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Math Digest

On Media Coverage of Math

Edited by Mike Breen and Annette Emerson, AMS Public Awareness Officers
Contributors:
Mike Breen (AMS), Claudia Clark (writer and editor), Lisa DeKeukelaere (2004 AMS Media Fellow), Annette Emerson (AMS), Anna Haensch (Duquesne University), Allyn Jackson (Deputy Editor, Notices of the AMS), and Ben Pittman-Polletta (Boston University)


ZhangLurie

Yitang "Tom" Zhang (left) and Jacob Lurie (right), MacArthur "Genius Grant" recipients. Photos courtesy of the MacArthur Foundation.

"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: 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: "First Impressions of the Second Heidelberg Laureate Forum," "Making Conferences Easier for Families"

Celebrating Martin Gardner's 100th Birthday, by Mike Breen and Annette Emerson

Gardner portrait by Bruce Torrence

In honor of what would be Martin Gardner's 100th birthday on October 21, Colm Mulcahy (Spelman College) and Dana Richards (George Mason University) have written a fond remembrance of Gardner and the many years and ways he inspired so many. "Like a good magic trick, a clever puzzle can inspire awe, reveal mathematical truths and prompt important questions. At least that is what Martin Gardner thought. His name is synonymous with the legendary Mathematical Games column he wrote for a quarter of a century in Scientific American." Mulcahy and Richards give some background on some of the concepts Gardner introduced to a wider audience, such as hexaflexagons, polyminoes, the Game of Life, Penrose tilings, and RSA encryption. Gardner's column influenced many to pursue mathematics professionally, and entertained and informed many others. One of his successors at Scientific American, Ian Stewart, said, "Martin Gardner was an impossible act to follow...What we did try to do was replicate the spirit of the column: to present significant mathematical ideas in a playful mood." Gardner discontinued the column in 1980 but still continued to write about recreational mathematics and wound up writing over 100 books. To this day, his work is celebrated in the biennial Gathering 4 Gardner conference, in less formal Celebration of Mind events, and the clever work of mathematicians and magicians, as evidenced in the 30 days of activities celebrating Mathematics, Magic, and Mystery, the theme for Mathematics Awareness Month 2014--and, well, for every month, especially this October as we celebrate Martin Gardner.

The image here is "Martin Gardner - Master Puzzler," by Bruce Torrence (Randolph-Macon College, Ashland, VA), on Mathematical Imagery. Torrence describes the work as follows: "This portrait of Martin Gardner (1914-2010) was made by coloring the individual tiles on a kite and dart Penrose tiling. This particular tiling exhibits fivefold rotational symmetry (can you find the center?), and was created by "deflating" a wheel of five kites eight times. Gardner's oft-cited January 1977 Scientific Americancolumn introduced the public to Penrose's aperiodic tiles."

See "Math Games of Martin Gardner Still Spur Innovation," by Colm Mulcahy and Dana Richards, Scientific American, October 2014, pages 90-95. (The full article is available only by subscription.) See also: Selected articles and websites about and by Martin Gardner.

--- Mike Breen and Annette Emerson

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'Among The 'Brilliant Ten,' A Math-Loving Biologist, by Anna Haensch

Katia Koelle

This month, Popular Science’s "Brilliant Ten" list is a jaw-dropping roster of young scientists who are making a huge impact on the world. One that particularly caught our eye was an evolutionary biologist whose first love was, you guessed it, math!

Katia Koelle specializes in Ecology and Population Biology ("Katia Koelle Models How Viruses Turn Deadly"). She uses math modeling and statistics to understand how certain measures can stem the spread of dangerous infectious diseases. Lately she’s been crunching the numbers with vaccination and vector control, basically asking, what happens to the spread of Dengue when the Orkin man comes in and nukes all the mosquitos? Not what you’d think, the work out of her labs shows. Controlling the mosquito population of course means that people get infected less frequently, but consequently they don’t build up the same storehouse of antibodies to fight the disease.

Koelle also studies the evolution of influenza. In a talk at the Kavli Frontiers of Science last year, she describes a mathematical model to understand the seasonal and yearly chronology of flu outbreaks, and the evolution of the virus itself. Koelle hopes that these, and other fresh ideas from her lab, can be used to inform public health policy.

Some of PopSci’s other Brilliant Ten honorees include a mechanical engineer who studies bat colonies to make better drones, and a biochemist harnessing the power of snot.

