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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 Evelyn Lamb and Brie Finegold, 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: "Highly Unlikely Triangles and Other Beaded Mathematics" and "Blogging in Math History Class."
This article discusses The Imitation Game, a film about the legendary mathematician Alan Turing which came out in theaters in the UK this week. The subject of this article is Joan Clarke, a cryptanalyst who worked alongside Turing at Bletchley Park during World War II, who is a character in the film (which stars Benedict Cumberbatch as Turing and Keira Knightley as Clarke). Clarke was a close friend of Turing's and briefly his fiancée. He broke off the engagement, telling Clarke that he had homosexual tendencies. Despite her clear skills and talents, Clarke was paid less and received less recognition than the male cryptanalysts she worked with at Bletchley. She had been an outstanding student at Cambridge, earning a "double first" in mathematics in 1939, though not a full degree; women could not earn full degrees at Cambridge until 1948. Kerry Howard, who researched the role of women at Bletchley Park, is quoted in the article as saying: "Up until now the main focus has been on the male professors who dominated the top level at Bletchley." In order to find any information on the women involved, she said, you have "to dig much deeper."
See "Joan Clarke, woman who cracked Enigma with Alan Turing," by Joe Miller. BBC, 10 November 2014.
--- Allyn Jackson
The Imitation Game is a new biopic about scientist and mathematician Alan Turing's life and work. With the recent premiere (see coverage of the premiere by Roger Friedman on his blog Showbiz 411) and a cover story in Time magazine, there's no shortage of media coverage on the film, but Dan Rockmore's review in The New Yorker is a welcome deeper look into the intellectual life of the film's protagonist. Turing is most famous for his work in computer science and artifical intelligence, exemplified by the eponymous concepts of the Turing machine and the Turing test. Turing was also a homosexual, and his conviction for "gross indecency" and the subsequent sentence of chemical castration led to his suicide 16 days before his 42nd birthday. These facts provide the "narrative hooks" for the new movie, which, according to Rockmore, focuses on Turing's work cracking the Enigma code during World War II. But Turing was also a pioneer in logic, number theory, and mathematical biology, modeling the brain and development. Rockmore, chair of the Department of Mathematics and professor of computer science at Dartmouth College, uses his review of The Imitation Game as an opportunity to highlight one of Turing's most prescient and impressive intellectual works--his essay "Intelligent Machinery." In this paper, Turing sets down his ideas about how a thinking machine might be built. He puts forward a simple model of a network of neurons, and ideas for how it might be educated from "experience"--and especially from rewarding and aversive stimuli--which are foundational to the influential connectionist paradigm in mind and brain research ("Connectionism," Wikipedia).
This paper, as well as others collected in editor B. Jack Copeland's The Essential Turing (reviewed by Andrew Hodges in the AMS Notices), such as "The Chemical Basis of Morphogenesis," illuminate critical issues in science with a clarity rarely seen in today's literature. For instance, in "Intelligent Machinery, a Heretical Idea," Turing describes how "indexes" might be used to organize information in memory. "New forms of index," he suggests, "might be introduced on account of special features observed in the indexes already used." Here and elsewhere, Turing exemplifies his own rationale for modeling human thought. "The whole thinking process is still rather mysterious to us," he says in "Can Machines Think?", "but I believe that the attempt to make a thinking machine will help us greatly in finding out how we think ourselves." Revisiting Turing's work reminds us how much we have to learn from history--how not only the emotional, but also the intellectual struggles of our forebears, mirror and inform our own. Indeed, this is an idea Turing himself discusses in "Intelligent Machinery." At the end of the essay, he proposes that essentially all problems are search problems, and discusses both evolutionary and intellectual searches in this light. "The remaining form of search is what I should like to call the 'cultural search'," he writes, "... the isolated man does not develop any intellectual power ... the search for new techniques must be carried out by the human community as a whole."
See "What's Missing From 'The Imitation Game'" by Dan Rockmore. The New Yorker, 6 November 2014.
--- Ben Pittman-Polletta (posted 11/20/14)
These are exactly the terms in the harmonic series. Doolittle and her team were surprised to find that the songs of Hermit Thrush contain this same harmonic series.
What is interesting about this, is that tones in the harmonic series, although so familiar to our human ears, are not really a human aesthetic construct. It's just math! So while the results from Doolittle and her lab are surprising, they don't suggest that birds have some understanding of music theory. But as Doolittle points out to The Smithsonian, "If an aspect of music is found not only in humans, but also in a variety of non-human species, this would suggest that there may be something in our shared biology that predisposes us to find that aspect interesting, or attractive, or easy to sing."
See "This Bird's Songs Share the Same Mathematical Qualities as Human Music," by Allison Eck, NOVA, 4 November 2014.
