited page space offered by peer-reviewed journals poses a potential problem for scientists trying to fully explain their mathematics. Do you think that the onset of online journals might provide a solution to this problem?
As I understand it, all of the online journals produce printed copies as well, so page space still poses a challenge. Publishers allow journals a certain page allocation every year, and so journals are under pressure to reduce the length of the articles that they publish. Although many of these journals are now predominantly read online, there is still a challenge posed by limited page space.

However, appendices are often published exclusively online so page space is not constrained within these sections. In fact, our analysis shows that if authors put a lot of their mathematics in an appendix, other scientists do not seem to be deterred from citing their articles.

So a compromise can be reached whereby the online appendix supplements the printed article?
Yes, that’s right. This is a pragmatic solution, given that there is such a strong constraint on page space for the main article. If you can include the majority of your mathematics in an appendix, as long as you have carefully explained the assumptions of your work, you can keep the detail intact whilst maintaining the attention of your peers.