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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 : "Regression, Twitter, and #Ferguson," "Medaling Mathematicians."
There must be something in the red rock of the New Mexico desert that's good for interdisciplinary science. The state is home to both the Los Alamos National Laboratory and the Santa Fe Institute, a research center dedicated to the study of complex phenomena using tools from physics, mathematics, biology, social science, and the humanities. There's so much science in New Mexico that the Santa Fe New Mexican features a column written by researchers from the Santa Fe Institute. This month, Ben Althouse, an Omidyar Fellow who uses the science and mathematics of complex systems to study viral epidemiology, takes the helm. Althouse points out that, as opposed to non-infectious diseases, such as cancer and heart disease, the study of virally-transmitted infectious diseases is complicated by the fact that an individual's susceptibility to them depends not only on his or her own health behaviors--how much sleep they get and how often they wash their hands--but also on the health behaviors of those they interact with. With his collaborator Sam Scarpino, Althouse has begun to reveal how the existence of asymptomatic carriers of whooping cough have been crucial to the recent resurgence of the disease. His work also focuses on the spread of mosquito-transmitted viruses, such as dengue fever and Chikungunya, common in the Caribbean and Florida. These diseases introduce the extra complication of interactions between species.
Beyond virally transmitted diseases, Althouse has employed new technologies to study public health more generally, using Google search terms to study patterns in health-related behaviors. With his collaborator John Ayers and others, Althouse found that searches related to quitting smoking, and healthy behaviors more generally, are more common early in the week, on Sundays, Mondays, and Tuesdays ("Circaseptan (weekly) rhythms in smoking cessation considerations," by John Ayers et al; "What's the healthiest day?: circaseptan (weekly) rhythms in healthy considerations," by John Ayers et al). Google searches also reveal the health burden of the 2008 recession--after which queries related to the symptoms of headaches, stomach ulcers, heart disease, and joint and tooth pain increased unexpectedly and dramatically (Population health concerns during the United States' great recession," by Ben Althouse et al).
Althouse's most-cited paper, though, reveals how the impact factor--a measure of the scientific influence of a journal based on the number of citations its articles receive--varies over time and across disciplines ("Differences in impact factors across fields and over time," by Ben Althouse et al). It turns out that, as science has grown, so have impact factors; and that differences in impact factors across fields depend more on which citations are counted than on which fields are growing fastest.
--- Ben Pittman-Polletta (Posted 9/15/14)
Nothing ruins a day at the beach like washed-up garbage. Unsurprisingly, not just our beaches, but also the oceans themselves are piling up with garbage. But where does it all come from? As reported by nbcnews, a group of scientists from the University of New South Wales (Austrailia) may have found a mathematical approach to understanding how our garbage travels through our oceans. (Image courtesy of Flickr, epSos.de.)
The earth’s oceans are partitioned into 5 distinct gyres--or vortices--and these describe the major ocean currents. Scientists previously thought that the gyres should be self contained. In particular, they believed that once a piece of garbage got swept up in the North Pacific gyre, it would get drawn to the center and join its fellow debris in a so-called garbage patch somewhere in the North Pacific. But recent efforts to track and identify garbage has shown that this junk is traveling farther than we had thought. (Image courtesy of Wikimedia Commons.)
To better understand this flow of trash, Gary Froyland, a professor of mathematics at the University of New South Wales, and his colleagues have approached this problem in a totally new way: by modeling it is a dynamical system. They modeled the surface of the oceans using a Markov chain model, which is able to account for the three-dimensional upwelling and downwelling of the ocean. Using this model, they identified the major attracting regions. And although these regions were mostly consistent with the known ocean gyres, they did find some unexpected inter-connectedness between some really distant parts of the oceans. This has also led to their follow-up study: how hard is it for floating garbage to cross the boundaries of a gyre?
What this means is that we may all be more connected than we thought. Even though oceans may separate us, we are all connected by our joint responsibility for our shared oceans and our planet.
See "Math Might Help Nail Oceans' Plastic 'Garbage Patch' Polluters," by Miguel Llanos. nbcnews.com, 2 September 2014.