See "The Brilliant Ten of 2014," by Veronique Greenwood and Cassandra Willyard, Popular Science, October 2014 issue, posted 9/17/14. (Photo courtesy of Katia Koelle.)

--- Anna Haensch (Posted 9/24/14)

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On a math teacher who won one million dollars on Wheel of Fortune, by Mike Breen

Sarah Manchester

During Teachers' Week on the television show Wheel of Fortune, middle school math teacher Sarah Manchester became the third person in the show's history to win its $106 grand prize. Manchester is also the coach of the math team at her school, Takoma Park Middle School, which is where she herself went to school. After her win, Wheel of Fortune host Pat Sajak asked Manchester if she had figured out the probability of winning a million dollars. She answered, "I assessed that the probability was low, but even unlikely events sometimes happen!"

You can see video of her performance at the link below.

"Silver Spring math teacher, Sarah Manchester, wins $1million on 'Wheel of Fortune,'" Jay Korff. WJLA ABC 7, 17 September 2014.

--- Mike Breen


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Math Geniuses, by Ben Pittman-Polletta

Zhang Lurie

Yitang "Tom" Zhang (left) and Jacob Lurie (right). Photos courtesy of the MacArthur Foundation.

Each year, the MacArthur Foundation (of John D. and Catherine T. fame, as those who grew up watching public television will know) invites hundreds of nominators, known for their accomplishments in a wide array of fields of human endeavor, to nominate the most creative people they know. Out of this group, a smaller committee selects 20 to 30 MacArthur Fellows, who receive no-strings-attached financial support for the next five years. Although the past accomplishments of candidate Fellows are reviewed during the selection process, the award is given primarily on the basis of future potential for creative work. The Fellowship is intended to free recipients from financial constraints, allowing them to exercise their creativity to its fullest (see MacArthur Fellows: Our Strategy", on the MacArthur Foundation website). Past recipients include not only artists and academics, but labor organizers (including this year's winner Ai-Jen Poo), papermakers, blacksmiths, barbershop owners turned literacy advocates. The Foundation (somewhat ineffectually) discourages the use of the word "genius" to describe the grants and their recipients ("Five Myths About the MacArthur 'Genius Grants'," by Cecilia Conrad for The Washington Post, September 20, 2013).

Of the 918 awards given since the awards' inauguration in 1981, 28 have been given to practitioners of the mathematical arts (see "MacArthur Fellows Program" on Wikipedia). This year, two of the recipients are mathematicians, and two more use mathematics in their work. Yitang "Tom" Zhang, whose gigantic first step towards a proof of the twin primes conjecture rocked the math world last May, is one of the 2014 class. So is Jacob Lurie, a mathematician at Harvard University who uses the theory of infinity-categories to generalize homotopy theory, and other topological aspects of algebraic topology. Lurie's work on quantum field theories links the categorical concept of duality to the topology of manifolds, as well as providing a classification scheme for quantum field theories. "I think of mathematics as a large number of interconnected stories, and I feel like my job as a mathematician is to take one or a few of those stories that I understand well and try and tell them in a way that other mathematicians can appreciate, enjoy, and maybe use in their own work," says Lurie. He is also a teacher, and in his interview for the MacArthur Foundation, he shares his opinion on the quaqmire that is mathematics education. "Mathematics is a giant playground filled with all kinds of toys that the human mind can play with, but many of these toys have very long operating manuals, but some of them don't, and I think that there are a number of mathematical insights that are very interesting that you really could teach to someone in a freshman course," he says. "I would like it to be viewed as just part of the intellectual culture in the same way that taking a class in Plato or taking a class in Shakespeare would be..."

Fellow Craig Gentry, a computer scientist, has proven that it is possible to manipulate encrypted data without ever lifting the encryption, and physicist Danielle Bassett uses graph-theoretic measures to study the dynamic reconfiguration of brain networks over time, with learning, memorization, and disease. Bassett has discovered that those who learn the best have the most flexible brain networks, suggesting the MacArthur Foundation's emphasis on creativity and the popular press' fascination with genius may not be orthogonal after all.

See "Meet the 2014 Winners of the MacArthur 'Genius Grants'," National Public Radio, September 17, 2014, and Meet the Class of 2014 MacArthur Fellows. Also, read about some of their previous awards.

