The Unreasonable Effectiveness of Operations Research, by Sanjay Saigal. As we rush to get hold of the newest and fastest computer processor, we remain unaware of the research that provides us this speedy access to information. Over a period of 15 years, year-long computations became one-second tasks. This was recently pointed out by another post on a New York Times blog . But what has caused this drastic improvement? Advances in operations research (OR) have increased speeds of calculation of software by a factor of 30,000 over 15 years while faster processors have increased hardware speeds by only a factor of 1,000 over the same time span. Those unfamiliar with the area of OR can refer to one of blogger Sanjay Saigal's earlier posts which uses OR to determine the most efficient way to grill steaks.
Specifically, cumulative advances in linear optimization have paved the way for more efficient software. Also, better connections between software and the data it uses have added to improvements. Saigal laments the low profile of OR in his post. But he also points out that rather than there being one headlining breakthrough in the area, a slow but steady evolution has taken place due to input from academics and industry specialists in both mathematics and computer science. Thus the title of his post rings true.
Sierpinski Triangle Talk and Sierpinskitaschen, by Dan Finkel and Katherine Cook. How many different ways can the Sierpinski Triangle be constructed and described to high school or middle school students? Dan Finkel's 25-minute video provides a trio of such descriptions in terms of recursive removal of triangles, number theory (from Pascal's triangle), and L-systems. In the course of the video, he introduces students to the idea of Hausdorff dimension (non-integer dimension), eliciting probing comments and sounds of surprise from the audience. Then, in a later post, a finite approximation of Sierpinski's triangle is realized in the form of a baked good dubbed "Sierpinskitaschen"!
The main purpose of this blog is to chart the experiences of its Seattle-based writers in the area of mathematics education. The two writers give workshops and organize events to educate the public, especially children, about mathematics. Finkel's video is of a presentation he gave to a Math Counts group, and his theme was that "Anything worth doing once is worth doing twice." He uses the three very different ways of viewing this fractal object to drive home the point that the deepest and most interesting connections in mathematics are found when we go over (or stumble over) familiar territory but in a different way.
--- Brie Finegold
"Brown professor's love of math just multiplied," by G. Wayne Miller. The Providence Journal, 28 March 2011.
In this front-page article, the Providence Journal profiled the Society and its executive director, Don McClure, who was a professor at nearby Brown University for four decades. At first Miller is a little leery of mathematics and the research books he sees, but after talking with McClure, he begins to appreciate its beauty. McClure describes how he got interested in mathematics: “It was a mental challenge, and I found it to be very interesting....I just enjoyed figuring out how to crack hard problems. Solving a challenging math problem is probably like prevailing today in a challenging video game.” Miller finishes by writing that Mathematical Moments "are visually appealing, though not flashy or overly slick, like the AMS itself, this organization headquartered in a cinder-block building."
--- Mike Breen
"Pioneer of High-Dimensional Spaces Wins Abel Prize," by Dana Mackenzie. Science, 23 March 2011;
This is a small sampling of the extensive worldwide coverage of the news that John Milnor (left) has been selected to receive the 2011 Abel Prize, an approximately US$1-million award given by the Norwegian Academy of Science and Letters. Milnor is one of the greatest mathematicians of modern times. A recipient of the Fields Medal, he is the only person to have received all three AMS Steele Prizes: the prize for exposition, the prize for a seminal contribution to research, and the prize for lifetime achievement. The citation for the latter award, given in 2011, says: "Milnor stands out from the list of great mathematicians in terms of his overall achievements and his influence on mathematics in general, both through his work and through his excellent books." One of his biggest results, concerning smooth structures on the 7-sphere, shaped the subject of differential topology starting in the 1950s, along with his work on surgery theory for manifolds. In finding a counterexample to the Hauptvermutung---a conjecture about geometry that was formulated at the beginning of the 20th century---he helped to create a "big picture" of the relation between the topological, combinatorial, and smooth worlds. His seminal work with Michel Kervaire helped to establish the subject of four-dimensional topology. In the past thirty years, Milnor has played a prominent role in the development of the field of low-dimensional dynamics. The Abel Prize recognizes his deep and wide-ranging impact on mathematics. (Photograph by Marco Martens.)
--- Allyn Jackson
"Mathematical Budding Model Revealed in a Lily," by Tim Wall. Discovery News, 22 March 2011.
