Blog on Math Blogs

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), and Allyn Jackson (Deputy Editor, Notices of the AMS)


Miura-ori

Movie of folding, of Miura-ori , licensed under the Creative Commons Attribution-Share Alike 3.0 Unported. (Read about Developments in Origami.)

"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 post: "A Different Perspective: Mathochism and the Calculus Diaries" and "Return of the Statistics Blogs" by Evelyn Lamb.

The math of deploying snowplows and salt trucks, by Annette Emerson

Boston streets

"Clearing all that snow as quickly and cheaply as possible requires choosing the most efficient routes, one with no back-tracking or scenic routes. And how do you do that?" Math, writes Marcus Woo in Wired. Math that's also used to most efficiently deliver mail and pick up trash for city residents. In the 18th century mathematician Leonhard Euler proved that one could find a route across all the bridges connecting islands in Königsberg just once without doubling back, but his solution required that every intersection consist of an even number of roads. That sure doesn't apply to Boston, where many roads end in a "T" or suddenly turn one-way. So how to most efficiently plow the over 100" of snow in the city? "In 1962, Chinese mathematician Mei-Ko Kwan introduced the problem in the general case with both even and odd intersections. He called it the postman problem, and proposed a solution." But there are further complications: priority is given to major arteries, there are multiple snowplows and salt trucks at work, and, cities want to avoid having to pay overtime wages to the drivers. "But you don't need the perfect solution—just one that gets the job done," concludes Woo. "So engineers can break the problem down, for example, by dividing a network of streets into smaller networks that they can tackle individually (using the postman algorithm, for example)."  The city of Toronto uses ArcGIS software that incorporates all the variables and "automatically spits out an optimized route," which has saved some money. The Boston Mayor's Office of New Urban Mechanics is using math, algorithms and software to find the best way to clear the streets of this season's record-breaking snow—with inconsistent success.

Snowy sidewalk

See "The Mathematics Behind Getting All That Damned Snow Off Your Street," by Marcus Woo. Wired, 23 February 2015.

Now if only there were a mathematical solution to getting sidewalks cleared; the solution will most likely be spring.

--- Annette Emerson (Posted 2/25/15)


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Drones for good, by Annette Emerson

African elephant

Poachers in Africa killed 1,215 rhinos and 30,000 elephants last year, and that makes for an "unsustainable situation." A team at the University of Maryland's Institute for Advanced Computer Studies is now using "analytical models of how animals, poachers and rangers simultaneously move through space and time by combining high resolution satellite imagery with loads of big data--everything from moon phases, to weather, to previous poaching locations, to info from rhinos' satellite ankle trackers--and then applying our own algorithms." The aim is to better place rangers to thwart the poachers. The author, one of the researchers, states that "the real game changer is our use of unmanned aerial vehicles (UAVs) or drones." But of course Africa is too large to launch drones randomly, so that's where big data and analytical models are informing the rangers and gaining success in arresting poachers of these magnificent animals.

See "Satellites, mathematics and drones take down poachers in Africa," by Thomas Snitch, The Conversation, 27 January 2015.

--- Annette Emerson

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A Math Proof is a Journey, by Annette Emerson

"A proof is like the mathematician's travelogue. Fermat gazed out of the mathematical window and spotted this mathematical peak in the distance: the statement that his equations do not have whole-number solutions. The challenge for subsequent generations of mathematicians was to find a pathway leading from the familiar territory that the mathematician has already navigated to this foreign new land. [It's] a bit like Frodo's adventures in Lord of the Rings," explained Marcus du Sautoy in a talk at Oxford University that writer Charlie Jane Anders attended and covered for io9. She notes that a proof is like a journey, "from the familiar to the new," and points to the archived video of the talk plus the Q&A session after it.

See "How Is A Mathematical Proof Like Frodo's Journey In Lord Of The Rings?," by Charlie Jane Anders, io9, 21 January 2015.

--- Annette Emerson

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On an auction of a Turing notebook, by Mike Breen

A notebook of Alan Turing's that hadn't been seen in public until recently will go up for auction in April. Turing made the notes, which foreshadow some of his later foundational work on computing and logic, while working to break the Enigma Code. Andrew Hodges, author of Alan Turing: The Enigma, says that "This notebook shines light on how, even when he was enmeshed in great world events, he remained committed to freethinking work on pure mathematics." Turing left the notebook to his close friend Robin Gandy, who added his own personal notes to the notebook and kept it until his death in 1995. Perhaps because of interest in Turing generated by The Imitation Game, the notebook is expected to sell for over US$1 million.

See "Turing's '$1m' notebook goes to auction," by Barney Thompson. Financial Times, 19 January 2015.

--- Mike Breen (posted 1/23/15)

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CCTV covers Zong's Conant Prize given at the 2015 Joint Mathematics Meetings, by Lisa DeKeukelaere

At the 2015 Joint Mathematics Meetings in San Antonio, Texas, Peking University professor Chuanming Zong made history as the first China-based professor to win an AMS award. This CCTV video clip features interviews with Dr. Zong about his work on how to fill space effectively with objects like tetrahedra, a problem that dates back 2300 years to the time of Aristotle. Zong and his research partner, Jeffrey Lagarias from the University of Michigan, won the 2015 Levi L. Conant award for their work expounding upon the history and ideas behind this problem (see the news release). The video also features AMS President David Vogan, who heralds Zong and Lagarias' work for its accessibility, particularly in an era when new mathematics research is often comprehensible to only a very small group of people. Zong concedes that finding the answer to Aristotle's question may still take centuries, but he is grateful for the support he has received for his efforts.

