Mathematical Calisthenics: Healthy for Everyone

Mathematics is the language of science. Scientists and engineers need to understand mathematical tools and reasoning. Otherwise, bridges fall down. But mathematical skills are essential for everyone in a modern society, not just the scientific elite. Often, decisions about risk or daily life require a certain mathematical analysis. Furthermore, people judge us by our ability to present logical arguments- mathematics gives us the practice we need to think and argue lucidly.

Albania's recent civil unrest and great financial collapse are largely due to failures of mathematical understanding. Pyramid schemes are a financial version of chain letters. They reward those who already participate in the scheme but promise to give large rewards to those who join now, at the expense of many new members who choose to participate later. Eventually, though, the supply of new members will slow and end, and the scheme will collapse. A large fraction of Albanian citizens invested in schemes which depended essentially upon the exponential growth of new participants. More analysis or mathematical fluency could have in this case saved considerable death, suffering, collapse and unhappiness. Though striking, this example may seem somewhat distant. Closer to home, we should think about widespread participation in ill-advised gambling and lotteries as some sobering food for thought, as should be the popularity of such books as "How to Lie with Statistics" and "How to Lie with Maps."

In political and social settings, a mathematical perspective is frequently essential. John Allen Paulos, author of "Innumeracy" and other popular works about the role of mathematics in modern society, described the proposed requirement considered recently by airline regulators. Out of concern for the safety of babies in airline accidents, there was a proposal to require babies to fly in their own seats in a a car seat, to protect them in the event of a crash. Currently, children under two are allowed to fly for free in the lap of an adult. Though this proposed change would improve the safety of the infant in that setting, a closer analysis revealed the following likely events- if parents were required to pay for a full seat for a flying baby, the added expense would result in a significant number of cases when they chose to drive instead. Driving is considerably more dangerous than airline travel, and the end result was a predicted overall increase in infant deaths and injuries. Though the ones who chose to fly would indeed be safer, that improvement would have been more than offset by the increase in highway injuries and deaths from those who would have driven principally for financial reasons. As society continues to change, relationships become increasingly confusing and complex. Computing the "cost" and "benefit" of what seem like non-mathematical decisions can be tricky and require some comfort with mathematical arguments.

Not only is mathematical fluency important for society as a whole, it is important for each individual. Whether we like it or it or not, on a daily basis, it is our obligation to convince those around us that we understand what is going on and that we are able to solve problems. Whether we study, teach, sell cars, write articles, help patients or build houses, our credibility is constantly on trial. In order to convince those near us that we do in fact understand what is going on, we need to be able to express ourselves clearly and present simple but well-thought out explanations. It is not merely our jobs to be understood- if I say "me hungry banana want", people will probably be able to figure out what I mean, but their confidence in my ability will be (understandably) low. They should regard my conclusions and opinions with suspicion in the future.

Mathematics presents a good opportunity for us to work with logical concepts and construct simple yet persuasive arguments. Even in the setting of simple mathematical ideas like arithmetic or geometry, it can take some practice before we are comfortable expressing our arguments precisely and convincingly. From this experience, we can learn the art of convincing others that we understand what is going on- an integral part of every life, mathematical or not.

Mathematical literacy is essential for us. Society needs to be comfortable with potentially subtle mathematical arguments to make reasonable decisions that affect us all. Individually, we need to be precise and accurate, for which mathematics is an excellent training ground. The study of mathematics is hard work and is not to be taken lightly, but it has its rewards-- for everyone.

Sean Cleary