See also: The AMS Blog on Math Blogs: Mathematicians tour the mathematical blogosphere. PhD mathematicians Evelyn Lamb, Anna Haensch, and Brie Finegold blog on blogs that have posts related to mathematics research, applied mathematics, mathematicians, math in the news, mathematics education, math and the arts, and more. Recent posts: "Caring For The Community," by Anna Haensch, and "How to Celebrate Math Poetry Month," by Evelyn Lamb.
On Noether and modern physics, by Allyn Jackson
This article discusses "Noether's Theorem," the monumental result of Emmy Noether that stands as a landmark in mathematics. Proved by Noether in 1915, the theorem also provides a profound unifying principle in physics, even though among physicists the theorem is not as well known as one might think. "Mathematicians do revere [Noether], yet despite [her] laying the groundwork for much of modern physics, physicists tend to gloss over her contributions," Goldberg writes. Partly this neglect is due to the complexity of the mathematics in Noether's Theorem, but it can also be traced to the fact that, as a woman, Noether faced discrimination despite her brilliance. The article weaves in a brief account of Noether's personal story while mainly concentrating on describing the influence of her theorem in physics, which Goldberg sums up this way: "Symmetries give rise to conservation laws." For example, the symmetries in the orbits of the planets around the sun are reflected in the principle of conservation of angular momentum. When symmetries are identified in a natural phenomenon, Noether's Theorem allows one to discover the associated conservation laws and start making meaningful calculations. Goldberg discusses how the theorem relates to the standard model of physics and supersymmetry. As physicists hunt for a "grand unified theory of everything," studying symmetries will guide the way, and Noether's Theorem will surely yield more physics insights.
See "The greatest physics theorem you've never heard of," by Dave Goldberg. New Scientist, 22 April 2015 (subscription required for full access). For more on Noether's Theorem, see "The Evolution of an Idea," by Robyn Arianrhod, in the August 2013 issue of the AMS Notices; in the piece Arianrhod reviews the English edition of The Noether Theorems: Invariance and Conservation Laws in the Twentieth Century, by Yvette Kosmann-Schwarzbach.
--- Allyn Jackson (Posted 4/27/15)
On the National Math Festival and the AMS, by Annette Emerson
The first National Math Festival was held in Washington DC, including a day of public events on Saturday April 18.
On Friday, April 17 Mathical: Books for Kids From Tots to Teens inaugural award winners were announced at the Mount Pleasant Neighborhood library. See the press release announcing the awards. Really Big Numbers by Richard Evan Schwartz, published by the AMS, received the award in two categories, for grades 3-5 and 6-8. The prize "honors books that foster a love and curiosity for math."
Read a review of Really Big Numbers, by Sondra Eklund, Sonderbooks, 21 April 2015.
On Saturday the festivities drew people of all ages to the Mall. There were talks, the Math Midway (kids rode a square-wheeled tricycle), hands-on activities (art, mazes), interactive mime and magic performances, and the AMS's Who Wants to Be a Mathematician game.
See a video segment about the festival and game, with information about the book awards on ABC7 News (if you can't view the video embedded below in your browser go to ABC7). Featured in the spot are AMS Public Awareness Officer Mike Breen and two of the Who Wants to Be a Mathematician contestants, who were great examples of students who love math--countering the host's introductory remark about how almost every high school student dreads math class.
See "National Math Festival underway in D.C.," by Brett Zongker (Associated Press), ABC7, 17 April 2014. And on the topic of math in media, see a video of Schwartz reading from his book Really Big Numbers at the Mathical award event.
--- Annette Emerson
On the job market, by Mike Breen
In this short piece on the The Chronicle of Higher Education's People page, Cleveland State University math chair John P. Holcomb, Jr. reflects about articles he's read concerning the job market for PhDs. The articles reflect his experience hiring: A tough job market in academia with hundreds of applicants for open positions, but an increase in demand outside of academia in data science. Holcomb thinks doctoral programs may want to consider the changing demand and advise graduate students accordingly.
See "What I'm Reading: Articles on the Ph.D. Job Market," by John P. Holcomb, Jr. The Chronicle of Higher Education, 17 April 2015, page A19. Also see the Report on 2013-2014 Academic Recruitment and Hiring in the May Notices.
