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On the Virtues of Theory / Mathematics...

Updated: Apr 4, 2019

For the most part, Biology is still having a hard time working hand-in-glove with theory / applied mathematics.

I'm sure that it has been said before, but I will say it again: biology has a mathematics problem.  For all the recent efforts put into championing interdisciplinary research, I would argue that, for the most part, the field is still having a hard time getting to grips with applied theory.


In general, I think that few would disagree that biologists, on average, are neither particularly well-versed nor enthusiastic about theory or mathematics.  Fine, you might think, its their choice, and everyone must have a specialty after all.  However, I will argue below that this is not entirely 'fine' for science in general.


What are the reasons behind the typical biologist's intransigence towards theory? Its hard to say. Although I am tempted to lay the blame at education's door. The reason is that, by and large, undergraduate degrees in biology only include minimal requirements to study mathematics in any detail. This is, of course, probably due to the fact that it does not form a cornerstone of the field, as it does with physics or engineering, for example. However, such a chicken-and-egg situation unfortunately denies future biologists proper access to an essential tool of modern quantitative science.  Perhaps more importantly, it also removes a deeply formative part of any budding scientists education.


Here, I'm afraid to say that Physics should be seen as the model to emulate. For the past century and more, mathematics, or 'theory', and experiment have worked hand-in-glove to spectacular effect. (Consider the herculean achievements made recently by the LIGO detectors, detailed beautifully in a lovely little book I just read by Janna Levin). It is, of course, impossible to be impartial, since I am a physicist myself.  However, I would like to stress that I am actually a proponent of how hard quantitative biology is, and that this has likely been a significant contributing factor holding back the development of use-able, effective theories of living systems.  Indeed, I plan to write another post soon on why I feel that biology is the contemporary frontier of classical physics.  Nevertheless, here are my arguments in favour of more maths and theory in biology. 


Maths for disambiguation


Let's consider what mathematics is? Well, for the most part, it is precisely defined, unilaterally agreed-upon language. That is, when an engineer in the UK writes the derivative dx/dt, then a physicist in France know what this means, without any ambiguity.  I really don't think that this point can be overstated.  Using subjective words to express ostensibly concrete quantifiable reproducible scientific claims is absurd.  Science deals in absolutes: even when things are uncertain, we are required to quantify that uncertainty. Results, relationships and trends etc., when expressed formally, can be scrutinized easily and improved, amended or discarded as appropriate. Without mathematics, the systematic study of biological systems (or indeed any subject) is made significantly harder than it should be.


This is compounded by the many unavoidable 'human' facets of science and publishing. Relaxing the expectation of making formal unambiguous statements leaves biology ill-equipped to deal with the highly competitive nature of modern science. For example, researchers are able to inflate, obscure or otherwise manipulate the presentation of their results more easily. This leads to a very confusing landscape of literature that is hard to unpick, and often attributes findings (and therefore citations) unfairly.  Here, I want to be clear: this is not to say that researchers are trying to be disingenuous, far from it, it simply places far greater emphasis on writing and presentation. This is especially pertinent given the international nature of science, since it exacerbates the already significant disadvantage of being a non-native English speaker.


Maths for calculation


Mathematics is also more than just a language, since it can be used to make formal statements of equivalence or comparison. Together, these can be used to form complex logical arguments, or proofs. Proofs are then combined and layered in order to make deductions that would otherwise not have been foreseeable at the outset. This is the business of doing calculations: working out the (often counter-intuitive) corollaries of our results and/or assertions.


In biology, however, such things are commonly referred-to as modelling. On a bad day, I find the term modelling degrading; it seems to presuppose approximation and lack of accuracy. To compound matters, such modelling is often consigned to either appendices or supplementary material, so as not to confuse the narrative. As you may have guessed, this is, in my opinion, completely the wrong way round. Mathematical statements provide clarity, and any deductions should be to of benefit to the manuscript, rather than squirreled away where nobody has to worry about them.


Maths as a formative part of science education


This brings me to my final point. Studying mathematics, or subjects like engineering and physics that are intertwined with maths, is highly formative. Why? Because such courses are, in my opinion, a sort-of gauntlet, the main objective of which is to dismantle a budding researcher's trust and reliance on intuition, and replace it with logically sound arguments and deductions. Humans are not computers, and it takes time to 'unlearn' what you have learned previously. For example, one quickly realizes that using verbal reasoning alone to obtain the answer to a degree-level physics problem is largely impossible (for those who are not exceptionally talented, at least). The effect is humbling, and develops a lasting and deep suspicion of conclusions not expressed formally, in the context of a specific and well-posed question. Of course, later, one can again begin to rely on intuition, but this is a new, more cautious intuition, which is grounded in the errors and successes of working within an unforgiving formal framework.


So, what do you think?

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