--- Anna Haensch (Posted 11/21/14)
In this article, Toby Walsh, Research Group Leader in the Optimization Research Group at NICTA, a research center in Australia, explains why the wildly popular game, Candy Crush, belongs to the class of NP problems. Walsh begins by introducing the reader to the different classes of problems, as well as the question of whether P = NP. Then, noting that the problem of finding a solution to a logical formula belongs to the class NP, Walsh shows how a logic puzzle can be reduced to a Candy Crush problem by "building" an electric circuit in a Candy Crush game, with candies representing wires, switches, and logic gates. "Expressed in terms of these electrical logic circuits," Walsh writes, "the puzzle in playing Candy Crush is deciding which switches to set so that the logic gates fire appropriately and the output bit is set to true." Walsh then describes how to do the reverse, i.e., reducing a Candy Crush game to satisfying a logical formula.
See "Candy Crush's Puzzling Mathematics," by Toby Walsh. American Scientist, November-December 2014, pages 430-433.
--- Claudia Clark
Rarely does mathematics inspire laughter, and it would seem downright impossible to find a mathematician who could sell out a 3,500 seat comedy show. Meet Matt Parker, a most unusual mathematician. Parker, who grew up in Australia, says he "never got the memo about maths being boring." Since he was a kid, Parker has always been fascinated by math, and now as an adult it’s his mission to spread that fascination around. And as The Independent explains in its recent article, Parker has found a most unconventional way to spread his good news--through stand-up comedy!
Parker maintains a Youtube channel full of videos of his stand-up and various other mathematical entertainment, along with other not so mathy things, like how to make ice cream using a fire extinguisher. In addition to his own channel, he is also a frequent contributor to the very popular Numberphile, where he gives his totally watchable take on some of our most pressing math questions, like why the heck can’t we divide by 0?
His most recent effort at connecting people to math is his new book, Things to Make and Do in the Fourth Dimension, full of games, puzzles, and explanations of all the exciting parts of math that we may have missed in school. Parker laments the fact that math is "the one thing you’re still allowed to be proud of being bad at…people are almost proud of being ignorant of this huge achievement of humankind." Parker is out to change that, and he sees that now is the time. "There has been a huge resurgence of maths as entertainment," Parker says, which we can see playing out all over social media. For Parker’s latest, follow him on Twitter @standupmaths.
See "'Stand-up mathematician' Matt Parker is using comedy nights to preach maths to big audiences," by Simon Usborne. The Independent, 30 October 2014.
--- Anna Haensch (Posted 11/10/14)
This piece presents a brief interview with Benedikt Wirth, a mathematician at the Universität Münster who is the 2014 recipient of the Alfried Krupp Sponsorship Award for young researchers. The award comes with 1 million euros. Asked why mathematics is perceived as "so unsexy," Wirth laughs and says "For us mathematicians, mathematics is certainly very sexy---the sexiest science around!" The final question in the interview asks Wirth about his mathematical work, which centers on questions of form and structure in medicine, biology, and engineering.
See "Math is the sexiest science around," by Valentin Betz. DW, 30 October 2014.
--- Allyn Jackson
The Chronicle of Higher Education published a special report on black men in science, technology, engineering, and mathematics (STEM). In an article about four black men in STEM, two are in the mathematical sciences. Read the inspiring stories of Karl Walker, assistant professor of math and computer science, University of Arkansas at Pine Bluff, and Ryan Charles Hynd, assistant professor of mathematics, University of Pennsylvania.
--- Allyn Jackson
And now a free app that allows people to aim their smart phones at a math problem and not only will the app give them the answer, but also it will show the steps to arrive at that answer! The company that created the app, MicroBlink, claims that its goal is not to allow students to "cheat," but rather to help students who don't have access to tutors or can't get individualized instruction. The app was written about by many and performed pretty well in a promotional video but, at least according to the review "Can you really rely on an app to do your maths homework?", point-and-solve technology hasn't arrived quite yet.
See "This app will help kids cheat on math tests," by Sonali Kohli. Quartz, 21 October 2014.
--- Mike Breen
Photos (left to right) National Museum of Mathematics Co-Executive Director Glen Whitney explains an exhibit to trustee Art Steinmetz; event organizers Whitney, Co-Executive Director Cindy Lawrence, and Chief of Design Tim Nissen; Steven Strogatz (L) and Alan Alda (R) discuss the butterfly effect; courtesy of the National Museum of Mathematics.