See "China's PKU professor wins American mathematics award,"CCTV, 15 January 2015 (video viewable using Internet Explorer browser), and "China's PKU professor wins American mathematics award," by Li Yan, ecns.cn, 15 January 2015.

--- Lisa DeKeukelaere

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The Harriss Spiral, by Claudia Clark

Harriss Spiral

In this article, we learn about the discovery of a new curve by artist and mathematician Edmund Harriss. Harriss constructed his curve using a technique similar to the one used to create the "golden spiral," a curve drawn through, increasingly smaller squares in a rectangle that has been subdivided into a smaller similar square and a smaller rectangle, which is then subdivided in the same way, and so forth. Instead, Harriss used a rectangle that could be subdivided into a square and two smaller similar rectangles, each of which could be subdivided in the same way, ad infinitum. The "main" spiral is formed by drawing quarter circles from corner to adjacent corner of some of the squares in the rectangle. Other spirals branch out from this spiral in a fractal pattern.

Harriss was delighted to discover this spiral because it is both aesthetically pleasing and based on a very simple mathematical process. At the same time, he was motivated by the desire to draw attention to what he calls 'proportion systems': "rectangles that can be subdivided into only squares and similar rectangles." The golden spiral and the Harriss spiral are formed from just two of many such rectangles, each of which, in fact, have a ratio between their sides equal to an algebraic number! Harriss is currently trying to prove that "every algebraic number is the ratio of a rectangle belonging to a proportion system."

To see how the Harriss spiral is created, and read more about proportion systems, go to "The golden ratio has spawned a beautiful new curve: the Harriss spiral," by Alex Bellos. The Guardian, 13 January 2015.

--- Claudia Clark

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The Importance of Failure, by Lisa DeKeukelaere

Ed Burger

Southwestern University President and mathematics professor Ed Burger talks to radio host Jennifer Stayton about why "effective failure"—learning from one's mistakes—is critical to becoming better thinkers. Burger opines that thinking and education should be focused on the outcome of being better thinkers, and that failing is a requisite step to achieving that outcome, because "there's no greater teacher than one's own mistakes." As an example, he notes that the first draft of a piece of writing is always a failure, and even Shakespeare had first draft "failures" as intermediate steps to creating his masterpieces. Burger notes that in his own classroom, he does not shy away from highlighting students' mistakes, nor does he ascribe to the "everyone gets a trophy" philosophy. Instead, he seeks to create an environment where students intentionally take risks and make mistakes in their thinking, so that he can use the exploration of why a student is wrong to empower the student as the teacher, and so that the student can learn enough from her setbacks to truly earn that trophy.

See "Higher Ed: The Importance of Failure to Learning," an interview with Ed Burger by Jennifer Stayton. KUT.org, 11 January 2015.

--- Lisa DeKeukelaere

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On attempts to verify a proof of the ABC Conjecture, by Allyn Jackson

Shinichi Mochizuki is a mathematician at the Research Institute of Mathematical Sciences in Kyoto (Japan). In 2012, he made headlines around the world when he posted a 500-page paper claiming a proof of the so-called ABC Conjecture, one of the central questions in modern number theory. Mochizuki is a well known and highly respected mathematician, so his claim to a proof has been taken very seriously by the mathematical community. However, because his paper has proven very difficult for others to understand, his proof has not been accepted as correct. The New Scientist article discusses a report that Mochizuki has posted on his web site, in which he describes the current status of attempts to verify his proof. "[Mochizuki] says that three researchers who studied it with his help have yet to find an error, but it will take a few more years for it to be fully confirmed," the New Scientist reports. According to Minhyong Kim, a mathematician at the University of Oxford who is quoted by the New Scientist, the proof needs to be presented in a form understandable to those who have not studied with Mochizuki. Kim said: "I sympathize with his sense of frustration but I also sympathize with other people who don't understand why he's not doing things in a more standard way."

See "Mathematician's anger over his unread 500-page proof," by Jacob Aron. New Scientist, 07 January 2015.

--- Allyn Jackson (Posted 1/15/15)

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Developments in Origami, by Claudia Clark

Valley fold diagram by Thomas Hull

The ancient art of origami has been "going through a renaissance over the past thirty years," notes Thomas Hull, a professor of mathematics at Western New England University. "New designs [are] being created at ever-increasing levels of complexity." In this article, Hull describes a little of what we have been learning about the mathematical rules that govern paper folding. "At heart, mathematics is about understanding the rules and patterns of the universe... In the case of origami, we need to look at the geometry of the crease pattern, where the lines intersect, what angles they form, and in what directions the creases fold." One such rule of origami models that fold flat is called Maekawa's Theorem: "at every vertex where creases intersect in a flat origami crease pattern, the difference between the number of mountain and valley creases is always two." (Image above: Valley fold, by Thomas Hull.)

Miura-ori

Movie of folding, of Miura-ori, licensed under the Creative Commons Attribution-Share Alike 3.0 Unported.

Hull also describes a few of the applications that have resulted from developments in origami design. One such design is the Miura map fold or Miura-ori, an origami tessellation, used by Dr. Miura "as a way to deploy large solar panels into outer space." Dr. Hull is working with a team of researchers that is studying the Miura map as a mechanical device. Another application is the development of self-folding materials, including extremely thin sheets of gel that could be used to deliver toxic cancer drugs directly to tumors.

See "Origami: mathematics in creasing," by Thomas Hull. The Conversation, 6 January 2015.

--- Claudia Clark

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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.