--- Ben Pittman-Polletta (Posted 9/24/14)

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On the Lévy flight movements of sharks, by Annette Emerson

shark

The movements of sharks and other predators are like Lévy flight, "a seemingly complex form of random walk comprising clusters of short step lengths with longer movements between them" to locate prey. Andy Reynolds, at Rothamsted Research, published his study in Proceedings of the Royal Society A, and notes Lévy flight "can be advantageous when searching for randomly distributed resources because they reduce 'over sampling' without the need for cognitive maps and sophisticated navigational abilities." In the case of sharks, they use turbulent waters around them as cues to change direction. The natural behavior seems to have worked, as sharks have survived for over 10 million years.

See "Sharks Act Like Math Geniuses," by Jennifer Viegas, Discovery News, 16 September 2014.

--- Annette Emerson

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On Jim Fowler and his online MOOCulus, by Claudia Clark

Jim Fowler

The last few years have seen tremendous growth in the number of online courses being offered by universities and organizations through sites like Coursera. In this article, writer George Anders describes one of Coursera's most popular courses—Calculus 1—and the man behind it: Jim Fowler, an assistant professor of mathematics at The Ohio State University. The "geeky, high-energy" Fowler is on "a one-man crusade to make secants sexy and integrals irresistible." His dynamic presentations, augmented by clever visuals and "a kicky musical soundtrack," have captured the interest of well over 100,000 students, many of whom are older adults. In addition to the 25 hours of lectures and quizzes provided on Coursera, Fowler also provides an online textbook and “highly nuanced problem sets that make the most of online learning’s feedback loops” on a separate site. Between the time he has spent developing the course, making improvements, visiting discussion boards, and providing one-on-one tutoring, Fowler has devoted some 1,350 hours to the online class. As a result of the success of the course, the university has placed Fowler—initially hired for a non-tenure track position—on the tenure track. (Image courtesy of Jim Fowler.)

Check out Fowler's lectures and quizzes for Calculus 1, and see all of the resources for the course.

See: "Forget Cat Photos: This Prof Is Making Calculus Go Viral," by George Anders. Forbes, 10 September 2014.

--- Claudia Clark


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New mathematics gallery to open at Science Museum (U.K.), by Mike Breen

Design of new math gallery

The Science Museum in London will open a new mathematics gallery that will "tell the stories that place mathematics at the heart of our lives, exploring how mathematicians, their tools and ideas have helped to shape the world from the turn of the 17th century to the present." The gallery is made possible by a five-million pound gift (about US$8 million) to the museum from David Harding, a hedge fund manager in London who used mathematics in his trading. Harding says, "Mathematics is a fascinating and mysterious but, for some, forbidding subject. The new gallery has been created to convey something of that fascination in a way that will appeal to a wide audience." The new mathematics gallery will open in late 2016. (Image: View from East gallery entrance, Science Museum Mathematics Gallery, Zaha Hadid Architects.)

See "Science Museum unveils £5m plan for 'world's foremost' mathematics gallery," by Alex Bellos. The Guardian, 10 September 2014.

--- Mike Breen

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On the math behind how crustaceans swim, by Lisa DeKeukelaere

lobster

In a paper recent published in the Proceedings of the National Academy of Sciences, four mathematicians and a biologist describe how they used fluid flow modeling and dissection of crayfish nerves to understand how neural pathways of crustaceans direct their small, paddle-like limbs to provide efficient propulsion. The researchers discovered that the neural pathways activate each pair of paddle limbs to perform a front-to-back "power stroke" slightly before the next pair of limbs closer to the head, resulting in a tail-to-head Mexican wave motion. The fluid flow modeling indicated that staggered tail-to-head pair activations were more efficient than pairs paddling in unison or pair activation starting at the head, and the dissection showed that the crayfish nerve circuit reached equilibrium when paddle pairs operated about a quarter power stroke cycle apart—the same result the mathematicians found to be most efficient.

See "Math Explains How Lobsters Swim," by Clare Pain, ABC Science Online for Discovery News, 9 September 2014, and the original research paper "Neural mechanism of optimal limb coordination in crustacean swimming," (abstract) by Calvin Zhang, Robert D. Guy, Brian Mulloney, Qinghai Zhang, and Timothy J. Lewis. Proceedings of the National Academy of Sciences of the U.S., published ahead of print September 8, 2014.

--- Lisa DeKeukelaere

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Using Math and Google to Study Disease and More, by Ben Pittman-Polletta

Resisting the Spread of Disease

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.

See "A safer world through disease mathematics," by Ben Althouse, Santa Fe New Mexican, September 8, 2014. Hear a podcast interview with Mac Hyman about stopping the spread of disease.