Quantitative hedge fund owners may be notoriously secretive about strategy and earnings, but the high-powered, high-earning brains recently came together for a lavish--and, according to this article's title, geeky--affair: the Chaos Ball, to support the National Museum of Mathematics (MoMath) in Manhattan. Ball guests had the opportunity to create a fractal made of lights attached to a blackboard, play with 3-D printed geometric trinkets, and be mesmerized by metronomes and square-wheeled tricycles. Where other charity balls include performances by rock stars, the Chaos Ball had actor Alan Alda talking about chaos theory with mathematician Steven Strogatz. Where other balls have pop-culture celebrities, the Chaos Ball had a string theorist from Columbia University and the CEO of Wolfram Research. The Ball raised $830,000 for MoMath.
See "Billionaires and Mathematicians Crack Jokes at the Geekiest Event of the Season," by Bradley Hope. The Wall Street Journal, 19 October 2014.
--- Lisa DeKeukelaere
"If you are planning to post a present this Christmas, it is advisable to be good at maths, or at least go shopping with a tape measure and a pair of weighing scales," this article says. The Royal Mail has changed its prices for various types of parcels depending on their dimensions and weight. A 16-page booklet was needed to explain the changes. In Britain one can also send mail through private carriers, but their price configurations can be just as complicated. Adding to the confusion, some carriers specify volume instead of dimensions. One, MyHermes, uses something called "volumetric area." Packages sent must be under 225cm of volumetric area. The article quotes a MyHermes spokesperson as saying: "To work out the volumetric area, if you add the two shortest dimensions of the parcel and multiply them by two, add the length, the total calculation needs to be under 225cm." Instead of taxing one's brain with such arcana, the article recommends using a web site that does calculations and price comparisons automatically.
See "Why you need to be a maths genius to post a parcel," by Brian Milligan. BBC Business News, 10 October 2014.
--- Allyn Jackson
What makes the sequence 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 1, 1,… so cool? In his blog for The Guardian, Alex Bellos explains that along with its crazy mathematical properties, it also has the distinction of being the second entry in the Online Encyclopedia of Integer Sequences (OEIS). From the beloved Fibonacci sequence, to the more obscure Kolakoski sequence, the OEIS is a database of hundreds of thousands of integer sequences. It's a tremendous technical tool for mathematics researchers, but also a cool resource for the casually number-curious.
The OIES was created by Neil Sloane (left) when he was a graduate student at Cornell University in the 1960s. He was working with one particularly obscure sequence of integers, and it occurred to him that it would be handy to have a record of every integer sequence in the world. It started as a stack of 3 x 5 index cards on his desk, after a few decades became a book with 5,000 sequences, and eventually in 1996 a website with 10,000 sequences. Since then, the website has started crowdsourcing à la Wikipedia, and it now gathers about 15,000 new sequences each year.
The OEIS was honored at a conference at the Center for Discrete Mathematics & Theoretical Computer Science (DIMACS) at Rutgers University recently, coinciding with the encyclopedia's 50th anniversary, and founder Neil Sloane's 75th birthday--a twofold celebration! Recently, the OEIS and the work of Sloane also got a nod in Wordplay, The New York Times's blog on crossword puzzles.
But wait, I still haven't told the mathematical properties that make that sequence so cool. You can see that 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 1, 1,… is kind of boring, just 1's and 2's, so the numbers themselves aren't all that remarkable. But notice that they always appear in runs of 1 or 2. So if we count the numbers of 1's and 2's and make a sequence out of that, we get 1,2,2,1,1,2,1,2,2,1,… --the original sequence! Pretty neat. There is only one other sequence that does this, and you get it by just removing the leading 1 from the sequence above.
See "Neil Sloane: the man who loved only integer sequences," by Alex Bello. Alex's Adventures in Numberland--The Guardian, 7 October 2014.
--- Anna Haensch (Posted 10/20/14)
In this article, writer Jessica Lahey describes her conversations with Cornell University mathematics professor Steve Strogatz about a course for liberal arts majors that he is teaching. For Strogatz, the key to turning around many of these students' typically negative attitudes toward mathematics is to change the way the subject is taught. To that end, he is using the DAoM curriculum--Discovering the Art of Mathematics: Mathematical Inquiry in the Liberal Arts--developed at Westfield State College by Dr. Julian Fleron and three colleagues. "The DAoM approach," explains Lahey, "is rooted in inquiry-based learning: It focuses on student-led investigations into problems, experiments, and prompts…[It] aims to intellectually stimulate students, to provide cognitive gains, and get students engaged with math rather than passively listening to a teacher." After the first week of class, Strogatz reported to Lahey that it was going well: he described how students "shouted him down" when he tried to give them a hint that would help them solve a puzzle they had already worked on for 30 minutes. "They were having a true mathematical moment," Strogatz said. "That is, they were deeply engaged with a puzzle that made sense to them, and they were enjoying the struggle…Over the weekend I started to get emails from some of them, expressing the excitement they felt when they solved it." (Photo courtesy of Steven Strogatz.)
