October 2011
Brie Finegold summarizes blogs on historic female mathematicians and on music and math: "Five Historic Female Mathematicians You Should Know," by Sarah Zielinski. Surprising Science, Smithsonian.com, 7 October 2011. Quick, name five historic female mathematicians! Most people would struggle to name five famous mathematicians regardless of sex. But those who regard Lagrange and Gauss as household names will probably know the names mentioned in Zielinski's post: Hypatia, Sophie Germain, Ada Lovelace, Sonja Kovalevsky, and Emmy Noether. As the typical roads into academia were closed to them, these women took unconventional paths to pursue their passion for mathematics. Sophie Germain used a false name to write to Lagrange in fear that he would not read her letters if he knew she was female. A century later, Sonja Kovalevsky married a fellow academic so that she could leave Russia (where women could not attend university) and earn a doctorate at the University of Heidelberg. Even there, she was allowed only to audit classes and only with the permission of the professor. This post was made in honor of Ada Lovelace Day which was founded in 2009 to encourage bloggers to highlight the accomplishments of females in STEM fields. See Steve Wildstrom's post for a list of some more contemporary famous female mathematicians (some of whom are still working). For example, Wildstrom mentions Ingrid Daubechies, who this year became the first female president of the International Mathematical Union in its ninety year history. "Music and maths: joined at the hip or walking down different paths?," by Stephen Hough. The Telegraph, 7 October 2011. Accomplished pianist Stephen Hough writes in this post about the relationship or lack thereof between mathematics and music. Although he acknowledges that the theory underlying musical compositions has mathematical flavor, Hough points out good compositions often break the rules while good mathematics establishes rules and patterns. Hough argues that composers deliberately add superfluous notes, ambiguity, and uneven timing, while a mathematician looks for only the most concise, least ambiguous, most regular answers to problems. While students of calculus whose main job is to replicate algorithms (i.e. perform) might wholeheartedly agree with Hough's argument, a professional mathematician whose job is to create original work (i.e. compose) might disagree with Hough. One mathematician with whom Hough debated this issue was Marcus du Sautoy in a segment for the BBC. In this short discussion, du Sautoy points out that there are pieces of classical music which are concretely inspired by mathematics, while Hough brings up classical pieces that lack any identifiable patterns. One interesting point made by du Sautoy is that a listener who recognizes a lack of pattern is seeking one and therefore thinking mathematically. Hough insists that mathematics lacks the soulfulness and humanity of music wherein great compositions are great both because of the notes on the page and interpretation thereof. But perhaps attending an artful lecture given by the founder of a new and exciting result might be compared to watching a great musical performance; even if the audience lacks knowledge of the genre, the beauty of the piece comes shining through.  Brie Finegold "Popular Science's Brilliant 10: Computational Contortionist," by Ryan Bradley. Popular Science, October 2011, page 63. Ever thought about how the surface of a Coke can gets all mangled when you crush it? As a graduate student in mathematics and computer science, Eitan Grinspun spent years and years thinking about this problem and getting to the bottom of how external forces can change the shape of surfaces. As a result a whole new field of geometry was born, discrete differential geometry, which allows engineers to better predict how cables will fall to the sea floor and allows animators to create more realistic animations. As for the picture? Grinspun says "I get to take any interesting physical problemsay, spaghetti movement. Toss it in the air, and it falls on the ground and it twists and coils. Why does it move that way?" Grinspun's work rendering complex objects earned him inclusion in the 2011 Popular Science Brilliant 10. Photo: John B. Carnett.  Baldur Hedinsson
"David Lynch adds art to maths," by Benjamin Secher. The Telegraph, 29 October 2011; The Fondation Cartier for contemporary art in Paris is hosting an exhibition "MathematicsA Beautiful Elsewhere" through March 18. The idea behind the exhibition came from the foundation's director Hervé Chandès who wanted to explore the aesthetic potential of mathematics, which Chandès calls the "abstract art par excellence." He contacted JeanPierre Bourguignon, head of the l'Institut des Hautes Études Scientifiques (IHES), who, along with other prominent mathematicians, came up with some contemporary ideas in mathematics that would lend themselves to artistic interpretation. Chandès also got in touch with film director David Lynch, who contacted artists and coordinated the exhibition. Lynch said of his experience, "I guess in an abstract way I thought of the great mathematicians as artists, but then when I met these mathematicians I saw it way more clearly. They're just like painters, but their medium is equations and numbers. They're all fired up, they love life, they're happy.... Mathematicians are bright and shiny." Michalowski and Smith have mixed reviews of the exhibition. (Image: "O Paraiso, 2011" by Beatriz Milhazes, courtesy of the Fondation Cartier.)  