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On Media Coverage of Math
Edited by Mike Breen and Annette Emerson, AMS Public Awareness Officers
"The news should start with mathematics, then poetry, and move down from there," from The Humans, by Matt Haig.
See also: The AMS Blog on Math Blogs: Two mathematicians tour the mathematical blogosphere. Editors Brie Finegold and Evelyn Lamb, both PhD mathematicians, 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 : "Alan Turing on Stage and Screen," " Mathematician Presents Flawed Proof – in a work of fiction," " The Inaugural Breakthrough Prizes in Mathematics," "Visualize Your Algorithms".
At some point when we were kids, maybe 8 or 9, we stopped counting on our fingers and answers started to just…sort of appear in our brains. As a recent article in the Detroit Free Press explains, this transition, while easier for some that for others, turns out to be a pretty good predictor of the course of a kid's mathematical life. Youngsters who make this transition easily will likely excel, and those who don't, often face severe difficulty later in life. A recent study funded by the NIH examines what exactly goes on the grey matter during this transition. (Image Courtesy of Jimmie, via Flickr Creative Commons.)
The study was carried out by Professor Vinod Menon and his team at Stanford. Menon put 28 lucky kids into a brain-scanning MRI machine and asked them to solve simple addition problems. First they gave the kids equalities, like 2+5=8, and had them press a button to indicate "'right" or "wrong" (hint: that one's wrong). Next, the kids did the same exercise, but the researched watched them face-to-face, to see if they moved their lips or used their fingers.
Then they did the whole thing again, nearly a year apart. Turns out, kids who relied more on their memory--signified by an active hippocampus--were much faster than the kids who showed heavy activity in their prefrontal and parietal regions, areas associated with counting.
The hippocampus (left, courtesy of Wikimedia Commons) is sort of like a traffic staging area. When new memories pull in, a traffic controller directs them into a more long-term parking spot for later retrieval. But for memories that come in and out often, they get used to the routine. They always go to the same parking spot and eventually don't even need the help of traffic control to get there. So for frequently accessed memories, like 2+5=7, we don't even need to rely on our hippocampus.
What does this mean for kids learning simple arithmetic? Practicing multiplication tables, with the end goal of rote memorization, actually helps to shape a kid's brain. And this is particularly helpful in the long run, because kids who work too hard to understand the simple arithmetic, will often feel confused and fall behind as soon as more complicated topics are thrown into the mix.
So bust out those flashcards and fire up that hippocampus. Your future self will thank you.
See: "Brain scans show how kids' math skills grow," by Lauran Neergaard, Detroit Free Press, 19 August 2014.
--- Anna Haensch (Posted 8/26/14)
Being asked to review a 50 page paper can be a frightening proposition, and debugging someone else's code can be a nightmare. Imagine the horror, then, of being asked to review Thomas Hales' computer-assisted proof of the Kepler conjecture, over 300 pages long and depending on approximately 40,000 lines of custom code ("Mathematical proofs getting harder to verify," by Roxanne Khamsi, New Scientist, 19 February 2006). The reviewers charged with this task by the Annals of Mathematics spent five years vetting the proof. "After a year they came back to me and said that they were 99% sure that the proof was correct," says Hales in the above article. To eliminate this uncertainty, the reviewers continued their evaluation. "After four years they came back to me and said they were still 99% sure that the proof was correct, but this time they said were they exhausted from checking the proof."
The Kepler conjecture asserts that no sphere packing (i.e., arrangement of spheres in three dimensions) can be denser (i.e., have a larger ratio of sphere to empty space) than the "greengrocer's" or hexagonal lattice packing. Hales' original proof comes in six chapters, and is frankly bewildering. As far as I can tell, it involves finding the minimum value of a function of 150 variables over a set of ~50,000 sphere configurations, each of which represents some neighborhood of a compact topological space, the points of which represent sphere packings ("A Formulation of the Kepler Conjecture," by Thomas C. Hales and Samuel P. Ferguson, a chapter from The Kepler Conjecture, Springer, 2011, available for a fee). With the help of graduate student Samuel Ferguson (who seems to have disappeared from at least the internet after his graduation from the University of Michigan in 2007), Hales spent six years solving around 100,000 linear programming problems to complete his computer-assisted proof.
