Brie Finegold summarizes blogs on a proof of the Virtual Haken Conjecture and on the Abel Prize.
"Exciting News on Three Dimensional Manifolds: The Virtually Haken Conjecture," by Gil Kalai. Combinatorics and More, 1 April 2012;
"Agol's Virtual Haken Theorem: (Parts 1, 2, and 3)," by Danny Calegari. Geometry and the imagination, 26, 27, 28 March 2012;
"After the VHC," by Jesse Johnson. Low Dimensional Topology, 30 March 2012.
In the study of three manifolds, where the objects of study can have "ends," "loose ends" might be easy to find. But Danny Calegari wrote that Ian Agol's recent announcement concerning his proof of the Virtual Haken Conjecture ties up virtually every loose end left over on the list of problems in three manifold topology from Thurston’s famous Bulletin article "Three dimensional manifolds, Kleinian groups and hyperbolic geometry." A manifold is virtually Haken if it has a finite cover that is Haken. At a Paris workshop at the Institut Henri Poincaré, Agol and Jason Manning recently gave talks explaining the proof. Their presentations are summarized on Calegari's blog. The proof of the conjecture (which was open only for hyperbolic three manifolds) uses ideas from geometric group theory. In Combinatorics and More, Gil Kalai discusses some of the reasons that this result is so significant, and includes some excerpts from Thurston's article. Not surprisingly, the group blog Low Dimensional Topology includes many posts on the Virtually Haken Conjecture (VHC), including some of its history as well as some reflection on how the field may evolve to focus more on applications now that the geometrization conjecture and other long-standing conjectures like the VHC have been proven.
"Hungarian Scientist Receives Top Prize in Mathematics," by Veronika Gulyas. Wall Street Journal's Emerging Europe blog, 21 March 2012.
The Abel Prize, which comes with a little over a million dollars, was recently awarded to Hungarian mathematician Endre Szemerédi. Hailed as having an "irregular mind" in a collection of papers celebrating his achievements, Szemerédi has published in a variety of fields including combinatorics and machine learning. Szemerédi, who is the twelfth mathematician to earn the prize, asserted that what gave him the most satisfaction "is not my own personal achievement, but recognition for this field of mathematics and Hungarian mathematicians." Tim Gowers gave a speech explaining some of Szemerédi's accomplishments to a lay audience. For more information on Szemerédi's work, the interested learner might investigate the web page of this combinatorics minicourse. [See more coverage of the Abel Prize.]
--- Brie Finegold
"Geometer Tries a New Angle: Leading a College," by Peter Monaghan. The Chronicle of Higher Education, 30 March 2012.
Mathematician Donal B. O'Shea (left), whose research area is singularities of high-dimensional manifolds, has been hired as the president of New College of Florida, a liberal arts and sciences honor college. O'Shea had been chair of the math department at Mount Holyoke College as well as the college's dean of the faculty and vice president for academic affairs since 1998. Monaghan writes that Mount Holyoke's former president said that O'Shea "has boosted science education at Mount Holyoke as well as the number of minority students and the representation of women on the faculty." (Photo: Courtesy of New College of Florida.)
--- Mike Breen
"What the theory of everything might look like," by Sandrine Ceurstemont. New Scientist TV, 28 March 2012.
Physicists have long sought a "theory of everything" that would unite under one theory the fundamental forces of nature. This brief animation is a geometric interpretation of such a theory, based on the mathematical structure known as E_{8}. E_{8} hit the headlines in 2007, when mathematicians announced a major advance in understanding its structure.
--- Allyn Jackson
"The Mighty Mathematician You’ve Never Heard Of," by Natalie Angier. The New York Times, 26 March 2012.