Mike Breen "Mathematicians think of everything as rubber," by Elizabeth Quill. Science News, 22 October 2011. The field of topology has come a long way since 1940, when the mathematical genre at the time undefined in the dictionary captivated participants at the Columbus science meetings. A resurrected Science News clip from those meetings describes the "relatively new" and "strange" field as a departure from traditional Euclidean geometry, basing comparison of two figures on whether they can be stretched or distorted (without cutting or gluing) into identical forms. Even farther back in time, Leonard Euler's solution to the problem of whether it is possible to complete a closedloop walking tour of the city of Konigsberg, Germany crossing each of the city's bridges exactly once was an early example of applying topographic thinking. As of 2011, mathematicians have used topography to make contributions in a variety of scientific fields, and questions about the size and shape of the universe exhibit potential for a topographical solution.  Lisa DeKeukelaere "String theory finds a bench mate," by Zeeya Merali. Nature, 20 October 2011, pages 302304. Collaboration between string theorists and condensedmatter physicists, ignited by two former Moscow State University roommates reunited in New York, is reinvigorating both fields. When condensedmatter physicist Dam Thanh Son sought out his old friend Andrei Starinets, a string theorist, he discovered that Starinets' equations looked much like those he was using himself to compute the characteristics of "fireballs" created in particle accelerators. Working together, the pair was able to translate difficult condensed matter physics equations into a parallel, fourdimensional, string theory universe in which equations are much easier to solve. Translating back into threedimensional space, the work yielded a predicted value for the fireballs' viscosity that was later proven in a laboratory. As a consequence of this collaboration, some of string theory's star power is rubbing off on condensedmatter physics, and string theory is gaining validation for its utility, but additional concrete and novel results are still needed to quell the skeptics.  Lisa DeKeukelaere "Using Math To Piece Together a Lost Treasure," by Holger Dambeck. Spiegel International, 19 October 2011. This article discusses the restoration of frescoes in a church in Padua, Italy, in which mathematical methods played a major role. The frescoes were shattered in 1941 during World War II bombing raids. Shattered pieces88,000 of themwere collected and stored, and in 1992 they were cleaned, sorted, and photographed. But with so many pieces, restorers were unable to reassemble the frescoes. Mathematician Massimo Fornasier, now a professor at the Technical University of Munich, stepped in to help. He and his team developed an algorithm that could make very good guesses about the placement of a fragment. After the algorithm was run on a computer, the placements could be verified by restorers. "Ultimately, Fornasier's team managed what many had thought impossible: They found the original position of almost every piece of shattered plaster that was large enough to be identified," the article says. The pieces were reassembled on the church wall, a process that was finally completed in 2006.  Allyn Jackson
Articles on recordsetting calculation of Pi: Earlier this month, Japanese engineer Shigeru Kondo calculated the value of pi to 10 trillion digits, besting a 5 trilliondigit record that he set in August 2010. To perform the 12month task, Kondo used a homebuilt computer with a 48terabyte hard drive. While the cost of electricity to run the computer was high—approximately 30,000 yen (about $390) per month—the heat generated by the hard drive warmed the computer room in his Nagano home to 104 degrees Fahrenheit. "We could dry the laundry immediately," said his wife, Yukiko, to Japan Times.  Claudia Clark "The Telltale Tiles," by Burkard Polster and Marty Ross. The Age, 17 October 2011. Australian mathematicians Polster and Ross dissect an invitation to an event at the geometrictilecovered Storey Hall in Melbourne and, in the process, explain the basics of aperiodic tiling of a plane. Beginning with the simple example of using orderly rows of squares or triangles to "tile," or cover without overlaps or gaps, a plane, the authors describe the concept of being periodic, or conforming to a grid of identical parallelograms. An aperiodic tiling, the authors explain, is a set of shapes (tiles) that cannot be rearranged into a periodic tiling. The first set of aperiodic tiles, discovered in 1964, contained 20,246 items, but mathematician Roger Penrose later constructed special shapes that, taken in pairs, constitute aperiodic tilings. Penrose's tile pairings are responsible not only for the aesthetics of Storey Hall's exterior, but also this year's Nobel Prize in chemistry. (Photo of Storey Hall, RMIT (Royal Melbourne Institute of Technology), courtesy of Burkard Polster.) Of related interest: Penrose Tiles Talk Across Miles," by David Austin.  Lisa DeKeukelaere
"Finding Archimedes in the Shadows," an exhibition review by Edward Rothstein. New York Times, 17 October 2011;
