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May 2010
"How to navigate a 'career obstacle course'," interview with Barbara L. Krumsiek by Adam Bryant. International Herald Tribune, 24 May 2010. This piece appeared in the "Corner Office" column, which presents brief interviews with outstanding leaders from the business world. Krumsiek is the chief executive and chair of Calvert Group, an investment firm. "I'm not a trained business or organization development person," she remarked. "I'm a mathematician. I was an analyst and had no one working for me for the first seven years of my career." She worked with other departments in the firm to create a new business strategy, and soon she found herself with 200 people working for her. She was a mathematics major at Rutgers University and received a master's degree in mathematics from the Courant Institute at New York University. In the interview she recalled that, when she was a teenager, a neighbor told her that girls and women "don't do math". "I remember thinkingwhatever I was13 or something, thinking very calmly to myself, `He doesn't know what he's talking about.'"  Allyn Jackson "How Much Oil’s Spilling? It's Not Rocket Science," by John Allen Paulos. abcNews, 23 May 2010. The question of how much oil is leaking into the Gulf of Mexico has been on everyone’s mind since the break on April 20. BP has stated that they believe about 5,000 barrels are leaking every day and have made a big deal out of how difficult this number is to determine. In this column, Paulos explains that arriving at an estimate is not really that difficult, requiring little more than a basic understanding of geometry and high school mathematics. Steve Wereley, an engineering professor at Purdue University, has come up with a very reasonable and understandable formula. The main idea is to think of the spill as having a cylindrical shape (since that is the shape it has while it’s still in the pipe), and therefore the amount of oil spilled is really the volume of a cylinder, which can be calculated by multiplying its crosssectional area times its length. The first piece of data is well known to BP since they know the radius of the pipe (10.5 inches). The length is not so easy to come by, but Wereley studied the poor video clip that was released by BP on May 12 and was able to come up with an approximate rate of flow for the oil. One can then compute the length of the cylinder by just multiplying the rate of flow by the time the oil has been flowing. Wereley’s estimate is that the rate of spill is about 90,000 barrels a day. He admits that this is just an estimate and that he may be off by 20 percent above or below this number, but this is still almost 20 times the number given by BP. Paulos then raises a few interesting and troubling questions. Did no one at BP have the required basic understanding of geometry? If they did, why did they keep this quiet? Why was video released so late, when it clearly was a key factor in determining the rate of flow of the spill?  Adriana Salerno
Obituaries of Martin Gardner: Martin Gardner, known for popularizing recreational mathematics, passed away on May 22 at the age of 95. The Associated Press obituary (which was picked up widely by the media) quotes from Allyn Jackson's "Interview with Martin Gardner" (Notices of the AMS, March 2005), in which she wrote, Gardner "opened the eyes of the general public to the beauty and fascination of mathematics and inspired many to go on to make the subject their life's work... [His] crystalline prose, always enlightening, never pedantic, set a new standard for high quality mathematical popularization." Yam's profile begins, "He wrote Scientific American's Mathematical Games column, educating and entertaining minds and launching the careers of generations of mathematicians." Gardner is widely known for introducing puzzles, fractals and M.C. Escher to the general publicin his column for 25 years and in his 50 books. The AMS awarded Gardner the Steele Prize for Mathematical Exposition in 1987 for his work on math, particularly his Scientific American column. Gardner had a devoted following, many of whom met at the annual Gathering for Gardner. The New York Times obituary quotes cognitive scientist Douglas Hofstadter: "Martin Gardner is one of the great intellects produced in this country in the 20th century," and notes that W. H. Auden, Arthur C. Clarke, Jacob Bronowski, Stephen Jay Gould and Carl Sagan were admirers of Mr. Gardner. Interestingly, Gardner never took a college math course, but said his "talent was asking good questions and transmitting the answers clearly and crisply." (Photograph by "Card Colm" Mulcahy, Spelman College.)  Annette Emerson
"Noted UWMadison mathematician Rudin dies at 89," by Deborah Ziff. Wisconsin State Journal, 21 May 2010. Walter Rudin, whose texts Principles of Mathematical Analysis, Real and Complex Analysis, and Functional Analysis are familiar to generations of graduate students, died May 20 at the age of 89. Rudin was born in Austria. He and his family fled to France in 1938 after the Anschluss. They then moved to England in 1940 after France surrendered to Germany. He served in the British Navy during World War II and came to the U.S. after the war. In 1949 he received his PhD from Duke University. Rudin then became a C.L.E. Moore Instructor at MIT before joining the faculty at the University of WisconsinMadison. In 1993 he won the AMS Steele Prize for Mathematical Exposition for Principles of Mathematical Analysis, and Real and Complex Analysis. Rudin's autobiography, The Way I Remember It, was published in 1997. He is survived by his wife, Mary Ellen, a noted topologist who was also a mathematics professor at the University of WisconsinMadison, four children and four grandchildren. (Photo courtesy of Ken Ono.)  