"Scientists are a famously anonymous lot, but few can match in the depths of her perverse and unmerited obscurity the 20th-century mathematical genius Amalie Noether." So begins this revealing profile of Noether, whose seminal theorem "undergirds much of today’s vanguard research in physics, including the hunt for the almighty Higgs boson." Remarkably, Noether remains relatively unknown, but on the occasion of her birthday (March 23, 1882) and appropriately for Women's History Month, this article highlights "Emmy" Noether's fascinating life and important contributions to science. Despite being "a female in Germany at a time when most German universities didn't accept female students or hire female professors and being a Jewish pacifist in the midst of the Nazis' rise to power.... Noether was a highly prolific mathematician, publishing groundbreaking papers, sometimes under a man's name, in rarefied fields of abstract algebra and ring theory." Noether's theorem expressed "the deep tie between the underlying geometry of the universe and the behavior of the mass and energy that call the universe home." Among her contemporary admirers and advocates in Germany were David Hilbert and Felix Klein. Among today's scientists, Lisa Randall, professor at Harvard, is among those who note how "critical" the theorem is to modern physics. In Noether's time, though, she found it impossible to serve as a permanent faculty member at the University of Göttingen because of her gender (but still accomplished much nevertheless as a guest lecturer), and then she was forced to flee Germany because she was Jewish. She came to the U.S. and, with the help of Einstein, was given a position at Bryn Mawr College. The article includes more about Noether, her influence, and the applications of her work.
--- Annette Emerson
Coverage of the Abel Prize:The Hungarian combinatorialist Endre Szemerédi--most famous for Szemerédi's theorem, which proves the existence of arithmetic progressions in large subsets of consecutive integers--was announced as the winner of the 10th annual Abel Prize on March 21st, as reported in New Scientist, Science, Nature, and many other media outlets (a Google search yields 91 news articles). Szemerédi, the student of another famous Hungarian problem-solver, Paul Erdős, was cited for his manifold contributions to discrete mathematics and theoretical computer science. Szemerédi's theorem says that if you take a large enough set of consecutive integers, you can examine as small a subset as you like and still find an arithmetic sequence of a given length. It is proven by a mapping of the problem to graph theory, and the "regularity lemma" that appears in the proof is a much-applied gem of probabilistic combinatorics. The remarkable lemma says, very roughly, that any large graph can be broken into small, similarly-sized subgraphs, and that the connections between these small subgraphs are random. A second proof of Szemerédi's theorem by Hillel Furstenberg involves dynamical systems and ergodic theory, forming a bridge between number theory and dynamical systems, and Szemerédi's regularity lemma has been applied to problems in machine learning.
Szemerédi started his professional life as a medical doctor, and worked in a factory before Erdős noticed his mathematical talent and took him on as a student. The festschrift published on his 70th birthday was titled "An Irregular Mind"--a play on his famous lemma, but also a testimonial to his unique approach to mathematics. Terrence Tao described reading the paper in which Szemerédi proves his theorem--which features a complex graph on 23 vertices depicting the logical flow of the argument--as "watching an expert juggler throwing a dozen balls in the air and catching them all flawlessly". As Tim Gowers states in his remarks on the occasion of the award (enlightening even to lay readers), Szemerédi has over 200 published papers--including a very fast parallel sorting algorithm and many others as a member of the blockbuster Hungarian combinatorics trio Ajtai, Komlos, and Szemerédi--and "at the age of 71 he shows no signs of slowing down". Photo: Sergio01, CC-BY-SA.
--- Ben Polletta
"Q&A Barry Mazur: The maths raconteur," an interview by Jascha Hoffman with Barry Mazur. Nature, 22 March 2012, page 405.
Nature's 'Books & Arts' segment talks to Harvard mathematician Barry Mazur about the overlapping realms of mathematics and the imagination. Mazur recently edited a collection of essays on mathematics and narrative with author Apostolos Doxiadis. Mazur and Doxiadis asked mathematicians, historians and literary scholars to write about mathematics and narrative and then gathered all the authors to a conference in Greece. To make their essays more accessible the authors interviewed each other. The interviews are available online courtesy of the non-profit Thales + Friends, which works to bridge the chasm between mathematics and other forms of cultural activity.
(Photo of Mazur by Jim Harrison.)
--- Baldur Hedinsson
"Peterborough Math Teacher Saves Choking Student." WMUR-TV, 16 March 2012.