Sunday, October 16, marked the opening of an exhibition at the Walters Art Museum in Baltimore, Maryland, that showcases the history, restoration, and meanings of the Archimedes Palimpsest. This Palimpsesttypically a parchment manuscript on which more than one text has been writtencontains the oldest existing copy of Archimedes' work, including the only known copy of two works: "Method" and "Stomachion." The title of the exhibitLost and Found: The Secrets of Archimedesreflects the nature and history of this text, initially a 10th century copy of the thirdcentury B.C. writings of Archimedes, which was "recycled" 3 centuries later into a prayer book. "That book was apparently in use for centuries at the Monastery of St. Sabbas in the Judean Desert," writes article author Edward Rothstein. Then, in 1906, Danish Archimedes scholar Johan Ludvig Heiberg found the book in Istanbul, where he deciphered much of the scarcely visible, original textwhich runs perpendicular to the prayers copied over itand photographed the pages. The book's location was unknown for most of the 20th century until it was reported sold for $2 million at a Christie's auction in 1998 to an anonymous buyer. In response to a request to exhibit the book from the Walters' curator of manuscripts, William Noel, the buyer “not only deposited the book with Mr. Noel [in 1999] but also provided funds for the project, as scientists and other experts took it apart for restoration and research." To learn more about this exhibition, which is open through January 1, go to the Walters Art Museum website. This story was reported by several media outlets, including CBS News, Daily Mail, and The Washington Post.  Claudia Clark "Super Science Suggestions: House Panel Lays Out Spending Preferences," by Science News Staff. Science, 17 October 2011. Scientists are preparing for a cut of US$1.5 billion in the 2012 research budget. The cut is as a part of a budget deal between the White House and Congress passed in August. In dealing with the funding shortfall Democrats have stressed the need to find new funding opportunities, while Republicans see a chance to cut funding for specific programs. Alternative energy and climate research will be hit hard if Republican leaders of the House of Representatives Committee on Science, Space and Technology get their way. According to Samuel Rankin III, head of the Consortium for NSF Funding and head of the Washington office of the American Mathematical Society, all members of the Science committee recognize the value of for basic research, such as mathematics. (Photo: Samuel Rankin.) Baldur Hedinsson
"Q&A: Persi Diaconis The mathemagician," by Jascha Hoffman. Nature, 27 October 2011, page 457; Magicianturnedmathematician Persi Diaconis has coauthored a new book, Magical Mathematics: The Mathematical Ideas That Animate Great Magic. According to the article in the Chronicle of Higher Education, the book is "part math textbook, part magic primer, and part history book, tracing how magic and math have long traveled under the same cape," which prompted Nature and the Chronicle to profile Diaconis and explain a bit about his interest in magic, the mathematics of magic, and the other applications of his discoveries. For instance, (also from the Chronicle) "his best known mathematical finding is that it takes seven shuffles of a standard deck of cards to randomly mix them. The conclusion turns out to have implications far beyond card tables: Someday it may help manufacturers determine how much mixing is necessary in industrial processes, or give spies a better way to tell how complex their secret codes need to be." Although Diaconis is still involved in magic and the magician community, Young writes that "he sees himself first and foremost as someone attempting to solve the toughest problems of mathematics." The online article of Young's piece also includes a video.  Annette Emerson
Articles on the Nobel Prize in Chemistry to Daniel Shechtman: Dan Shechtman, the first to identify quasicrystals in nature, was awarded the Nobel Prize in Chemistry for 2011. Shechtman's compelling story made headlines around the world. In 1982, he observed in his laboratory an unusual pattern in the atomic structure of an alloy. The structure appeared to be a crystal, but the crystal pattern did not repeat itselfthese are the hallmarks of a quasicrystal. In mathematics, objects with this type of structure were studied as abstract phenomena but were thought not to exist in atomic structures. When Shechtman announced that he had observed a quasicrystal, his findings were met with disbelief and ridicule, and he was asked to leave his laboratory. He persisted for years, and over time the naysayers were convinced. The Nobel Prize was the ultimate vindication. The Nature article notes that, around the same time as Shechtman's discovery, mathematicians Paul Steinhardt and Dov Levine were completing a rigorous theory of the threedimensional version of Penrose tilings. The threedimensional objects they were studying were just what Shechtman had observed in his lab. Steinhardt called them "quasicrystals" because they exhibited neither the regular periodicity of crystals nor the disordered structure of glass. For more on the mathematics of quasicrystals, see "What is a Quasicrystal?", by Marjorie Senechal (AMS Notices, September 2006), and "Quasicrystals and geometry", a book review by Charles Radin (AMS Notices, April 1996).  