Strogatz explains the class activity in the photo: This was taken during an activity using dance to make group theory--the math of symmetry--come alive. Specifically, the students are exploring what happens when you combine two transformations to make a third. In the activity shown here, the student on the far right strikes a pose. The student in the middle transforms that pose by (in this case) rotating it 180 degrees about a vertical axis. The student on the left then applies a different transformation (in this case, a mirror reflection in a vertical plane between the left and middle student).
The question they're exploring is: how is the pose of the student on the left related to that of the student on the right? More abstractly, what symmetric transformation do you get by combining a 180 degree rotation with a mirror reflection? As they discovered, the answer turns out to be a "glide reflection"--a reflection through a mirror plane down the midline of the left student's body, along with a translation (a glide) down the line they are all standing on. These kinds of investigations are described on pp.10-11 of the free book, Discovering the Art of Mathematics: Dance.
--- Claudia Clark
Demographers use a variety of means to study the structures of populations--human, animal, and otherwise--and their evolution through birth, death, migration, and aging. Like mathematicians in every discipline, mathematical demographers model their objects of study--in this case populations--and derive relationships that make the work of their experimental collaborators easier, or even feasible. Carey's equality is a relationship describing the age structure of a so-called stationary population, one in which birth and death rates are equal. In a stationary population, one could say the number of individuals of age zero is the same as the number of individuals whose remaining lifespan is zero. Carey's equality, remarkably, suggests that this is true for all ages: the number of individuals who will die in a given time span is the same as the number of individuals who have already lived exactly that long. This equality was first put forward by entomologist James Carey in 2004 while he was searching for a way to estimate the age distributions of wild populations of Mediterranean fruit flies. The existing techniques for estimating the ages of so-called medflies--such as examining captured individuals for mechanical, chemical, or genetic markers of aging--were proving woefully inadequate. Carey began investigating how the lifespan distribution of a captive population might be used to estimate the age structure of the corresponding wild population. A simple life table model suggested that the lifespan distribution was not just an estimate of the age distribution--it was identical. The result turned out to be true for continuous and nonstationary populations ("Demographic window to aging in the wild: constructing life tables and estimating survival functions from marked individuals of unknown age," by Hans-Georg Müller, Jane-Ling Wang, James R. Carey, Edward P. Caswell-Chen, Carl Chen, Nikos Papadopoulos and Fang Yao, Aging Cell, Volume 3, Issue 3, June 2004).
Carey's equality got its name and its (paragraph-long) proof in a 2009 paper by mathematical demographer James Vaupel ("Life lived and life left: Carey's inequality," by James Vaupel, Demographic Research, January 2009). Recently, a new proof--and a new insight--came to light, when Carey met mathematical modeler and applied mathematician Arni Rao at Ohio State University's Mathematical Biosciences Institute. As Carey described his result and illustrated it with several graphical examples, Rao saw another equality emerge before his eyes: for a stationary population of individuals captured at a random point in their lifespans, the distribution of pre-capture and post-capture lifespans would be identical. This, combined with the set theory Rao had already used to study how the aging dynamics of subpopulations contribute to stability within a population ("Population stability and momentum," Arni S.R. Srinivasa Rao, Notices of the AMS, October 2014), gave rise to a new proof of Carey's equality, to appear in the Journal of Mathematical Biology. "Understanding age structure in these insect populations is a huge deal worldwide," said Dr. Carey in a recent Science Codex post. "It's the older mosquitoes that vector the West Nile fever, malaria, yellow fever, and so forth."
(Image: When individuals from a population are captured at a random time during their lifespan (top, inset), the ordered distribution of the times they spend in captivity matches the distribution of their ages (top), as well as the ordered distribution of the times they spend out of captivity (bottom). Image courtesy James R Carey.)
See "New theorem determines the age distribution of populations from fruit flies to humans," Science Codex, 6 October 2014.
--- Ben Pittman-Polletta (posted 10/28/14)
Mathematician George Lusztig (left), an MIT professor who recently visited Hong Kong to receive the Shaw Prize for his work weaving together geometry and algebra, explains that he does math for the beauty of it, rather than for the prospect of real-world applications. He notes that understanding the beauty requires years of study, which is why many people never see it. Recalling that he spent hours each day solving math problems during his childhood in Romania, Lusztig says that doing math had the benefits of minimizing his exposure to politics and allowing him to be judged on his merits. He opines that success in mathematics requires a "good mind" and good luck, and he notes that he has a single-minded focus when trying to solve problems. The annual Shaw Prize honors recipients with $1 million for achievements in the categories of astronomy, medicine and life sciences, and mathematics.
See "When problems equate to happiness," by Raquel Carvalho. South China Morning Post, 30 September 2014. (Photo: Massachusetts Institute of Technology.)
--- Lisa DeKeukelaere
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