Harvard mathematicians Haiyi Liang and L. Mahadevan have discovered a new model for how the delicate structures of flowers bloom. Previous ideas of how flowers unfolded involved different growth rates between the inner and outer layers of petals or motion in the midrib. But Liang and Mahadevan marked lily buds with a series of dots and watched as they opened in a time-lapse video, and found that "the flower petals burst forth from their buds by elongating their edges more than their middles. The outside edges grow up to 40 percent more than the interior midrib, which causes the petals to wrinkle. The wrinkling creates stresses in the bud until... the stresses force the bud to open, and the petals then curve and curl into the shapes that humans find so beautiful." This new "wrinkly-edge" model "not only helps scientists understand how flowers open but could lead to advances in bio-mimicry, or the engineering of devices based on models from nature, such as thin-film motors and actuators."
--- Annette Emerson
"The man and his math," by Sangeetha Devi Dundoo. The Hindu, 22 March 2011.
"[Srinivasa Ramanujan] was a genius far ahead of his times and math was his creative expression of numbers and not his means to make money. His was an extraordinary, inspiring and emotional journey," says film director Dev Benegal. The filmmaker is interviewed about a film he plans to make on the life of mathematician Ramanujan, who grew up in poverty in Kumbakonam, India. Benegal, who has been researching Ramanujan's life for four years, says "the film will explore his life at an emotional level--the struggle of his parents, particularly his mother; Ramanujan's relationship with his wife, which is one of the greatest love stories of our times; the sacrifices that the wife had to make which are unknown and unheard of; and the bond that Ramanujan and G.H. Hardy shared." (Image: Wikimedia Commons.)
--- Annette Emerson
"The mathematics of being nice: Interview with Martin Nowak." Interviewed by Michael Marshall. New Scientist, 21 March 2011.
In this interview, mathematical biologist Martin Nowak discusses human cooperation and how it can be analyzed mathematically. In particular, his research uses evolutionary dynamics, evolutionary game theory, and experimental tests of human behavior in order to explore questions about why cooperation arises in human societies. He categorizes human cooperation into five different types, one of which is called "group selection." The interviewer notes that the notion of group selection has been around for some time and has recently been attacked by evolutionary biologists. Nowak concedes that the original definition of group selection was imprecise. "But recent mathematical models explain very clearly when group selection can promote the evolution of cooperation," he says. "There must be competition between groups and migration rates should be low." The interviewer also asks whether Nowak is hoping to put all of biology on a mathematical footing. He answers yes, noting that this has happened in many other scientific disciplines. "Without a mathematical description, we can get a rough handle on a phenomenon but we can't fully understand it," he says. "In physics, that's completely clear. You don't just talk about gravity, you quantify your description of it. The beautiful thing about mathematics is that it can decide an argument. Some things are fiercely debated for years, but with mathematics the issues become clear." The interview also touches on Nowak's religious beliefs.
--- Allyn Jackson
"Danville teen wins Intel Science Talent Search and $100,000," by Rich Hurd and Eric Louie. San Jose Mercury News, 15 March 2011;
Seventeen-year-old Evan O’Dorney’s solution to a challenging math problem recently won him $100,000 and a meeting with President Barack Obama. O’Dorney, a home-schooled student from Danville, CA, was selected as this year’s winner of the Intel Science Talent Search, for his formula for predicting whether two methods for estimating square roots using fractions had infinitely many results in common. O’Dorney is no stranger to the limelight, however; he scored an introduction to former President George H.W. Bush for winning the Scripps National Spelling Bee in 2007 and chatted with President Obama on the telephone after having the second-highest individual score in the International Mathematical Olympiad in 2010. He is also a two-time winner (2010 and 2011) of the national AMS contest Who Wants to Be a Mathematician. O'Dorney, who is headed to Harvard University in the fall, says it took him a year to solve his winning math problem for specific cases and several months afterward to generalize the solution to a formula. In the Science article, there is some background on O'Dorney and his answers to three questions. When asked about his working style, he said, "For two weeks, when I was really getting the main ideas, I worked all day ... It's just the excitement of the math. I never need [caffeine] ... I almost have the opposite problem. If I get into math, I have to remind myself that I'm hungry and I need to eat."
