# Math Digest

## On Media Coverage of Math

Edited by Mike Breen and Annette Emerson, AMS Public Awareness Officers
Contributors:
Mike Breen (AMS), Claudia Clark (freelance science writer), Lisa DeKeukelaere (2004 AMS Media Fellow), Annette Emerson (AMS), Anna Haensch (Drexel University), and Allyn Jackson (Deputy Editor, Notices of the AMS)

### January 2015

On the NSA and the math community, by Allyn Jackson

An article in Science (reference below) discusses reactions in the mathematical community to the revelations, made by Edward Snowden, of the extensive intelligence activities of the National Security Agency (NSA). As the article describes, the NSA has close ties to the mathematical community: For example, the agency is probably the world's largest employer of mathematicians, it runs a small research grants program, and it has designated 55 U.S. educational institutions as "Centers of Academic Excellence," where, the article says, "a full-time NSA 'representative' is embedded on campus." After the 9/11 terrorist attacks, some mathematicians who had previously had nothing to do with the NSA decided to lend their expertise to the agency out of a sense of duty to their country to prevent future attacks. "Lately, however, that sense of moral clarity has clouded for some mathematicians," the article says. One particular point of discomfort for some is the ties between the AMS and the NSA: The AMS manages the refereeing of proposals in the NSA's mathematics research grants program. Some, such as University of Chicago mathematician Alexander Beilinson, have called on the AMS to sever ties to the NSA. Another voice calling for such action was that of MIT's David Vogan, who served as AMS president during 2013-2014 and who tried to urge the AMS to take a stand against the NSA. Vogan was shocked to find that his urging fell on deaf ears. Evidently, most mathematicians are simply not that worried about what the NSA is doing. The Science article appeared in German translation in the Sueddeutsche Zeitung: "Vertrauensbruch," 2 February 2015.

Ulrich Tottenberg is a mathematician at the Fraunhofer-Institut für Algorithmen und Wissenschaftliches Rechnen in Cologne. In his article in the Sueddeutsche Zeitung, he recalls the sense of personal responsibility some physicists felt when the atom bombs were dropped during World War II and asks whether mathematicians bear some responsibility for the massive spying apparatus that is now trained on humanity.

See "Breach of Trust," by John Bohannon. Science, 30 January 2015; and "Gute Zahlen, Schlechte Zahlen (Good numbers, bad numbers)," by Ulrich Tottenberg. Sueddeutsche Zeitung, 15 January 2015.

The AMS Notices has hosted a discussion of the Snowden revelations:

--- Allyn Jackson

On hyperbolic crocheting in the classroom, by Lisa DeKeukelaere

Chalk. Pencil. Crochet needle? McDaniel College math professor Ben Steinhurst helps his students visualize hyperbolic geometry by crocheting doily-like spirals (see examples below). Unlike the classic, five-axiom Euclidean geometry that forms the basis of most primary math education, hyperbolic geometry addresses a world closer to reality, where it’s impossible to draw a perfectly straight line to infinity. Steinhurst’s class teaches not only how to maneuver a crochet hook, but also the evolution of geometric axioms--the different types of “lenses” mathematicians use to view the world. Although a Russian mathematician, Nikolai Lobachevsky, first conceptualized hyperbolic geometry in the 1800s, mathematicians didn’t know how to illustrate it until the late 1990s, when Diana Taimina, a Cornell professor with a crochet hobby, discovered that she could build a replica in yarn using a certain hyperbolic algorithm. Steinhurst’s students appreciate their creations not only as learning tools, but also as a pleasant escape from typical classroom activities. Photos: McDaniel College.

See "Arts, crafts and high-end math," by Jonathan Pitts. The Baltimore Sun, 30 January 2015.

--- Lisa DeKeukelaere

Drones for good, by Annette Emerson

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

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

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. Post-auction update: The notebook fetched a little over a million from an unidentified buyer at the auction at Bonhams in New York. See "Turing's '$1m' notebook goes to auction," by Barney Thompson. Financial Times, 19 January 2015.

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

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

The Harriss Spiral, by Claudia Clark

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

The Importance of Failure, by Lisa DeKeukelaere

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

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; "Monumental proof to torment mathematicians for years to come," by Davide Castelvecchi, Nature, 28, July, 2016

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

Developments in Origami, by Claudia Clark

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.)

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

On discovering Ramanujan, by Mike Breen

This is an acount of Srinivasa Ramanujan and the author's travels to Ramanujan's home town in India for the 125th anniversary of his birth. Schneider is the lead singer of The Apples in Stereo, but more aptly is a PhD student at Emory University working with Ken Ono who led the trip. This is a very in-depth and sometimes mystical look at Ramanujan and modern efforts to understand his work, especially the mock-theta functions. The article also includes an interesting account of Richard Askey's efforts to make good on a promise made by the Indian government to Ramanujan's widow to honor her husband with a sculpture and the impact that made on Ono and his father. (Left: Small version of the AMS poster celebrating Ramanujan's 125th birthday.)

See "Encounter with the infinite," by Robert Schneider with Benjamin Phelan. The Believer, January-February 2015.

--- Mike Breen

From rubber sheets to happy apps, Discover tunes in to the top math stories of 2014, by Anna Haensch

The January-February 2015 issue of Discover Magazine features the top 100 science stories of 2014. Included among them are 5 stories about boundary-breaking mathematics and mathematicians that have taken center stage this year.

One such boundary breaker was Maryam Mirzakhani, who became the first woman to win the Fields Medal at this year’s ICM (International Congress of Mathematicians, held in Seoul) . Her work is in geometry and hyperbolic surfaces and Etienne Ghys of the Fields Medal committee describes it as "amazing formidable work." Her life and work were beautifully described by Quanta Magazine.

Breaking through a layer of mold, a team of researchers found a set of ancient bamboo strips which appear to be the world’s oldest calculator. The set belongs to a larger collection of 2,500 strips which are marked with numbers 1/2 to 90 and could have been used just like multiplications tables.

At Brown, a team came up with a mathematical formula to describe how rubber surfaces fold. Their equation can predict precisely how a material will fold given its composition and stiffness, and how much pressure will be need to flatten it out. Obviously this is a breakthrough for materials engineers, but people in the medical field can also use this to analyze what happens to the skull in a traumatic head injury. The original article appeared in the Proceedings of the Royal Society.

Another captivating story came out of the University College London, where researchers discovered that the key to happiness is lowered expectations. In small experiments conducted in the lab, and larger ones conducted using a smart phone app, they found that people’s happiness was highest when they just got more than they expected. The original article appeared in PNAS (Proceedings of the National Academy of Sciences of the United States of America).

A final story is on number theorist Ken Ono and his collaborators, who made a key discovery about the beautiful and captivating Rogers-Ramanujan identities last summer. According to Ono, he and his collaborators Michael Griffin and Ole Warnaar were studying these identities, and "found a framework that shows why they’re true.…They turned out to be two golden nuggets that suggested the existence of a whole mother lode of identities out there."

To pick the top story of the year, Discover is asking readers to vote and the story about the Rogers-Ramanujan identities has made the Final Four. Go here to cast your vote in the semifinals (by December 17), because wouldn’t it be cool if the number one science story of the year was about math!