“When will we ever need to use it?” It is the question perpetually asked in math classrooms up and down the country and indeed around the world.
The pandemic has provided some very early responses. In recent years, we have been hearing regularly about the potential for cases to increase exponentially. The news reports regularly reported reproduction number information, R. Others reported, in vain, that we could almost reach mathematically defined herd immunity thresholds.
We relied on mathematical models, not only to understand the current situation, but to predict what could happen in the future, from the impact of mitigations to the effectiveness of vaccines. We used math to determine the most efficient order to administer vaccines during vaccine launch and to plan the roadmap for getting out of the block in early 2021. Mathematics was at the heart of most of the time.
Even outside of times of crisis we see math in the headlines every day. We use it to determine if our politicians are telling the truth about unemployment. The math allows us to track exchange rates during currency crashes. It is invaluable for pollsters who determine the popularity of our political parties and for fact-checkers who take account of politicians.
Aside from the headlines on the front page, math is the language of science. It appears everywhere, from physics to engineering and chemistry, helping us understand the origins of the universe and building bridges that won’t collapse in the wind. Perhaps a little more surprisingly, mathematics is also increasingly an integral part of biology. Scientists in my specialist area of mathematical biology are helping develop treatments for diseases and answer the question of how the leopard got the spots.
In addition to academia, we are increasingly using math in sports to improve the performance of our top athletes. We use it in movies to create computer-generated images of scenes that might not exist in reality. More trivially, we often use math in our daily life when we shop or when we follow a recipe, when we indicate the time or when we prepare the budget for the future. Most of the time we do this without even realizing it.
Of course, much of the math we learn early in school we use directly in our daily life. Other topics that we may have learned later, or perhaps never delved into, are essential for the functioning of modern society even if we often do not directly see their use.
There are certainly fragments of mathematics (especially pure mathematics) for which it is more difficult to imagine a direct use. But isn’t that true for every subject? Should we keep geography, for example, at the same rigorous standards of utility that we expect from mathematics? I don’t remember the last time I put my hard-won knowledge of oxbow lakes to good use. Likewise, in chemistry, when was the last time you needed to write the chemical reaction diagram depicting esterification? Probably not very recently.
It is not a question of denigrating these arguments, but of pointing out that it is not a specific math problem. Perhaps mathematics suffers more because it is more difficult to visualize the direct application of an algebraic equation than to represent, for example, the flow of water in a river. We all remember sitting by a river watching the water flow, but fewer of us, I would suggest, can imagine spreading our picnic blanket on the complex plane of an Argand diagram.
By necessity, mathematics tends to deal with generalities and therefore with abstractions from reality. But, at least in part, it is generality – abstractness – that makes math so pervasive.
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In college I teach students that a single abstract equation can describe the diffusion of heat through the radiator, the diffusion of a drop of food coloring into a glass of water, and the random scattering of cells on a petri dish. With such a diverse array of applications you can begin to see how powerful it is to study a seemingly abstract, lifeless equation for the profound insights it can provide about seemingly unrelated systems.
It is not for nothing that the philosopher Eugene Wigner wrote of “the unreasonable effectiveness of mathematics” to describe the natural world. Many simple mathematical ideas emerge over and over in different areas. The “normal distribution” – or bell curve – for example, can be used to describe people’s IQ and height, and has hundreds of other applications as well.
The problem math faces may be that it has too many applications. Perhaps we should answer the question: “When will we ever need to use it?” with the counter, “When won’t you?”
Kit Yates is Senior Lecturer in the Department of Mathematical Sciences and Co-Director of the Center for Mathematical Biology at the University of Bath