--- Anna Haensch (Posted 9/16/14)
Long before there were computers, the term "computer" referred to people who were adept at performing arithmetic operations. In this article, Hayes introduces us to "one of the finest computers of the Victorian era," William Shanks, and Shanks's work calculating the value of Pi to 707 decimal digits. You might not be surprised to find that some errors crept into Shanks' calculation--beginning at around digit 530--and it is Hayes's attempt to determine the possible reasons for these errors that makes up the bulk of the article. Hayes begins with the fact that most calculators of Shanks' era used arctan formulas (and their equivalent infinite series) for determining the value of Pi. Shanks worked with a formula discovered by mathematician John Machin in 1706 that required the evaluation of two arctan series: π/4 = 4arctan(1/5) – arctan(1/239). Hayes then explores some of the computational methods that Shanks may have used. Finally, Hayes describes the method he uses to identify, and provide a reasonable hypothesis for, three of Shanks' errors.
--- Claudia Clark
When Professor Tim Chartier (left) from Davidson College wanted to get an honest opinion on his new math book, his not-so-enthusiastic-about-math sister was the obvious choice. When she not only finished it, but admitted that she actually kinda liked it, he knew he was onto something.
In this latest book, Math Bytes, Chartier explores topics in mathematics from middle school math up to college-level linear algebra using clever hands-on activities, and relatable--sometimes even delicious--tools to get his message across. One activity, which he performed live on WCCB News in Charlotte, uses approximation methods to turn a photograph into a tasty M&M mosaic.
Below is another M&M mosaic that he and his family put together for Make Magazine earlier this year.
Many of the activities, Chartier explains, were developed in a seminar that he taught for public school teachers in Charlotte. So while they are primarily geared towards middle and high school students, they are really adaptive, and can be fun for people at any level. “It has a very broad appeal,” he says, “that doesn't mean that everyone can understand all of it, but I know if this part gets a little more complicated, then you'll catch me on the other side.”
“I want people to have a positive story about math,” he says, “a lot of times people stop at algebra. But it’s like you’re at the buffet of math and only made it to the salad bar. You’ve missed all the other good stuff.”
Next up, Chartier is working on a companion website and software to help students take their activities to the next level. For more fun math bits and bytes, follow Chartier on Twitter. @timchartier(Images courtesy of Tim Chartier.)
See "Davidson College Professor Teaches Non-Traditionally With 'Math-Bytes'," by Jennifer Miller, WCCB-TV, 28 August 2014.
--- Anna Haensch (posted 9/8/14)
Imagine that you are an architect in a small, two-dimensional town--either planar or spherical--having only six buildings: three homes, and three utilities--a water plant, a gas plant, and an electric plant. You are trying to connect each home to each of the three utilities, but with a very strict aesthetic: you don't want to connect the homes serially - each home must have its own connection to each utility - and you don't want any of the connections to cross. The task you've set for yourself is the utilities problem, also known as the water, gas, and electricity problem. Go ahead and take a crack at it, I'll wait.
Now imagine that you are a pregnant woman in the Congo during the '60s, looking for a medicinal tea to help you induce labor. Chances are, you'll reach for a medicinal tea that goes by the name kalata kalata, made from the plant Oldenlandia affinis. The active ingredient of kalata kalata is a peptide, named kalata B1. Kalata B1 is a ring of around 30 to 40 amino acids, interrupted at six places by the amino acid cysteine. The six cysteine residues are connected in pairs by three disulfide bonds. The six links between these cysteine residues--three disulfide bonds, and three chains of amino acids--make kalata B1 a protein incarnation of K3,3, with cysteine residues as vertices. In fact, kalata B1 is only one of a huge family of plant proteins known as cyclotides, all of which share the topology of K3,3. In these proteins, the linked cysteines are a constant, but the sections of amino acids between them are highly variable, containing different functional motifs. The cyclotides all share a remarkable rigidity and stability, thanks not only to their disulfide bonds but also to their peculiar topology, and a high level of resistance to digestion. They have potent insecticidal properties, and are being explored as a backbone for peptide drugs designed for oral administration (see "Cyclotide," Wikipedia.)
