Blog on Math Blogs

Math Digest

On Media Coverage of Math

Edited by Mike Breen and Annette Emerson, AMS Public Awareness Officers
Mike Breen (AMS), Claudia Clark (writer and editor), Lisa DeKeukelaere (2004 AMS Media Fellow), Annette Emerson (AMS), Samantha Faria (AMS), and Allyn Jackson (Deputy Editor, Notices of the AMS)

Sandpile simulation

(Image of sandpile model: Wesley Pegden.)

"The news should start with mathematics, then poetry, and move down from there," from The Humans, by Matt Haig.


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Click here for a list of links to web pages of publications covered in the Digest.

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: "Celebrating our sisters in STEM," and "Math in Pictures," by Anna Haensch, "The Pi Day Link Roundup of the Century," and "Topology Teaching Blogs," 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)

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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.

Really Big Numbers

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 and 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 families 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

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Engaging mathematics…outside of the box, by Samantha Faria

Tim Chartier at National Math FestivalWhen 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)

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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."

Pacific Ocean garbage patch

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)

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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)

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On sandpiles, by Allyn Jackson

Sandpile simulation 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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On the origin of numbers, by Lisa DeKeukelaere

Is mathematics invented or discovered? A bit of both, according to astrophysicist Mario Livio, who will delve into this question while hosting "The Great Math Mystery" on PBS’s NOVA program on April 15. In an interview with Discover, Livio explains that humans invented natural numbers by abstracting what they observed in the natural environment: two eyes, two legs, etc. Humans then discovered the relationships between those numbers, such as the Pythagorian theorem. Livio notes that fractions and imaginary numbers are human inventions followed by discoveries, as well. When asked about math education, Livio opines that math should be treated as part of the human culture, like literature and history, particularly in an age where so much of our daily lives involve technologies reliant upon mathematics. He notes as an example that cell phones rely on satellite communications that use Einstein's theories of special relativity and general relativity.

See "The Numbers Game," an interview with Mario Livio by Gemma Tarlach. Discover, April 2015, page 12, and a trailer of "The Great Math Mystery" NOVA program.

--- Lisa DeKeukelaere

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Media coverage of the 2015 Abel Prize, by Annette Emerson

Nash and Nirenberg, 2015 Abel laureates

(Photos: Nash (left): © Peter Badge/Typos 1 in coop. with the HLF - all rights reserved 2015 and Nirenberg (right): © NYU Photo Bureau: Hollenshead.)

As soon as the Norwegian Academy of Sciences and Letters announced 2015 Abel Prize winners John F. Nash Jr. and Louis Nirenberg, the news spread on Twitter and elsewhere--many not able to resist connecting Nash with 'A Beautiful Mind,' the book and film about his life. (Nature puts as its title "'Beautiful mind' John Nash adds Abel Prize to his Nobel," and underneath that, "Mathematician made famous by Hollywood will share US$765,000 award with Louis Nirenberg for work in the field of geometric analysis.") Nash, who spent most of his career at Princeton University, and Nirenberg, professor emeritus at New York University's Courant Institute of Mathematical Sciences, receive the Abel Prize "for striking and seminal contributions to the theory of nonlinear partial differential equations and its applications to geometric analysis." The Abel prize committee wrote with the citation: "Their breakthroughs have developed into versatile and robust techniques that have become essential tools for the study of nonlinear partial differential equations. Their impact can be felt in all branches of the theory." Nash and Nirenberg have separately received prestigious awards and honors for their work in mathematics, but were nevertheless surprised to receive the Abel. New Scientist quotes Nash's quip, "I must be an honorary Scandinavian," and Nirenberg as saying, "I'm overwhelmed. I was asleep when the phone range yesterday, and I was simply astonished, just flabbergasted."

Philip Ball's piece in Nature provides more depth--a summary of just some of the work of the laureates, and bit of their lives. He quotes from a past interview in which Nirenberg said how he enjoyed collaborating in mathematics: "It's a very nice, warm family," and "That's the thing I try to get across to people who don't know anything about mathematics, what fun it is!" The recipients will be presented with their awards in the Abel Prize ceremony in Oslo in May.

See "A Beautiful Mind mathematician wins Abel prize," by Jacob Aron. New Scientist, 25 March 2015; "'Beautiful mind' John Nash adds Abel Prize to his Nobel," by Philip Ball, Nature, 25 March 2015; and "'A Beautiful Mind' Mathematician, John Nash, Wins Prestigious Prize," by David Freeman, The Huffington Post, 25 March 2015; "Bluefield's Nash wins highest mathematics honor," (with video of Nash after he received the Nobel Prize in Economics) by Marcus Constantino, Charleston Daily Mail, 30 March 2015. Other media, such as the New York Times and ABC News, picked up the announcement on the Associated Press newswire.

--- Annette Emerson (Posted 3/27/15)

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In honor of Emmy Noether, by Annette Emerson

To mark the occasion of mathematican Emmy Noether's 133rd birthday, Google celebrated with a google doodle. Noether, born 23 March, 1882, made outstanding contributions to the field of abstract algebra and theoretical physics. She was asked to address the International Congress of Mathematicians in 1928 and again in 1932. After being dismissed from the University of Göttingen in 1933 by the Nazis because she was Jewish, she made her way to the U.S. where she accepted a professorship at Bryn Mawr College. She was highly respected by prominent mathematicians of the day and was praised by Albert Einstein as a "creative mathematical genius."

The video, "Emmy Noether and The Fabric of Reality," is a talk by Ransom Stephens about Noether's Theorem, which "ties the laws of nature--from Newton's laws to thermodynamics to charge conservation--directly to the geometry of space and time, the very fabric of reality."