--- Ben Pittman-Polletta (Posted 9/15/14)

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Going from math professor to university president, by Mike Breen

Edward Burger is the professor in question. A former math professor at Williams College and now the president of Southwestern University in Texas (but as a photo shows, not beneath helping students move in), Burger answers questions about being a president and the difference between his current and former jobs. When asked how he made the transition from professor to university president, he said: "Maybe some of our problems in education today stem from the fact that someone like me is considered an unconventional choice. Maybe academic institutions should be run by academics, the way they used to be."

See "A Professor in the President's Chair: Pushing for a 'Friendly Revolution'." People, The Chronicle of Higher Education, 5 September 2014, page A34.

--- Mike Breen

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On Vladimir and his new approach to verifying mathematical proofs, by Claudia Clark

Voevodsky

Can you imagine a time when using computer software to construct and verify your own, as well as other people's, proofs becomes the standard way to do mathematics? According to mathematician Vladimir Voevodsky, this is on the verge of happening. Writer Florian Meyer describes how Voevodsky "has developed an approach [to doing mathematics] that could... revolutionize mathematics and its foundations: He has been able to show in principle that homotopy theory, which deals with the deformation of geometric objects, expresses the same ideas as the theory of programming languages and mathematical logic, only in a different language." The result of his work means that mathematical proofs will be able to be "translated into a programming language for computer proof assistants much more easily than they can be today." (Image: HLFF/Kreutzer).

See Voevodsky present his ideas at the Heidelberg Laureate Forum, and read more about the theory Voevodsky is developing, known as homotopy type theory

See "A new foundation for mathematics," by Florian Meyer, R & D Magazine, 3 September 2014, and the original piece in ETH Zurich News.

-- Claudia Clark

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Math Explains How Your Old Water Bottle Made It All the Way to a Beach in India, by Anna Haensch

Garbage

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.) 

Ocean gyres 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)

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On a math teacher who's running for the U.S. Senate, by Mike Breen

Amanda Curtis is a math and science teacher in Montana who is also the Democratic nominee for the U.S. Senate. A member of the state legislature, which is a part-time job, Curtis got the nomination after the incumbent, John Walsh, pulled out following charges of plagiarism in his master's thesis. Did Curtis always like math? "No, I really struggled in high school. And the first college course I took was a remedial math course. [But at Montana Tech] a professor laid out the beautiful picture that is calculus, and all of a sudden I understood it. It just clicked for me."

See "Newsmakers: Three Q's." Science, 29 August 2014, page 987.

--- Mike Breen

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Math Bytes Shows Fun And Tasty New Ways To Teach Math, by Anna Haensch

Tim ChartierWhen 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.



M&M rendition of Obama

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)

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On bicycle sharing, by Lisa De Keukelaere

bikes

As bike sharing programs spring up in cities around the world, mathematicians are tackling the problem of how to ensure a steady supply of bikes in all stations in spite of user habits that tend to leave some stations empty and others full. Researchers from Vienna to New York are fine-tuning algorithms for efficiently guiding bike-moving trucks to "rebalance" stations by predicting empty and full stations based on the season, the day of the week, and the weather. A computer scientist in Vienna explains that his algorithm resembles those that package delivery services use, and provides updates throughout the day. Bike-transfer truck drivers are still working out the kinks of applying the theories in practice, however, in particular when the algorithm advises picking up less than a full load of bikes or unloading at a station difficult to reach under certain traffic conditions.

See "Wheels when you need them," by Chelsea Wald. Science, 22 August 2014, v. 375 issue 5199, pages 862-863.

--- Lisa DeKeukeleare

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A Famous Graph Makes an Appearance on a Very Small Stage, by Ben Pittman-Polletta

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.

Welcome back. I hope you didn't spend a long time trying to draw those cables and pipes, because connecting the three houses to the three utilities without having a gas line cross a water pipe turns out to be impossible. Viewing the three houses and the three utilities as vertices of a graph, the connections between them form a complete bipartite graph, also known as the utility graph or K3,3. K3,3 is non-planar - that is, there is no embedding of this graph in a two-dimensional space of genus zero ("Why the Complete Bipartite Graph K3,3 is Not Planar", by Rod Hilton from his blog Absolutely No Machete Juggling, 29 October 2011), although it can be embedded in a torus. Not only is K3,3 nonplanar, it is in some sense one of only two nonplanar graphs. According to Kuratowski's theorem, a graph is nonplanar if and only if it contains a subgraph homeomorphic to either K3,3 or K5, the complete graph on 5 vertices.

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.)

Polymer graphsFinally, 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)

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Math Digest Archives || 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.