When Hales was met with the reasonable doubts of his reviewers, he began the FlysPecK Project -- an attempt to provide a Formal Proof of the Kepler conjecture -- and made the natural choice of computer-assisted peer review for a computer-assisted proof. Flyspeck consists of three parts: a classification of the so-called tame graphs, which "enumerates the combinatorial structures of potential counterexamples to the Kepler conjecture"; a "conjunction of several hundred nonlinear inequalities," which I can only assume are related to the minimization of the function described above, and which were broken into 23,000 pieces and checked in parallel on 32 cores; and a formalization of the proof, combining the above two pieces. The automated proof checkers utilize two "kernels of logic" that have themselves been rigorously checked. "This technology cuts the mathematical referees out of the verification process," says Hales. "Their opinion about the correctness of the proof no longer matters."
Whether the rest of the mathematical community is any more likely to trust automatic proof checkers than computer-assisted proofs -- not to mention the automatic theorem generators that have recently come into existence and gone into business ("Mathematical immortality? Name that theorem," by Jacob Aron, New Scientist, 3 December 2010) -- remains to be seen. In the meantime, we can take comfort in Wikipedia's list of long proofs. While a cursory glance suggests that proofs have gotten longer over the years, a second look suggests that the long proofs of the past have been made vastly shorter by advances in our collective mathematical sophistication. Perhaps the long proofs of today, even those mostly built and checked by computers ("Wikipedia-size maths proof too big for humans to check," by Jacob Aron, New Scientist, 17 February 2014), await only time and the slow accumulation of mathematical insight to be cut down to size. As for Hales, he's no longer holding his breath. "An enormous burden has been lifted from my shoulders," he says. "I suddenly feel ten years younger!"
See "Proof confirmed of 400-year-old fruit-stacking problem," by Jacob Aron. New Scientist, 12 August 2014.
--- Ben Pittman-Polletta (Posted 8/22/14)
Each week on a page called "The Shortlist," The New York Times Book Review publishes reviews related to a certain theme. In the August 3 issue, the topic was math. Jennifer Ouelllette writes short reviews of How Not to Be Wrong by Jordan Ellenberg, The Improbability Principle by David J. Hand, The Norm Chronicles by Michael Blastland and David Spiegelhalter, Infinitesimal by Amir Alexander, and The Grapes of Math by Alex Bellos. She likes them all. The Reviews page has links to more reviews of books, as well as reviews of plays and films.
See "The Shortlist: Math," by Jennifer Ouellette. The New York Times Book Review, 3 August 2014, page 30.
--- Mike Breen
I will begin by confessing that Leonardo DiCaprio, all decked out in a crisp white Polo and Ray-Bans, angrily throwing $100 bills off the side of his ginormous yacht is pretty in-line with how I picture big-shot Wall Street types. But a profile of successful Wall Street trader and financial entrepreneur Elie Galam on cnn.com paints a much different picture -- that of a quiet math nerd, more concerned with probability theory than parties and yachts.
Galam is part of a new breed of Wall Street denizens called quantitative analysts, or more colloquially, "quants." This means he spends his days using complex mathematical concepts to try and understand financial markets. Because of the number-crunchy nature of this work, many math types are finding themselves increasingly at home in the world of finance.
And statistics suggest that it's a great job and likely to boom in popularity over the next decade. The number of quants is expected to grow by 41% from 2010 to 2020, and according to the Federal Bureau of Labor Statistics, the mean annual salary for a quant is $91,620--a veritable fortune to a poor grad student.
For Galam, Wall Street came calling and plucked him out of graduate school after only one year, but for other mathematicians considering making the transition, Cathy O'Neill wrote this great article for Notices summing up her experience moving from the ivory tower to Wall Street.
See "Math nerds are taking over Wall Street," by Jesse Solomon. CNN.com, 26 July 2014.