Mike Breen "Proof at last for Boltzmann's 140yearold gas equation," by Jacob Aron. New Scientist, 18 May 2010. The first sentence of this article incorrectly states that Boltzmann's equation, a differential equation from statistical mechanics, has only now been proved to be correct. The differential equation, which was first derived by Boltzmann and Maxwell about 140 years ago, is widely used to describe and predict the location and momentum of gas molecules over time. The significance of the recent discovery is the proof that, given initial conditions sufficiently close to equilibrium, the equation has a global classical solution that rapidly decays to equilibrium. This means that, in some sense, the solutions are not very sensitive to small perturbations. As one of the researchers, Phillip Gressman, states,“Even if one assumes that the equation has solutions, it is possible that the solutions lead to a catastrophe, like how it’s theoretically possible to balance a needle on its tip but, in practice, even infinitesimal imperfections cause it to fall over,” Professors Gressman and Robert Strain presented their solution and discussed the history of the discovery of local solutions in the March 30 issue of Proceedings of the National Academy of Sciences (abstract). Their solution uses fractional derivatives, which are not typically used for analyzing the physical world. The New Scientist article closes by attempting to discuss the hypotheses of the theorem, stating that the equation produces "the right answer" when gases are close to equilibrium but not necessarily in other cases "such as a storm."  Brie Finegold "Metric Mania," by John Allen Paulos. The New York Times Magazine, 16 May 2010, pages 1112. In this article, Temple University professor of mathematics John Allen Paulos argues for the wise and careful use of numbers to influence or measure the impact of public policy. Paraphrasing Albert Einstein, Paulos writes that “unless we know how things are counted, we don’t know if it’s wise to count on numbers.” He points to two areas where care must be taken: in the assumptions about how data to be counted should be categorized, and in the choice of the criteria used to rank that data. For example, according to a plan New York City began to use a few years ago to evaluate its schools, “much of a school’s grade was determined by whether students’ performance on standardized state tests showed an annual improvement.” Aside from the fact that so much weight was placed on “essentially random fluctuations,” and that schools would focus on teaching test topics, schools that were already doing well—“and had little room for improvement”—might receive mediocre grades while schools that performed poorly “could receive high grades by improving just a bit.”  Claudia Clark "Do the Math: Best Cram School," by Jyoti Thottam. Time: Best of Asia 2010, 13 May 2010. Dubbed Best Cram School within Time magazine's Best for the Mind series, the Super 30 Program was founded in an effort to give children who are bright but extremely poor a chance to work in science and technology. Having missed out on a chance to go to Cambridge due to his family's poverty, Indian mathematics instructor Anand Kumar started his program while he was still a student in mathematics at Patna College of Science. Each year, to help them pass the entrance exam to one of India's Institutes for Technology, he gives a a set of 30 specially selected students a full year of free tutoring, room and board. Since 2003, 182 out of the 210 students who he's trained have passed the exam. Rather than soliciting donations, Kumar uses the profits from evening classes for students preparing to take other tests. Most recently, Kumar met with the Prime Minister to discuss the possibility of expanding his program to help rural children. The success enjoyed by those students who pass the entrance exams is not discussed, but Shashi Narayan, one of Kumar's former students, is currently pursuing his master's degree at the University of Malta. There are success stories posted on the program's website for two other Super 30 alumni.  Brie Finegold
"When origami meets rocket science," by Rachel Saslow. The Washington Post, 11 May 2010, page HE01. Origami is the art of folding paper. Sounds simple, right? It was, until the mid20th century when Akira Yoshizawa created a language of arrows and lines to show people how to fold different designs. This begged the question of whether this new abstract language could lead to the creation of new origami designs. Robert Lang, a former laser physicist, who folded the work pictured on the left, is at the forefront of this new origami revolution, especially in an area called computational origami, which is focused on using mathematics and computers to create art. Not only has he been able to create new breathtaking designs, but also he has been instrumental in applying origami design to science and technology, like designing a lens that could go into space as well as new ways to fold car airbags. But Lang is not the only scientist working in this intersection between art and science. Other researchers have used origami to create stents, which need to be small enough to fit inside blood vessels but then can be expanded to hold the artery or vein open. Tom Hull, a mathematics professor at Western New England College in Springfield, MA, uses origami to illustrate concepts in calculus, number theory, geometry, and algebra. MIT mathematician Erik Demaine studies how origami relates to protein folding inside the body (which could give insight into diseases like Alzheimer’s and Parkinson’s). Demaine is also working with Lang on a paper about the tree method of origami design, and has collaborated with his own father in making sculptures, which can be seen on display in the Museum of Modern Art in New York City. Computational origami, which Demaine says “was initially a very crazy idea,” has proved to be essential to both the evolution of an ancient art and the creation of a whole new area of scientific development, which is not something one would expect to say about many areas in mathematics. (Anna's Hummingbird, opus 466 & Honeysuckle, opus 468 courtesy of Robert J. Lang, www.langorigami.com. Click on the image for a larger version.)  