As a student of biophysics, I find myself riding the line between theory papers riddled with equations an d biology papers avoiding them at all costs. However, these types of work must be made to foster communication between fields, and I find that too often that doesn’t occur. There exists an overarching fear of mathematics in biology, and this fear must be addressed to induce discussions between members of different fields who may study similar problems.
We can address this problem in a number of ways. Theorists could avoid the use of mathematics in their publications altogether, nontheorists could study the required techniques to properly address the papers, or we could reform the educational system. The first option is an obvious failure. How can fellow scientists properly review such work without the work’s methods? Like a molecular biologist who includes protocols for every immunostain, sequencing technique, and data analysis, so too must theorists provide their techniques. The mathematics act as a prerequisite for effective peer review.
How can this caveat be overcome, then? I proposed two additional solutions, both focused on the education of the established researchers and the young who aspire to these roles. Education is not an appropriate solution, just yet. While I believe that an educated society is a successful society, this takes time. It will be decades until those in secondary school are running labs. Those who are already established do not have the time or motivation to take on new coursework, and rightly so. While the reader and the writer share responsibilities in the transport of knowledge, the writer can address this issue.
How, then, can theorists, biophysicists, quantitative biologists, and any of those who require the use of maths address this? I stated above that they cannot go without the use of equations. However, a temporary solution does exist. Here, then is my recommendation for using mathematics in biology and medicine. .
First, remove all equations from the main text. From these, decide which are integral to understanding and believing the thesis. With those, write as many out as can be accomplished in terms to which others can relate. For example, “F=ma” can be simplified as “acceleration is proportional to force and inversely proportional to mass” or “Force=mass*acceleration” to properly define terms and reduce the use of Greek or Cyrillic symbols. Grouping complex terms also helps the reader in this scenario. In a recent writeup of mine, an equation took the form, “X=c*k1*a*b*g/(k2+k3*p)” which I could simplify to, “displacement=force/stiffness” or Hooke’s Law. This grouped equation replaced my more practical (for experimentation) equation, while remaining accurate and becoming more illustrative for a reader. For all other equations, remove them. These only confuse the reader.
Where do these equations go? With the advent of electronic publications, the answer is simple. Place them in the supplementary material. Curious readers will pursue this information, and all others will not be distracted.
You may claim that doing so detracts from the paper, but I disagree. Mathematics as applied to biology should inform biologists. If few read the work due to distracting equations, communication is reduced in quality. All the information still resides in elsewhere for other theorists (and let’s be honest, collaborators and peer reviewers who already understand your work and may be familiar with the maths).
This technique makes your papers more tractable and better cited. It can lead to further collaborations. There are countless positive aspects of this technique. The only downsides of which I am aware would be the nuisance of opening the supplement and a less intimidating paper.
If your goal in science is to educate rather than intimidate, then let your writing show it.