Finally, imagine you are polymer chemist Yasuyuki Tezuka. Polymers are macromolecules composed of many repeating subunits. Their behavior in aggregate--they may form materials that are tough, viscous, elastic, or combinations of all three--are dictated by their molecular properties. While many interesting things can be done with linear polymers--molecules made up of chains of subunits--you are interested in the unexplored frontier of cyclic polymers. You want to know how a plastic made of Hopf links or figure eights might behave. So, you develop a process allowing for the creation of molecules with simple but nontrivial topologies--such as a "theta" shape or an unfolded tetrahedron. Now you want to set your sights higher, to create a mathematically interesting as well as potentially useful cyclic polymer. What graph would you look to sculpt out of molecular bonds? As you've certainly guessed, Tezuka and his team set out to synthesize a tiny version of K3,3. They succeeded in part because K3,3 has an exceptionally compact 3D shape, when compared to other topological arrangements, allowing it to be isolated from these other molecules, and perhaps helping it to "achiev[e] exceptionally thermostable bioactivities" ("Constructing a Macromolecular K3,3 Graph through Electrostatic Self-Assembly and Covalent Fixation with a Dendritic Polymer Precursor" by Suzuki, et al.). Tezuka credits his graduate student Takuya Suzuki, the paper's first author, with recognizing the utility of K3,3's compactness. "It's a very nice example of Japanese craftsmanship!" he says. But they aren't finished yet. "There are many other structures that are not easy to make at the nanoscale," he says. The "Konigsberg bridge-graph" appearing in their paper suggests what Tezuka's group might look to build next.
Image: The K3,3 graph, on the far right, has the smallest volume of all configurations shown, making it the fastest molecule in size-exclusion chromatography. Image courtesy of Dr. Yasuyuki Tezuka.
See "Materials scientists, mathematicians benefit from newly crafted polymers." R&D Magazine, 26 August 2014 (from Tokyo Tech News, 19 August 2014).
--- Ben Pittman-Polletta (posted 9/4/14)
Examining Rene Thom's quote that "any mathematical pedagogy… rests on a philosophy of mathematics," columnist Ifran Muzaffar posits that while the quote may hold true for university professors, most K-12 teachers organize their instruction based on a blend of philosophies, rather than standing by a single philosophy to shape their approach to teaching. The article describes three philosophies and how each would be applied in the classroom: 1) mathematics as an objective reality to be discovered , as theorized by G.H. Hardy; 2) mathematics as a set of abstract rules and procedures to be memorized; and 3) mathematics as an iterative process of conjectures to be tested, as popularized by Karl Popper. Muzaffar recounts observing a fourth-grade teacher who adeptly used multiple techniques--without knowing about the underlying philosophical constructs--to meet the multiple demands of school mathematics.
“On the mathematical landscape,” by Irfan Muzaffar. The News on Sunday, 24 August 2014.
--- Lisa DeKeukeleare
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 in 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 children 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's 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." (Image: Thomas Hales talking about sphere packing at the 2010 Arnold Ross Lecture in Pittsburgh.)
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)
"Top Math Prize Has Its First Female Winner", by Kenneth Chang. New York Times, 12 August 2014.
"Fields-Medaille an Iranerin Maryam Mirzakhani: Das gab es noch niemals zuvor. Eine Frau hat die höchste Auszeichnung für Mathematik erhalten, die Fields-Medaille (Fields Medal to Maryam Mirzakhani: This has never happened before. A woman has received the top honor in mathematics, the Fields Medal)", by Manfred Lindinger. Frankfurter Allgemeine Zeitung, 13 August 2014.
Above are links to a sampling of the worldwide coverage of the 2014 Fields Medals, which were presented on August 13 at the International Congress of Mathematicians (ICM) in Seoul. Though often called the "Nobel Prize" of mathematics (there is no Nobel in mathematics), the Fields Medal differs from the Nobel Prize: The medal is given every four years and, instead of honoring a career-long body of work, it is presented to young (under 40 years of age) mathematicians as an encouragement to further achievements. [See a summary of an article about the Fields Medal's label as the "Nobel" of mathematics.]
