Engaged Mathematics
Perhaps the greatest gap between the public importance of an academic area, and its reputation for ease of access, is in mathematics. As Temple University mathematician and popular author John Allen Paulos has written regarding his classic book Innumeracy: Mathematical Illiteracy and Its Consequences, "at least part of the motivation for any book is anger, and this book is no exception. I'm distressed by a society which depends so completely on mathematics and science and yet seems to indifferent to the innumeracy and scientific illiteracy of so many of its citizens." Paulos, in books such as Innumeracy, A Mathematician Reads the Newspaper, and A Mathematician Plays the Stock Market, has done a lot to show the practical importance of mathematics and make it accessible.
Another laborer in the same vineyard is Douglas N. Arnold, Director of the Institute for Mathematics and its Applications (IMA) and Professor of Mathematics at the University of Minnesota. Arnold has been widely quoted in the popular press for his insights into two intriguing phenomena: the size of the claimed world-record muskie, and the odds of winning the Powerball jackpot. In the muskie case, Arnold and several other mathematicians used projective geometry to raise some cautions about the apparent size of the fish. In the Powerball case, he used striking comparisons to dramatize the long odds:
- "You have a seven times higher chance of being killed in a car accident if you drive one mile to the store for a ticket and one mile back home than you do of winning this Powerball jackpot."
- "For an average American, the chance that you will die in the next 30 seconds is greater than the chance that your Powerball ticket will hit the jackpot,"
- "You would need to buy 101 million randomly selected tickets in order to have a 50 percent chance of winning the jackpot. You would have to buy one ticket per minute for 193 years to purchase that many tickets. And don't forget that the cash value of the jackpot is only $177 million, and that gets reduced to $120 million after federal and state taxes."
The Institute for Mathematics and its Applications applies the highest level of modern mathematics to a broad array of real-world problems, including cardiology, telephone networks, power blackouts, robotics, computer security, microstructure of magnetic alloys, solid propellants in rockets, and many industrial applications. These diverse applications result from intense collaborations and mutual education between mathematicians and specialists in other areas - just the sort of reciprocal partnership through which we define engagement.
The IMA's funding was recently renewed with a $19.5 million grant over five years from the National Science Foundation (NSF), the largest single research investment the NSF has ever made in mathematics. It's yet another example of how high-quality engaged research can pay off financially as well as intellectually and practically.