--- Lisa DeKeukelaere
"Q&A: Why Do We Celebrate Pi Day?," by Feifei Sun. Time Newsfeed, 14 March 2011;
These articles are about the number Pi, its allure, and what people did this year to celebrate Pi Day (3-14). In the Time article, David Blatner--author of The Joy of Pi--says that although trillions of digits of Pi have been calculated, there are still questions, such as are the digits distributed uniformly? Blatner said that when he was researching his book, he "was just amazed at how many places Pi shows up from cartoons to movies...And the fascination and lure of Pi really is this sense of mystery that it points to." In the Chicago Tribune article, Ford writes of activities in Chicago-area schools. At Walter Payton High School, students threw hot dogs on a grid in illustration of Buffon's Needle Problem. Students who recited digits of Pi past "the first few" got a piece of pie. The size of the slice of pie increased by one degree for each digit. Raytheon delivered hundreds of apple pies to middle and high schools within a 3.14 mile radius of its headquarters in Waltham, MA. The AMS celebrated by conducting Who Wants to Be a Mathematician at Providence College, which attracted the Governor of Rhode Island, Lincoln Chafee. See the University of Rochester video (on YouTube) saluting Pi.
--- Mike Breen
"Pythagorean Theorem: There's More To This Equation," by Robert Siegel. All Things Considered, 9 March 2011;
NPR host Robert Siegel interviewed husband and wife Robert and Ellen Kaplan about their new book, Hidden Harmonies. Interestingly, not only are the Kaplans both mathematicians but during the interview Siegel mentions that he was a math tutor in high school before hosting All Things Considered. In the interview the math trio discuss all things geometry. How the Pythagorean Theorem wasn't really discovered or proved by Pythagoras, but by one of his followers and how another follower named Hippasus fell out of favor for proving that the square root of two is an irrational number. Legend has it that Hippasus was forced to throw himself off the nearest cliff for the irrational proof. Mitchell writes about how the Kaplans got involved in mathematics and their reason for writing the book: "We want to have people coming to love math as they do music."
--- Baldur Hedinsson
"Research center inaugurated at Brown," by Gina Macris. The Providence Journal, 8 March 2011.
The inauguration of the Institute for Computational and Experimental Research in Mathematics, housed at Brown University, was reported by The Providence Journal. The Institute, which will be funded by a renewable, five-year, $15.5 million National Science Foundation grant, will sponsor a series of semester-long programs intertwining computation and mathematics, and encompassing both research and education. A scientific advisory board including officials from corporate partners Microsoft, Google, and IBM will help shape the Institute's research programs, while an education advisory board will explore ways to improve math and computer education in Rhode Island. Speakers at the inauguration, including Rhode Island's two senators, Jack Reed and Sheldon Whitehouse, Brown President Ruth Simmons, and Representative James R. Langevin, praised the Institute as an engine of both intellectual and economic growth, and predicted it will boost U.S. competitiveness in the global knowledge economy. Headed by Jill Pipher, an analyst and cryptographer at Brown, the Institute is the result of the joint efforts of Brown's mathematics and computer science faculty. In addition to providing positions for postdoctoral and visiting researchers, the Institute will host a number of international mathematics conferences, 10 of which have already been planned. (Photo (left to right): Sastry Pantula of the NSF; ICERM Director Jill Pipher, Providence Mayor Angel Taveras, Brown Provost David Kertzer; Brown President Ruth Simmons; Sen. Jack Reed, Sen. Sheldon Whitehouse, and Rep. Jim Langevin. Photo by Mike Cohea/Brown University.)
--- Ben Polletta
"Pythagoras's Theorem ain't Pythagoras's," by Burkard Polster and Marty Ross. The Age, 7 March 2011.
In this piece, Maths Masters columnists Polster and Ross describe several examples of misattributed mathematical insights. The authors begin with Cambridge University mathematician John Barrow’s recently published paper, which applies to the field of competitive rowing. “Barrow’s breakthrough was to realize that the commonly used left-right arrangement of the oars causes a boat to wobble, and that certain other arrangements are theoretically more stable.” However, Polster and Ross note, “some reports have overstated the newness of Barrow’s idea”: not only have rowers used more stable arrangements for many years—which Barrow himself pointed out—but the “underlying mathematical principle” was presented in a 1977 paper by mathematician M. N. Brearley.