Allyn Jackson "Don't get math? Researchers home in on the brain's problem", by Sharon Noguchi. Medical Xpress.com, 5 October 2011 (originally appeared in San Jose Mercury News). This article discusses new brain research that might improve understanding about why some people seem to lack basic mathematical ability, including the ability to estimate quantities. In one study that tracked 249 students from kindergarten, researchers found that, as ninth graders, some of these students were unable to estimate a quantity of dots that was flashed on a screen, or to distinguish a set of 15 dots from a set of 20 dots. Such students tend to do poorly in mathematics classes. This type of disability, called "dyscalculia", is the counterpart to dyslexia but has been studied far less. Tests of brain activity in children with dyscalculia show that they are not using a part of the brain that is active when children without the disorder perform estimations.  Allyn Jackson "It's just an illusion: Mathematician uses thousands of Lego bricks to recreate Escher's gravitydefying images," by Nadia Gilani. Daily News, 2 October 2011. Dutch artist MC Escher was famous for incorporating astounding optical illusions into his drawings. Now Andrew Lipton, a British mathematician, has constructed LEGO® replicas of some of Escher's acclaimed work and incredibly the LEGO® structures create the same astonishing optical illusions. Lipton used thousands of Lego bricks and spent countless hours building the LEGO® replicas. Though he will not say how he achieved the seemingly impossible angles and strange perspectives in his creations, he swears that they are genuinely constructed out of LEGO® without using glue or any other adhesive. See more of Lipton's LEGO® structures. Lipson's collaborator on this work is Daniel Shiu. (Photo: Escher "Relativity" copyright by Andrew Lipson. Click to see larger image.)  Baldur Hedinsson "Ig Nobel prize awards 2011," New Scientist, 3 October 2011. Well, October 21 has come and gone without the world coming to and endwhich is why Harold Camping (among other doomsday predictors) received the 2011 Ig Nobel Award for Mathematics. Media worldwide covered the annual Ig Nobel Awards Ceremony, hosted by Marc Abramson, editor of the Annals of Improbable Research. Mathematics was one of the awards announced. As noted by New Scientist, "A long list of selfappointed prophets whose predictions of the end of the world have thankfully failed to come to pass shared the mathematics prize. As the Ig Nobel committee says, their failure has taught "the world to be careful when making mathematical assumptions and calculations." Among the prize winners is Harold Camping, who has so far prophesied the end of the world on 21 May 1988, 7 September 1994, 21 May of this year, and ... 21 October 2011." Seriously, "The Ig Nobel Prizes honor achievements that first make people laugh, and then make them think. The prizes are intended to celebrate the unusual, honor the imaginative—and spur people's interest in science, medicine, and technology," states Abramson.  Annette Emerson "A formula for justice," by Angela Saini. The Guardian, 2 October 2011. Thomas Bayes, though long dead, was recently thrown out of a British court. Well, not Thomas Bayes himself, but his eponymous and notoriously hard to understand theorem. Bayes' theorem relates the conditional probabilities of multiple events  relating the probability of A given B to the probabilities of A, B, and B given A  and can be used to show that doctors are very bad at understanding the results of medical tests. Bayes' theorem, it turns out, is (or was) very much alive in the modern courtroom, where it is used to calculate how much a given piece of evidence shifts the probability of a individual's guilt or innocence. The theorem ran afoul of the law in the appeal of a convicted murderer, who we (because we are mathematicians) can call "X". One of the pieces of evidence arrayed against X was a shoeprint found at the scene of the murder, which seemed to match a pair of sneakers found at X's house. The likelihood that the pair of sneakers observed at the crime scene was in fact the same as X's pair was calculated using Bayes' theorem. Applying Bayes' theorem required information like the number of sneakers sold each year, and the number of different tread patterns on those sneakers. When this kind of information is not available, expert witnesses often make educated estimates or guesses. The judge on X's appeal decided that he didn't like the guesses made in X's case, but he threw Bayes' baby out with the bathwater. Given how poor humans are at probabilistic reasoning  "We like a good story to explain the evidence and this makes us use statistics inappropriately," says University College London psychologist David Lagnado  this is a big problem. "From being quite precise and being able to quantify your uncertainty, you've got to give a completely bland statement as an expert, which says 'maybe' or 'maybe not'. No numbers," explains Professor Norman Fenton, a mathematician at Queen Mary, University of London, a frequent expert witness. Of course, the human inability to reason statistically means it is easy to misinterpret and misuse statistical arguments in court. The way forward is to get mathematicians and legal professionals together to devise constructive ways of applying probability  and avoiding its misuse  in court. This is just what Fenton and his colleague Amber Marks at Queen Mary have done. They and their 37 legal collaborators are now examining the prevalence of Bayes' theorem in court  and thus the impact of the shoeprint murder case, in the hopes of getting it overturned. Of course, as they admit and any math teacher knows, the most challenging issue is how to get jurors to understand the statistical evidence presented to them.  Ben Polletta

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