How mathematics explains the world

¶ … Math Explains the World

The title of James Stein's book, How Math Explains the World, is, perhaps, a bit deceptive. The reader who is expecting simplified explanations of complex mathematical principles will be disappointed. Although Stein has simplified many concepts, they will still be challenging for the reader who struggled with math in high school or who took only the minimum requirements in college. Math does explain the world, from understanding how a Ponzi scheme works to predicting the occurrence of a lunar eclipse. Most people do not, in their daily lives, use math the way Stein does in his role as writer and university mathematics professor. Everyone, however, is the beneficiary of the mathematical discoveries that have been made and applied through the ages. Stein's clear writing style, liberally laced with humor that is often self-deprecating, saves his book from being too esoteric and ensures that it will appeal to a wider audience than PhD's and other math geeks. Stein admits to taking a risk, citing Stephen Hawking's anecdote: Hawking's publisher told him that for each equation he included in his book (A Brief History of Time), the readership would drop by 50%. Hawking refused to underestimate his reading audience and ultimately made publishing history by selling more than ten million copies (Paris, 2007). Stein took the same risk and although his book has not achieved the same status as has Brief History, How Math Explains the World still explains a great deal, and in a style that will engage the mathematician yet provide clarification and meaning to the reader with much less formal mathematical background. Stein acknowledges that math is "scary." As a professor of mathematics, he encounters students (such as elementary education majors) who are required to take math but who are apprehensive. It was not their best subject in school, in many cases, and there has often been a gap between high school and college courses. Stein endeavors to set them at ease right away, quoting Albert Einstein, who said, "Do not worry about your difficulties with mathematics; I assure you mine are far greater." The reassurance Stein gives his undergraduate students is the same one he strives for with his readers. Most readers would agree that he is successful.

Stein demonstrates his knowledge and enthusiasm time and again as he details mathematical discoveries throughout history, dating back to ancient times. Some of the information presented is interesting, though not useful to the average person except as a point of trivia. For example, quadratic equations, a staple of the high school algebra class, were first solved by the Babylonians. It is an interesting fact and one that may be surprising -- quadratic equations are not a modern invention at all but an impressive mathematical accomplishment thousands of years old. Knowing this, however, does not provide any insight into how such a problem can be solved.

The subtitle of Stein's book is A Guide to the Power of Numbers, from Car Repair to Physics. Stein's down-to-earth writing style and considerable wit have him explaining, with apparently equal ease, the mathematical reasons why we cannot know exactly when our car will be ready at the repair shop, how the rules of probability can help one organize shoes in a closet, and how black holes were discovered. Even if the reader rarely puts to use any of the mathematical ideas Stein advances -- although, as Stein continually demonstrates, math is everywhere -- his explanations and examples make for fascinating, mind-stretching reading.

Of more practical interest to the present-day non-mathematician are Stein's explanations of probability, particularly with respect to card playing, and his extensive exploration of the topic of voting and elections. Most people who took American history in high school will recall the first failure of the electoral college, when Thomas Jefferson and Aaron Burr both received the same number of electoral college votes and the decision-making was thus transferred to the House of Representatives. As Stein points out, despite attempts over the years to fix the electoral college system, it is still mathematically flawed. Stein suggests, without overtly stating so, that there could be a real demand for change if more Americans understood this.

Stein's book relates to the health care field in two ways. First, math courses are required as part of college work in the pursuit of most degrees in the health care field. The level of required achievement is different, depending on the degree sought. For example, a student pursuing an LPN may take a semester or two of college algebra. A pre-med student is often required to take one or two semesters of calculus. A student pursuing a master's degree in health care administration will take courses in statistics, finance and accounting. The master's candidate can perhaps more easily see the relevance of the required math courses toward the future career. For the nursing student studying algebra or the pre-med student struggling through calculus, the correlation between academic study and actual practice may be unclear. They may wonder why they must undertake these courses, which seem to have little to do with the work in which they will eventually be engaged.

Reduced to its essence, mathematics is about problem solving. So, too, is the health care profession. Patients do not feel well. They exhibit symptoms. Doctors investigate so that healing can take place. Perhaps a care center has outgrown its physical facility; administrators may develop a fundraising campaign with the goal of building a new wing that will accommodate more patients or house the latest diagnostic equipment. Although mathematics may not be a major part of these endeavors -- outside the calculations needed for prescriptions, for example, or the accounting practices employed to track contributions -- it is the process of problem solving that math teaches us, and which we can apply to these and other situations that present themselves in the field.

Math teaches us that problem solving is a logical process. There are a series of steps that must be followed if there is any hope of reaching a conclusion. As Stein points out, not all mathematical questions have answers -- at least, not that can be found at the present time. It is not the answers fail to exist; we just do not currently have the tools or the information to find them. This is also true in health care, where the government has yet to find a solution to skyrocketing costs and access to good care by all citizens. There are still no cures for cancer, Alzheimer's disease, AIDS, diabetes, Lou Gehrig's disease, among others. We can treat the symptoms of the common cold -- at a cost of nearly $40 billion a year (Marketplace, 2011) -- but a cure is still elusive. Just as there are now solutions to math conundrums that once seemed impossible to solve, so, too, have advances been made in health care to address the problems mentioned, and others as well.