Since its establishment in 1936, the Fields Medal had never gone to a woman, until this year. Naturally, most of the coverage centered on the first-ever woman Fields Medalist, Maryam Mirzakhani. The article by Caroline Series, a distinguished British mathematician, provides insights on why it took so long for the Fields Medal to be awarded to a woman. "[T]he generation of women born after the Second World War and currently reaching retirement is really the first in which aspiring mathematicians have been able to pursue their chosen career without institutional obstacles in their path," she writes. "Combine this history with the level of concentration that is needed in those precious twenties and thirties---the years in which most of us want to be building a family, the years of juggling the demands of two careers in a discipline that may require relocating anywhere in the world, perhaps with a husband, who may, or may not, consider his wife's career as important as his own. It then becomes a little clearer why it is that women have lacked the support networks, the role models and the contacts that most people need to get to the very top."
Other firsts in this crop of Fields Medals: Mirzakhani is the first Iranian Fields Medalist, Artur Avila the first Brazilian, Manjul Bhargava the first of Indian origin, and Martin Hairer the first Austrian. The International Mathematical Union, which awards the Fields Medals, works hard to nurture and support mathematical development the world over. The Time magazine story quoted IMU President Ingrid Daubechies: "At the IMU we believe that mathematical talent is spread randomly and uniformly over the Earth---it is just opportunity that is not. We hope very much that by making more opportunities available---for women, or people from developing countries---we will see more of them at the very top, not just in the rank and file."
Because Mirzakhani dominated the coverage, the other IMU honors presented at the ICM received less attention: The Nevanlinna Prize went to Subhash Khot, the Gauss Prize went to Stanley Osher, and the first-ever Leelavati Prize went to Adrian Paenza.
Don't miss the outstanding articles on the work of the Fields Medalists that appear in Quanta magazine.
--- Allyn Jackson
In this article, Rosen tells the story behind a few of the fonts designed by the father-son team of Martin and Erik Demaine, an artist-in-residence and a professor in computer science, respectively, at MIT. Perhaps more well known for their work with geometric folding, the two have applied mathematics and computational geometry to design a number of fonts. The idea for the "conveyor belt" font--imagine letters formed from thumb tacks and elastic bands--occurred during a break the Demaines and a colleague were taking from working on the following question: Can a single 2-D conveyor belt be stretched around a set of wheels such that the belt is taut and touches every wheel without crossing itself? The "glass-squashing" font resulted from their interest in glass blowing: clear disks and blue glass sticks can be arranged in such a way that, when heated and pressed together horizontally, the blue glass sticks form letters. Both are called puzzle fonts because, in one form, the letters are difficult to discern. Visit their website to play with these and other fonts.
See "Father-son mathematicians fold math into fonts," by Meghan Rosen. Science News, 10 August 2014.
--- Claudia Clark
In preparation for the mid-August announcement of the 2014 Fields Medal winner, this article (published in early August) examines the history of the Medal and the intersection between mathematics and politics. Debunking the myth that Alfred Nobel neglected to create a mathematics prize to spite a Swedish mathematician rival, the article explains that mathematics simply was not important to Nobel, and Canadian mathematician John Charles Fields created the award in 1950 to unite the divided scientific community following World War II. The Medal did not gain widespread recognition--or the "Nobel of mathematics" tag line--until the 1960s, when media outlets championed the award to help Medal recipient Stephen Smale evade censure for alleged anti-Communist activities. Math and politics continue to be intertwined, as mathematicians consider the implications of military funding and working for the NSA, but the author argues that acknowledging this overlap bolsters the meaning and promise of mathematics.
--- Lisa DeKeukelaere
It's perhaps not quite media coverage, but definitely worthy of mention. August 4 was the 180th birthday of mathematician and logician John Venn, of Venn diagram fame. Google saluted him with a very clever animated Doodle, which you can still see in the Doodle archive. The site also has an interview with the Doodle's creators as well as images, such as the one at left, that show their thought process as they developed the Doodle.
--- Mike Breen
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