Susan Brewer, a seventh-grade math teacher, made the news by using the Heimlich maneuver on one of her students,12-year-old Bruce Craig. She was at her desk talking with another student when she looked up and saw Bruce standing there. She said that "His eyes were wide, as big as saucers. His mouth was open, and he just had a real panicked look on his face." She quickly performed the Heimlich maneuver and in about five seconds Bruce was breathing again. Here's what he said the next day: "I was very happy that she saved my life the previous day, and I thanked her again...And then at math time, my mom brought in the bouquet of flowers, and I hugged Ms. Brewer and said thank you."
--- Mike Breen
Articles about origami exhibition at UCSC and about Erik Demaine, one of the exhibitors:
"Q&A Erik Demaine: The origami geometer," by Jascha Hoffman. Nature, 15 March 2012, page 274;
"Origami Math--Computational Artists to Show Off Paper Masterpieces in Tribute to UCSC Professor," by Tanya Lewis. MercuryNews.com, 16 March 2012;
"UCSC exhibit makes link between artistic paper folding and the laws of mathematics," by Wallace Baine. Santa Cruz Sentinel, 5 April 2012.
A new exhibit at the University of California, Santa Cruz spotlights the nexus between mathematics and origami, displaying sculptures that combine aesthetics with computational prowess. The exhibit, in honor of former UCSC information sciences professor and origami enthusiast David Huffman, includes both abstract sculptures and realistic figures, including origami bugs and a life-size pond scene, crafted by computational origami artists. These mathematical artists, such as Robert J. Lang (work pictured at left) and MIT professor Erik Demaine, use origami not just to create art but also to tackle a range of scientific problems that involve folding, such as airbag design and protein folding in biology. A documentary of Lang and Demaine's work, Between the Folds, provided inspiration for the UCSC installation. The exhibit, which is designed to appeal to both adults and children, is free to the public and runs through June 16. In the Nature article, Demaine talks with Jascha Hoffman about his work and how he became interested in origami. Image: "Dragonfly TPS, opus 583," folded from one uncut square of Origamido paper, courtesy of Robert J. Lang.
--- Lisa DeKeukeleare
"ACM Awards Judea Pearl the Turing Award for Work on Artificial Intelligence," by Michael J. Miller. PC Magazine, 15 March 2012.
The Association for Computing Machinery (ACM) has announced that UCLA professor of computer science Judea Pearl has won its 2011 A.M. Turing Award for his work developing critical theoretical foundations in the field of artificial intelligence. The award will be presented to Pearl by the ACM in June, which also marks what would have been the 100th birthday of Alan Turing. According to ACM Executive Director John White, "Pearl's research was instrumental in moving machine-based reasoning from the rules-bound expert systems of the 1980s to a calculus that incorporates uncertainty and probabilistic models." Among his other work, Miller writes, Pearl "created the framework for what he called Bayesian networks (named for eighteenth century mathematician Thomas Bayes), which provides a compact way of representing probability distributions. In this way, it mimics the neural activities of the human brain." Pearl described this work in the seminal text, Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference.
See more coverage of the award announcement in the Software Development Times, San Jose Mercury News, The Wall Street Journal, and The New York Times.
--- Claudia Clark
"The Best of Our Knowledge," by Bob Barrett. WAMC, 14 March 2012.
In this edition of The Best of Our Knowledge, Professor Colin Adams will amaze you with his reports from the remarkable Williams College, where every tenth student is a math major, and many math majors publish articles before graduation (and not in one of those undergraduate math journals, either). Professor Adams rightfully thanks his lucky stars to be at Williams, but it seems Williams also has Professor Adams, and a plethora of professors like him, to thank for their surfeit of math majors. The key is teachers who can make math "come alive," and who involve undergraduates in the research process. That and a little word of mouth: "Math is really considered a cool major on the campus," says Professor Adams, frighteningly becoming the second person to say that word about math in a month. Dr. Adams not only gives interviews on the radio, but he also travels around the country giving talks as his alter-ego Mel Slugbait, a green-plaid-suit-wearing east Texan who sells real estate in hyperbolic space. These talks, which can be tailored to any level of mathematical sophistication, are designed to deliver the beauty of mathematics inside a bolus of comedy, and have become quite a success: "When I first started doing this character, I'd get invited to give talks, and now, Mel Slugbait gets many more invitations than I do."