--- Anna Haensch (posted 8/12/14)
Grigory Perelman is certainly a remarkable and unusual person. Among many remarkable facts about the man -- such as his role proving Thurston's geometrization conjecture and his grooming habits -- is the fact that he did not claim the Clay Insitute Prize or the Fields Medal, both of which were awarded to him for his work on the geometrization conjecture. Rene Azurin, a professor of management and "strategy consultant" singles out these facts as an indicator that Perelman is the harbinger of either a new era of human evolution, or the demise of a grand old one. "Clearly," says Azurin, Perelman "is the kind of individual for whom the acquisition of knowledge is the only goal worth pursuing in life. In this materialist day and age where wealth accumulation and conspicuous consumption is the measure not only of success but of virtue, that makes him a rare and highly unusual man." Photo: Fields Medal (the one Grigori Perelman did not accept), by Stefan Zachow (ZIB), courtesy International Mathematical Union.
At the risk of taking Azurin too seriously, I'm thankful that neither evolution nor human nature are as simplistic as he makes them out to be. For one thing, figuring out whether or not people are evolving is complicated ("Evidence for evolution in response to natural selection in a contemporary human population," by Emmanuel Milot et al, PNAS, 28 September 2011). One approach -- correlating traits of menopausal women with the number of their offspring -- allows a prediction of the phenotypic makeup of future generations, and (less plausibly) an estimate of the direction of evolutionary change. Based on a three-generation study of women in Framingham, Massachusetts, one group showed that the women in this population are evolving to be shorter and stouter, have lower cholesterol and blood pressure, and longer reproductive periods ("Natural selection in a contemporary human population," by Sean G. Byars et al, PNAS, 23 October 2009). (In other words, these traits are -- perhaps unsurprisingly -- associated with high reproductive rates.) But whether or not humans continue to evolve, no one knows if even a very long chain of causality links genetic and epigenetic variability to complex moral attitudes, such as the relative valuation of knowledge and wealth.
Perhaps Azurin means cultural evolution, instead. A person's context certainly affects their approach to the acquisition of material wealth. But it's one thing to recognize how business and government's short-sighted prioritization of growth and profit, combined with an immersive media environment that allows constant sensory bombardment, push human beings into a dissatisfying cycle of mindless consumption and overwork. It's quite another to bemoan "this materialist day and age" without any attempt to illuminate the structural and historical contingencies that have brought it about, or any serious attempt to frame the moral problems posed by the socioeconomic and technological realities of our time.
But even if we were having a serious conversation about the nature of wealth, and the good reasons someone might refuse a vast sum of money ("Do We Need $75,000 a Year to Be Happy?," by Belinda Luscombe, TIME, 6 September 2010, "8 People Who Refused Millionaire Offers" by Natalie Umansky, Oddee, 19 June 2013) -- such as, say, the fact that neither knowledge nor material wealth are sufficient for a balanced life of contentment -- I'm not sure mathematicians would make good examples. While mathematics is routinely listed as one of the "best" professions ("The 10 Best Jobs of 2014," by Adam Auriemma, Wall Street Journal, 15 April 2014), I think no references are needed to back up the assertion that there are better ways to make money. There are few better ways, though, to create a new piece of knowledge likely to stand the test of time. Is it really surprising, then, that a mathematician would be more pleased with the solution of a hard problem than any other reward? Paul Erdos, the incredibly prolific combinatorialist, lived out of a suitcase, and gave all the prize money he earned to charity (see Paul Erdős entry on Wikipedia) -- and maybe it's no coincidence that these two things went together. To put it another way, if you like thinking about mathematics more than you like thinking about anything else, why would you want to worry about what to do with a million dollars (or the best way to live your life, or the future of the human race)? That's just one more distraction from mathematics!
* The title of this post is taken from a recent article about the scrutiny of women's decisions ("I Don't Care If You Like It," by Rebecca Traister, New Republic, 16 July 2014), which is a distraction worth indulging.
See "Evolutionary advance or dead end?," by René B. Azurin. Business World Online, 23 July 2014.