--- Mike Breen
Engaging mathematics…outside of the box, by Samantha Faria
When he was young Tim Chartier imagined his future as a theater arts teacher and athletic coach. With a bit of prompting from his mother he decided to diversify his opportunities by studying mathematics. Fast forward to present day, Chartier, an associate professor in the Department of Mathematics and Computer Science at Davidson College, uses mime and theater to get students and adults interested in math. Together with his wife, Tanya, they perform their Mime-matics shows all over the country. “The way that math was traditionally taught was rote memorization, which is dull. Some people have a negative experience with that and quickly discount their ability to learn math. It is important to teach people in a way that excites them,” explained Tanya Chartier. There has been a huge push for STEM (science, technology, engineering, mathematics) education but the Chartiers want to see social sciences and arts included in this model. “… We like the idea of STEAM--STEM with the arts in it,” Tanya added. “Mime-matics is a shining example. We do not think of ourselves as mathematical artists. We are mimes, and Tim is a mathematician. We are just using math to create art.” (Photo of Tim Chartier at the National Math Festival)
See “Putting on a Show, Mixing Mathematics and Mime, for Fun and Profit,” by Robert Strauss, The New York Times, 16 April 2015 (page B7, Small Business section).
--- Samantha Faria (posted 4/27/15)
On the nature of mathematics, by Lisa DeKeukelaere
Is math something humans discovered or is it a human invention? This NOVA episode examines evidence for both explanations, from the correspondence between sunflower seed swirls and the Fibonacci sequence, to the fact that some phenomena--like the stock market--are largely unpredictable by current mathematical methods. On the "discovery" side, the program highlights the prevalence of ratios involving pi in our natural world, as well as the relationship between math and pleasing musical sound. Numerous mathematicians interviewed for the program explain that they see their research as akin to discovery, as a way to understand natural phenomena, and segments on human brain scans and exercises with lemurs suggest that our brains may be hardwired for mathematical ability. One physicist notes, however, that scientists apply what they know--mathematics learned in school--to problems amenable to using these methods, providing the perception of discovery when, in fact, there are other fields like biology and economics in which our models don't easily apply.
See "The Great Math Mystery." NOVA, 15 April 2015. The host of the show, astrophysicist Mario Livio, talked about it in an interview with Discover that appeared in its April issue. See "The Numbers Game."
--- Lisa DeKeukeleare
On using math to make a bale feeder, by Mike Breen
A bale feeder holds hay and allows farm animals to feed at its openings. Students in an agriculture education class at Soroco High in Colorado were making an octagonal feeder and had to get the angles right so that they didn't waste steel. Enter math teacher Maggie Bruski. She used the project to teach some geometry and trigonometry and show the students an application for some of the math they learn in class. Student Bailey Singer said, "...it's pretty amazing when you think all the different ways that you can use math, every day. Just building this, it shows--you do need math, you do need it." The students will sell the feeder at an auction to raise money for the school. Photo by Soroco High School agriculture education teacher Jay Whaley.
See "Real-World Math: A Bit Of Trig And Hay For The Horses," by Jenny Brundin. Colorado Public Radio, 15 April 2015.
--- Mike Breen
On Persi Diaconis and playing card smooshing, by Annette Emerson
As science writer Klarreich talked with Persi Diaconis at the 2015 Joint Mathematics Meetings he was shuffling playing cards. Diaconis, a professor of mathematics and statistics at Stanford University, has also been a professional magician for decades. "At 24, he started taking college classes to try to learn how to calculate the probabilities behind various gambling games. A few years later he was admitted to Harvard University's graduate statistics program on the strength of a recommendation letter from the famed mathematics writer Martin Gardner that said, more or less, 'This kid invented two of the best ten card tricks in the last decade, so you should give him a chance.'" But in this interview Diaconis shares how he has "employed his intuition about cards" in other ways. "Once, for example, he helped decode messages passed between inmates at a California state prison by using small random "shuffles" to gradually improve a decryption key." He also explains "smooshing," a different method of shuffling used in gambling casinos. But he notes "a mathematical analysis of smooshing will likewise have ramifications that go far beyond card shuffling. 'Smooshing is close to a whole raft of practical life problems.' It has more in common with a swirling fluid than with, say, a riffle shuffle; it's reminiscent, for example, of the mechanics underlying the motion of large garbage patches in the ocean, during which swirling currents stir a large collection of objects."