What about Pythagoras’s theorem? It was actually “known and used in ancient Mesopotamia, at least a thousand years before Pythagoras.” And the Chinese illustration of Pascal’s triangle, shown here? It is dated to 320 years before Pascal’s birth. The list goes on. What is the “moral” of this story, according to Polster and Ross? If you want your work to go down in mathematical history, “give your theorem a catchy name, make it very easy to locate, and prepare an exciting media release.” (Image: Yanghui triangle, by Yáng Hui ca. 1238–1298, public domain via Wikimedia Commons.)
--- Claudia Clark
"A formula for success," by Prince Frederick. The Hindu, 4 March 2011.
Mathematician Anand Kumar transformed the heartbreak of his own unfulfilled academic dreams into inspiration for lifting up smart but disadvantaged young students like he once had been. Kumar’s school, “Super 30,” provides not only education but also food and shelter for students in Patna, India with the goal of helping them pass the entrance exam for the Indian Institute of Technology. His program is funded by tuition that more privileged students pay to attend a separate mathematics institute he founded in 1992, and he has received recognition from President Obama’s office and major Western media. With a small staff of only four teachers, Kumar over the past eight years has coached 212 of his 240 students to pass the exam. He says that he has been physically threatened by people who run similar training institutes in Patna, but he forges ahead with his small endeavor and hopes to admit more students in need to his program in the future. (Photo: Anand Kumar teaching his students, courtesy of Super 30.)
--- Lisa DeKeukelaere
"Computing Pioneer's Papers To Stay in Public Collection." News of the Week, Science, 4 March 2011, page 1118.
Donations have allowed the Bletchley Park Trust to purchase rare offprints of the research papers of Alan Turing. Turing was a leading figure in efforts to crack the German code in World War II, and helped develop the Bombe, a computer that decoded messages sent by the Luftwaffe. Turing was one of the founders of modern computing.
--- Mike Breen
"Fractals, Chaos, and Pollock's Code," by Helen A. Harrison. The Sag Harbor Express, 4 March 2011.
In this article, Harrison, director of the Pollock-Krasner House and Study Center in East Hampton, New York, describes a recent visit to the center by mathematicians Marcus du Sautoy and Richard Taylor, and a BBC Television crew. They were there to film “Nature’s Building Blocks,” the second segment of “The Code,” a three-part series “about the structural systems that determine the form of everything.” Harrison also introduces the lay reader to Taylor’s analysis of Pollock’s drip paintings: according to Taylor, the patterns in these paintings—like patterns found in nature—are fractal. “Taylor and some of his colleagues developed a computer program to identify the fractals in Pollock’s paintings, and he’s written several articles on the subject, which he’s dubbed ‘Fractal Expressionism’.” To demonstrate for the camera on this day how such fractal patterns can be created by hand, Taylor operated a piece of equipment he called the Pollockizer, “a couple of modified clothing racks, from which a swinging pendulum”—which can be jogged to create chaotic motion—“releases paint in a steady stream.” In addition to stage-managing the proceedings, Taylor answered du Sautoy’s questions. Harrison remarks that “both scientists have the knack of making arcane scientific concepts understandable.” (Photo by Helen A. Harrison, Director, Pollock-Krasner House and Study Center.)
--- Claudia Clark
"Maximum Overhang, Optimum Reward," by Janie Chang (Microsoft). R & D Magazine, 3 March 2011.
R&D Magazine reports on how two groups of researchers revisited a classic question in mathematics and came up with a brand new answer. The question is known as the maximum-overhang problem and has been a source of fascination for more than 150 years: how to stack blocks on a table to achieve the maximum possible overhang the farthest horizontal distance from the edge of the table. The researchers came up with a radical ordering of the blocks that yielded much better results than the classic solution. So good was their new technique that it won them the prestigious David P. Robbins Prize from the Mathematics Association of America (MAA). One of the researchers, Yuval Peres, works at Microsoft and he explains how answering questions like the overhang problem is of crucial importance at Microsoft Research when it comes to scheduling jobs on different computers to minimize waiting times, deciding how frequently to crawl different websites when refreshing a search-engine index, and setting up a network that will connect a set of processors at minimal cost, to name a few. (Photo: Perez (right) received the Robbins Prize from MAA President David Bressoud at the 2011 Joint Mathematics Meetings. Photo by E. David Luria.)
--- Baldur Hedinsson
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