--- Ben Pittman-Polletta (Posted 8/1/14)
There's some question about whether the U.S. has too many people looking for STEM (science, technology, engineering, and mathematics) jobs or too few. In an effort to clarify the situation, the U.S. Census Bureau has created a graphic that shows the flow from the approximately 15 million college STEM majors to the approximately 5 million people who hold STEM jobs. The graphic is interactive, too, so that users can choose a category (such as computer science, mathematics, and statistics, as shown at left) and see in what fields people with those majors are employed or choose a job and see what those people majored in. Visitors to the site can also view the data on which the graphic is based, look at non-STEM majors, and narrow their search to gender or race. Image: The U.S. Census Bureau, Public Information Office (PIO). The length of each circle segment shows the proportion of people graduating in a major who are employed in each occupation group. The thickness of the curves between majors and occupations indicates the share of people in that major-occupation combination. Curves highlighted in color show the proportion of college graduates who work in STEM.
See "A fresh look at the STEM workforce." News, Science, 18 July 2014, page 245.
--- Mike Breen
Video: National Science Foundation.
Mathematicians are helping California farmers increase strawberry and raspberry production while minimizing water use--a key problem in that state--by using algorithms and models. Researchers from the American Institute of Mathematics (AIM), with funding from the National Science Foundation, are working with the farmers to develop mathematically driven answers to questions about what to plant and when to rotate crops based on growing patterns, cost, and groundwater levels. AIM Deputy Director Estelle Basor explains that AIM's work is attempting to lessen some of the risk inherent in farming decisions. Though focused at present on berry growers in California's Pajaro Valley, AIM researchers hope to apply their models to a range of crops throughout the country, from a wheat farm in the Midwest to a corn farm in the Southeast. This piece includes a short video in which the farmers and the researchers discuss the goals and value of this mathematical research.
See "How math is growing more strawberries in California," by Rebecca Jacobson. PBS News Hour, 11 July 2014.
--- Lisa DeKeukelaere
This profile piece describes the life of James Simons, a mathematician famous not only for his groundbreaking proofs but also for the philanthropic projects he undertakes with his $12.5 billion fortune. After receiving his PhD in math at age 23, Simons taught at MIT and Harvard before working on cryptography for the NSA and later running the math department at Stony Brook University on Long Island, where he won the nation's highest prize for his work in geometry. Simons then started Renaissance Technologies, a successful investment firm driven by scientific minds, and began pouring his wealth into projects such as a foundation to promote math education in public schools and a math museum in New York City. Simons notes that he is a terrible programmer and probably would not have performed well in math competitions in his youth, but he credits his success to pondering the world around him.
See: " Seeker, Doer, Giver, Ponderer," by William J. Broad. New York Times, 7 July 2014, and also "Jim Simons: Mathematician, Codebreaker And Hedge Fund Manager," by Clayton Browne. ValueWalk, 10 July 2014.
--- Lisa DeKeukelaere
In late June 650 origami aficionados from around the world gathered at the Fashion Institute of Technology in Manhattan for the OrigamiUSA annual convention, the world's largest origami convention. Attendees chose from over 200 classes, which were represented by a display of models, ranging from simple to complex. Several of the classes were full by the first morning of classes. These included a class with children's entertainer and juggler Jeremy Shafer, folding his "One-Piece Super Boomerang," as well as a class for folding a 3D origami cat, taught by physicist, engineer and origami artist Robert Lang. In addition to the classes, computer scientist Eric Demaine, with his mathematician and artist father, Martin Demaine, gave a lunchtime talk. (Photo: Robert J. Lang's 3D origami cat, subject of a sellout class at the event. Photo courtesy Robert J. Lang.
Watch a video about the event.
See: "Video: Origami Artists Don’t Fold Under Pressure," with video, by Elizabeth Yuan. Wall Street Journal, 2 July 2014.
--- Claudia Clark
By now we've all heard of Big Data. We're aware of the vast storehouses of data points being gathered on every imaginable thing, or non-things, under the sun. And we're probably aware of the challenges of analyzing such a humongous amount of data, in particular, in a sea of so much information, how does one separate the real trends from the background noise? The MIT News Office explains how one MIT mathematics professor is turning these mountains of raw data into meaningful answers.