See "Google doodle honors mathematician Emmy Noether," (+video) by Rowena Lindsay, Christian Science Monitor, 23 March 2015, which includes the above video and description of how doodler Sophie Diao went about incluiding mathemtics into the google doodle honioring Noether.

--- Annette Emerson (Posted 3/24/15)

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On generating memorable passwords with Markov models, by Mike Breen

It's not easy finding a password you can remember that is also secure. In New Scientist, Jacob Aron writes about a method created by John Clements that uses Markov models and, in this case, text from A Tale of Two Cities, to generate passwords that are long enough to be secure, but are much easier to remember than passwords garbled up with special characters. One example: The greed hispefters and. Using the Dickens' novel, Clements used pairs of adjacent letters and for each pair, determined a distribution for possible subsequent individual letters. Then given an intial pair of letters, the third letter in the password is chosen based on that distribution. Once the third letter is chosen, the second and third letters are used to determine the frequency and make the choice for the possible fourth letter (as was done initially with the first two letters), and so on. Clements uses Huffman trees, binary trees used in compression, to terminate the word. Starting with longer strings, rather than only two-letter strings, yields longer but more pronounceable passwords. He admits in his paper--"Generating 56-bit passwords using Markov Models (and Charles Dickens)"--that there are still questions about the method, but notes that its security is independent of the chosen text so that people could use their own email history to generate passwords.

See "Let Charles Dickens sort out your passwords," by Jacob Aron. New Scientist, 21 March 2015, page 28.

--- Mike Breen (Posted 4/7/15)

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On number theory, algebra and string theory, by Claudia Clark

In this article, Erica Klarreich writes about the work that has led to the publication earlier this month of a paper that proves the colorfully named Umbral Moonshine Conjecture, first proposed in 2012. She begins by describing the discovery in 1978 by mathematician John McKay of a connection between the special dimensions of the monster group and the coefficients of the j-function. This lead to the publication the following year of the paper "Monstrous Moonshine," in which mathematicians John Conway and Simon Norton "conjectured that these relationships must result from some deep connection between" this group and this function. Then in 1992, some 10 years after University of Michigan mathematician Robert Griess constructed the monster, Fields Medalist Richard Borcherds proved that string theory was the "bridge between the two distant realms of mathematics in which the monster and the j-function live." Some 20 years later, the Umbral Moonshine Conjecture "proposes that in addition to monstrous moonshine, there are 23 other moonshines: mysterious correspondences between the dimensions of a symmetry group on the one hand, and the coefficients of a special function on the other." Read the proof of the conjecture.

To read more about this conjecture, and the mathematicians who have worked on and proven the conjecture, see "Mathematicians Chase Moonshine's Shadow," by Erica Klarreich, Quanta Magazine, 12 March 2015.

--- Claudia Clark

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On data in medicine, by Claudia Clark

This article, which is adapted from Lohr’s soon-to-be-published book "Data-ism: The Revolution Transforming Decision Making, Consumer Behavior, and Almost Everything Else," discusses the life and work of Harvard math major and "number cruncher" Jeffrey Hammerbacher. At the age of 32, Hammerbacher has already applied his quantitative skills to building sophisticated computer models on Wall Street, using data to improve Facebook's service, and founding Cloudera, "a fast-growing company that makes software tools for data science." However, a diagnosis of bipolar disorder several years ago led him to explore and eventually apply his talents to the field of medicine, and to work with Dr. Eric Schadt at Icahn School of Medicine at Mt. Sinai, which "has begun an ambitious, well-funded initiative to apply data science to medicine." The reason for the initiative, Dr. Schadt explained, is that chronic diseases "are not caused by single genes, but are 'complex networked disorders' involving genetics, but also patient characteristics such as weight, age, gender, vital signs, tobacco use, toxic exposure and exercise routines--all of which can be captured as data and modeled."

At Mount Sinai, researchers have been doing work on cancer treatments tailored to individual patients. Hammerbacher and his team work on the "'computational pipeline,'... with the goal of making [these] treatments more automated and thus more affordable and practical. 'It's ultimately what cancer cures are going to look like,' he said."

See "On the Case at Mount Sinai, It's Dr. Data," by Steve Lohr, New York Times, 7 March 2015.

--- Claudia Clark

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On A full-scale computer simulation of the galaxy, by Lisa DeKeukelaere

Three centuries after Isaac Newton solved the two-body problem for describing the gravitational pull between the Earth and the Sun, researchers in the Netherlands and Japan are endeavoring to solve the 100-billion-body problem to describe the motions of all of the stars in a galaxy the size and shape of the Milky Way. Solving systems with less than a dozen bodies is achievable with sets of equations that provide the position and velocity of a body at any given time. Larger numbers of bodies, however, require numerical simulation to calculate each star's acceleration—based on the gravitational force of each other star in the system—over a brief change in time. Such a large number of computations is unfeasible at present, so the researchers reduced the required number of calculations by dividing the galaxy into cubic subvolumes to simplify some of the pairwise computations. The researchers also adapted their software to run on special parallel computing devices originally produced for video games. The researchers already have succeeded in simulating a 51-billion-body problem, and they hope that solutions to the full problem will yield new insights when compared to the results of the European Space Agency's effort, using the Gaia spacecraft launched in 2013, to map a billion stars.

See "The 100-Billion-Body Problem," by Brian Hayes. American Scientist, March-April 2015, vol. 103, no 2, pages 90-93.

--- Lisa DeKeukelaere

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Math Digest Archives || 2015 || 2014 || 2013 || 2012 || 2011 || 2010 || 2009 || 2008 || 2007 || 2006 || 2005 || 2004 || 2003 || 2002 || 2001 || 2000 || 1999 || 1998 || 1997 || 1996 || 1995

Click here for a list of links to web pages of publications covered in the Digest.