Garbage accumulation locations in the North Pacific Ocean. Image by the National Oceanographic and Atmospheric Administration (NOAA).
Klarreich then explains more about smooshing, smooshing tests, randomness, smooshing models, and potential applications. "The model does provide a framework for relating the size of the deck to the amount of mixing time needed, but pinning down this relationship precisely requires ideas from a mathematical field still in its infancy, called the quantitative theory of differential equations.... Diaconis is optimistic that the work will lead him not just to an answer to the smooshing question, but to deeper discoveries. 'The other shuffles have led to very rich mathematical consequences, and maybe this one will too,' he said."
See "For Persi Diaconis' Next Magic Trick ...," by Erica Klarreich, Quanta Magazine, 14 April 2015.
--- Annette Emerson (Posted 4/23/15)
On Escher, optical illusions, and math, by Annette Emerson
"The Mathematical Art of M.C. Escher," by the BBC. See a larger version on YouTube and other videos with the article.
Ian Stewart, professor of mathematics at University of Warwick (UK), author of many books, and recipient of the JPBM Communications Award, explains in the BBC video how M.C. Escher was able to connect art and mathematics. The online article includes images and embedded videos showing optical illusions and works by Escher, who was fascinated by the concepts of infinity, reflections, Möbius strips, Penrose tiles, and human perception, and whose works illustrate tessellations and symmetry.
Stewart rightly concludes, "Mathematicians know their subject is beautiful; Escher shows us it's beautiful."
See "Optical illusions: Is the cat walking up or down the stairs?," by Western Daily Press, 8 April 2015.
--- Annette Emerson (Posted 4/9/15)
On an interview with Yitang Zhang, by Lisa DeKeukelaere
Yitang Zhang ascended from a curious math student forced out of school and into the fields during China's Cultural Revolution, to a virtually unknown math lecturer at the University of New Hampshire who shocked the international mathematical community with a groundbreaking proof about prime numbers. In April 2013, Zhang submitted a proof to the Annals of Mathematics demonstrating that there are infinitely many pairs of prime numbers differing by some number N that is less than 70 million. The journal took only three weeks to review and accept Zhang's proof, which is a step toward solving the twin primes conjecture (there are infinitely many pairs of primes differing by 2). Zhang's story is remarkable not just because he overcame his lack of formal education as a teenager, but also because he fell out of academia for seven years after getting his doctorate in the U.S., a gap he ascribes to his own shyness in publicizing his abilities.
See "After Prime Proof, an Unlikely Star Rises," by Thomas Lin, Quanta, 2 April 2015.
--- Lisa DeKeukeleare
On sandpiles, by Allyn Jackson
Add a few grains of sand to a sandpile, and maybe nothing much happens. But add a few more, and you might suddenly find the structure of the pile shifting and morphing into a new shape. In mathematics, a sandpile is a model that captures the simplest aspects of the behavior of a real sandpile. In this article, Jordan Ellenberg describes the mathematical sandpile and its incredibly rich behavior. One can think of a mathematical sandpile as an infinite array of dots, each with a vertical pile of sand. The vertical piles cannot get too tall, so any pile with 4 or more grains must topple, sending one grain in each compass direction. Now imagine an infinite table onto which sand is dropped grain by grain in the center. A pile of 4 grains forms and topples; as more sand is added, an adjacent pile accumulates 4 grains and then topples, and so on. As the sand begins to spread over the table, patterns emerge in the sandpile. The article contains some beautiful computer-generated pictures showing sandpile patterns, as well as a fascinating video. The sandpile is one of the simplest examples of what is known as "self-organized criticality," a phenomenon that could be at the root of life itself. "Some biologists see self-organized criticality as a potential unified theory for complex biological behavior, which governs the way a flock of birds moves in sync just as genetic information governs the development of the individual birds," Ellenberg writes. (Image of "billion" grain pile provided by Wesley Pegden.)
See "The Amazing, Autotuning Sandpile," by Jordan Ellenberg. Nautilus, 2 April 2015. See also "What is a sandpile?", by Lionel Levine and James Propp, in the September 2010 issue of the AMS Notices.
--- Allyn Jackson (Posted 4/21/15)
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