Photo by Sandy Huffaker
Professor Alice Guionnet (above) uses a branch of mathematics called random matrix theory. By taking the data and putting it in in cleverly designed arrays, or matrices, Guionnet is able to tease out the important trends and separate them from the noise. In particular, Guionnet is interested in using these techniques to predict the likelihood of extremely unusual events occurring. She likens this process to sewing a patchwork quilt -- after analyzing the data she is left with many partial solutions, and the key is in deciding how these components fit together.
This field is particularly exciting, Guionnet says, because it lies at the intersection of so many branches of mathematics. "it crosses over into different fields," she says, "probability theory, operator algebra, and random matrices -- and I’m trying to advance these three theories at the same time." The techniques are also valuable across disciplines and have been used to analyze trends in statistics, telecommunications, and even neurobiology.
In 2012 Guionnet was a recipient of the Simons Foundation Investigators Grant.
See "Mathematical patchwork," by Helen Knight. MIT News, 27 June 2014.
--- Anna Haensch (Posted 7/29/14)
In this Ask A Physicist entry, Goldberg provides a short history of mathematician Emmy Noether, including a description of some of the professional barriers she faced as a female mathematician. He then explains how she provided "the mathematical foundation for much of the standard model of particle physics." Noether recognized that there is a mathematical relationship between symmetries of the natural universe and what are known as conservation laws. While there is a fair amount of mathematics behind it, the upshot of what's known as Noether's Theorem is essentially: Every symmetry corresponds to a conservation law. [Her theorem predicts] that the laws of physics don't change if you adjust the clock of the universe or move to a different place or point in a different direction. Photo: Portrait of Emmy Noether before 1910, Public domain-US-no notice per Wikimedia Commons.
For additional reading, check out Goldberg's new book, The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality, from which this article is adapted.
See: "The Most Important Mathematician You've Never Heard Of," by Dr. Dave Goldberg. io9, 25 June 2014.
--- Claudia Clark
Joshua Batson, the current AMS-AAAS Media Fellow, finds a collection of dusty plaster and string models of mathematical surfaces tucked away in a display case at MIT. As it turns out these models were manufactured over 100 years ago. One of the major builders of models of mathematical surfaces at the time, and an advocate for visual intuition, was mathematician Felix Klein. His laboratory in Göttingen manufactured plaster models of mathematical surfaces in an attempt "to keep algebra anchored to the physical world." It was not long after Klein's appearance at the World's Fair in Chicago in 1893 with models from his laboratory for sale that "major American universities had ordered hundreds of surface models from thick catalogs, and had them shipped thousands of miles over the Atlantic." However, "in the early 1900s, there was a growing realization that arguments made from geometric intuition, from drawing pictures and making models, might not be airtight logically," and the use of models eventually fell out of favor.
Read more of the story behind these types of models -- including how they were made and their influence on modern artists and designers -- and see some of the models in the collection at the University of Illinois at Urbana-Champaign. Photo: UIUC Altgeld collection.
See: "This Is What Math Equations Look Like in 3-D," by Joshua Batson. Wired, 25 June 2014.
--- Claudia Clark
In June, Russian investor Yuri Milner for the first time awarded his new "Breakthrough Prize" in mathematics to five mathematicians, who each received $3 million. Milner developed this mathematics prize, as well as prizes in physics and the life sciences, as part of an effort to celebrate and attract attention to science in a society that more frequently recognizes athletes and entertainers. In addition to Milner, other financial contributors to the awards include Facebook CEO Mark Zuckerberg and Google co-founder Sergey Brin. Three of the five mathematics Breakthrough Prize recipients previously received the prestigious Fields Medal, and most have indicated that they intend to use some of the money to support other mathematicians. Dr. Terence Tao, a Breakthrough Award recipient for his work with prime numbers and fluid flow, indicated he might use some of his award to finance open-access mathematics journals or large-scale online collaboration on important problems.
See: "The Multimillion-Dollar Minds of 5 Mathematical Masters," by Kenneth Chang. New York Times, 23 June 2014.
--- Lisa DeKeukelaere
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