Dr. Adams and host Bob Barrett also discuss some of the more threadbare topics in the math education tapestry, including how intimidating the subject can be, and how accepting people are of their own innumeracy. Still, it's nice to have Dr. Adams' accurate analyses: he attributes math anxiety to math's cumulative nature, which allows bad experiences that wouldn't derail a student's career in English or history to do so in math, as well as the uncomfortable position that being right or wrong, with no room for explanation, puts many students in; he also correctly labels proud mathematical illiteracy as a U.S. problem, rather than a math problem. More topically, Dr. Adams touches on the resurgence of mathematics in the current abysmal economic climate, thanks in part to the efforts of the Obama administration, and urges the importance of mathematical literacy amongst those making ethical and political decisions in the wake of the quant-created economic collapse. And if you're curious, he does a little Mel Slugbait around 4:40. Image: courtesy of Colin Adams.
--- Ben Polletta
"Sydney has our tower!," by Burkard Polster and Marty Ross. The Age, 12 March 2012.
According to Melbourne-based mathematicians Burkard Polster and Marty Ross, Melbourne is a great place to live. The city's mathematically inspired architecture brings the duo special joy. They find one thing missing though, an awesome geometric skyscraper such as the Sidney Tower. What impresses the mathematicians most is that the tower has a curved surface even though it is made with perfectly straight cables, i.e. it is a hyperboloid. The mathematicians walk the reader through how a hyperboloid is constructed and display different hyperbolic surfaces. The two definitely want a proper mathematical tower in the home town. Image: courtesy of Polster and Ross.
--- Baldur Hedinsson
"Khan Academy: Model for future of U.S. education?" by Sanjay Gupta. 60 Minutes, 11 March 2012.
In this segment of 60 Minutes, Gupta interviews Salman Khan, the founder of Khan Academy, described on its website as "a not-for-profit with the goal of changing education for the better by providing a free world-class education to anyone anywhere." What began in 2004 as a series of algebra lessons that Khan created and posted on YouTube for his niece has become over 3,000 lessons in mathematics, biology, physics, astronomy, medicine, history and finance that are currently accessed by more than 4 million people around the world each month. Khan attributes the success of his 10-minute digital lessons to the fact that "It really does feel like I'm sitting next to the person and we're looking at the paper together. [Most of the time, I'm] working through that problem real time or I'm thinking it through myself if I'm explaining something. People can see that [solving problems] is sometimes a messy process…I think that's what people like: the humanity of it." In addition to the lessons, the Khan Academy site offers exercises for students to complete as well as a dashboard that allows a teacher or coach to monitor students' progress in real time.
Currently, Khan Academy is being piloted in 23 U.S. schools. "What we're trying to do is take passivity out of the classroom so that [the] teacher will have more flexibility [to act as] more of a coach or mentor," Khan explains.
--- Claudia Clark
"Raytheon math exhibit to open at Smithsonian," by Ira Kantor. Boston Herald, 9 March 2012;
"Using math in the real world adds up to a cool job," by Moira E. McGlaughlin. The Washington Post, 17 April 2012.
Raytheon, a defense contractor headquartered in Waltham, MA, is sponsoring a new interactive exhibit at the Smithsonian International Gallery. Named MathAlive!, its part of the company's national MathMovesU program to improve students' math skills. The exhibit "allows students and teachers to explore science, technology, engineering and math-powered activities such as designing video games, riding snowboards and engineering cities of the future." Raytheon Chairman and CEO William H. Swanson tells the reporter that the goal of MathAlive! is to inspire students "to become the engineers and technology leaders of tomorrow." After being in Washington, DC for three months the exhibit will tour over several years to science centers and museums in 15 American and international cities. The article in The Washington Post has a description of four of the exhibits.
--- Annette Emerson
"Demi Moore Enters Celebrity Math Rehab," by Ellie James. The Spoof!, 9 March 2012.
This spoof "news" story (which seems apt given the first day of the month) wittily satirizes both inane celebrity news coverage and the lamentable state of math education in the U.S. It also drops names of some real mathematicians---such as Persi Diaconis and Linda Keen---who are supposedly enlisted to help Moore master mathematics.
--- Allyn Jackson
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