Adriana Salerno "How to Beat a Chess Grandmaster (Blindfolded)," by Burkard Polster and Marty Ross, The Age Education Resource Center, 10 May 2010. On the occasion of the 2010 World Chess Championships, mathematicians Burkard Polster and Marty Ross advise the reader on how to become—or at least appear to be—a chess grandmaster like George Koltanowski. In addition to having the ability to play multiple chess games while blindfolded, Koltanowski could do the following: “He would ask 64 members of his audience to write a word or phrase of their choice on a piece of paper, and to place them on the squares of a chessboard. Koltanowski would glance at the board and then, blindfolded, he would recite the 64 phrases. Moreover, he would start on a square selected by the audience, and he would recall the phrases by following a knight’s tour,” in which each move is “two along, one across” and “each square is visited exactly once.” While such a feat may prove too difficult for the average individual, if you are willing to forgo memorizing phrases, you can perform the “Beginner’s Koltanowski”: starting from any square, you recite a knight’s tour of the squares of a chessboard using a knight’s tour loop that you have already memorized. To be even more impressive, if you memorize the knight’s tour loop pictured here, and, starting with the first square, count down from 64, you will have constructed a magic square in which the sum of numbers in each row and each column is 260!  Claudia Clark "The Gospel of WellEducated Guessing,” by Tom Bartlett. The Chronicle of Higher Education, 7 May 2010, page A1. How much money is in a Brinks truck? How much does a roundtrip plane ticket from New York to Los Angeles cost? How much is the annual state budget of Delaware? These are questions whose answers can probably be found through an internet search (although the Brinks truck question is a little more sensitive and harder to find an exact answer to), but it only takes Sanjoy Mahajan, a lecturer at the Massachusetts Institute of Technology, a little time of scribbling on a piece of paper to make a very good guess. Mahajan is, in fact, famous for this uncanny ability to guess, and recently wrote a book summarizing some of the techniques he uses. In StreetFighting Mathematics: The Art of Educated Guessing and Opportunistic Problem Solving, he lays out some of the basic principles, like divide and conquer, take out the big part, and trust your gut. Mahajan teaches a class at MIT based on these same principles, and the students admit it takes some time to adjust from trying to get exactly the right answer to coming up with very close guesses. This article does a good job of giving the readers an insight into the mind of Mahajan, by carefully describing his thought process when trying to answer some of the questions stated earlier. It is also an encouraging portrait of how practical mathematics is not necessarily about getting the right answer, but about getting close enough. Read Mahajan's answers to readers' questions/challenges on a New York Times blog.  Adriana Salerno "Five or Six Reasons Why Parity Puzzles Are Fun," by John Allen Paulos. ABC News, 2 May 2010. In honor of April being Mathematics Awareness Month, John Allen Paulos decided to entertain readers of his column with a few parity puzzles. These are puzzles that have to do with numbers being either even or odd. Five of the puzzles Paulos presents are what he calls “straight math problems,” and then he presents an interesting example involving politics (although this last one is less clearly related to the idea of parity, and “doesn’t really count,” he says). The puzzles involve ideas ranging from simple addition and subtraction to more complex concepts like probability, and the common thread is that all of the solutions depend on the evenness or oddness of certain numbers. He also offers solutions to the problems, but encourages the readers to try the problems on their own first.  Adriana Salerno "The Bootstrap," by Cosma Shalizi. American Scientist, MayJune 2010, pages 186190. This overview of the statistical technique known as the bootstrap is aimed at readers who have some experience with the abstract principles underlying the field of statistics. Given a set of sample data, the underlying datagenerating mechanism will have a set of characteristics—called parameters— that can range in value, and the goal is to estimate the values of these parameters. The author describes the notion of simple estimators, such as the mean of the data and theoretical probability distributions, as an idea that at times favors mathematical simplicity over accuracy. The bootstrap method combines estimation and simulation by first finding a model for the data, then using the theoretical model to generate sets of simulated data which, based on their theoretical similarity to the sample data, provide a means to estimate the true value of the parameter. The author also explains the technique of splining and uses the stock market as an example to illustrate the key points.  Lisa DeKeukelaere

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