On Media Coverage of Math
Edited by Mike Breen and Annette Emerson, AMS Public Awareness Officers
The editorial, "Maths spying: The quandary of working for the spooks," discusses the extensive spying programs of the NSA and the GCHQ (Britain's intelligence and security oprganization), which have been revealed in documents made public by Edward Snowden. The NSA and GCHQ are major employers of mathematicians. In this New Scientist piece, University of Edinburgh mathematician Tom Leinster writes: "Mathematicians seldom face ethical questions. We enjoy the feeling that what we do is separate from the everyday world... That idea is now untenable. Mathematics clearly has practical applications that are highly relevant to the modern world, not least internet encryption." He poses the question of whether mathematicians should cooperate with the intelligence agencies. He ends his piece with the statement: "We are human beings first and mathematicians second, and if we do not like what the secret services are doing, we should not cooperate."
This piece appeared shortly after Leinster wrote an opinion column that appeared in the April 2014 issue of the London Mathematical Society Newsletter. Leinster's New Scientist piece was also syndicated in Slate on April 27, 2014.
See "Maths spying: The quandary of working for the spooks", by Tom Leinster. New Scientist, 23 April 2014.
Other articles on this subject have appeared in the popular press, including "The Perils of Hacking Math", by Edward Frenkel, Slate, 30 September 2013. The Notices of the AMS has published three pieces on the topic: Letter to the Editor, by Alexander Beilinson, December 2013; "Dear NSA: Long-Term Security Depends on Freedom,", by Stefan Forcey, January 2014; "The NSA Backdoor to NIST", by Thomas Hales, April 2014.
--- Allyn Jackson
The past few years Careercast has ranked "Mathematician" among the top jobs, based on work environment, job prospects, stress level, hiring outlook, and of course, salary. What they mean is "jobs that use math," or "jobs that employ individuals wtih a degree in the mathematical sciences," because there really aren't many job titles called "Mathematician." In academia, someone may be referred to as a "mathematician" -- but more likely "professor or associate or assistant professor" (of mathematics); in government, business, industry, medical fields, etc. there are many who use mathematical sciences in their jobs, but the job title is rarely "mathematician". What do mathematicians do? The CareerCast.com report (see also "Jobs Rated 2014: Ranking 200 Jobs From Best To Worst") doesn't detail how it defined or measured ideal "work environment" or "stress level" given all the possible positions in all sectors that employ individuals with undergraduate and graduate degrees in various fields of mathematical sciences. And is "University Professor (tenured)", ranked as #2 best job, included in the tally of "Mathematician" (ranked #1)?
The AMS's Mathematical Moments program presents over 100 ways mathematical sciences are applied in various fields -- in work related to aerospace, security, urban design, archaeology, medical research and applications, sports, film animation, weather and climate, and many more. (Many of these topics include podcast interviews with those explaining how they use mathematics.) Some of the researchers are in universities, while others whose job title is not "mathematician" work in business and industry. How did Careercast find them to be included in its data? In any case, "The Mathematical Sciences in 2025," notes in its preface that the mathematical sciences will continue to play key roles in -- and bridge -- basic research and applications in many areas of science and engineering:
"The vitality of the U.S. mathematical sciences enterprise is excellent. The discipline has consistently been making major advances in research, both in fundamental theory and in high-impact applications. The discipline is displaying great unity and coherence as bridges are increasingly built between subfields of research. Historically, such bridges have served as drivers for additional accomplishments, as have the many interactions between the mathematical sciences and fields of application. Both are very promising signs. The discipline's vitality is providing clear benefits to most areas of science and engineering and to the nation."
See some of the media coverage of the Careercast report: "The Best And Worst Jobs For 2014," Wisconsin Public Radio, 21 April 2014; "The best (and worst) jobs for 2014," by Cindy Perman, CNBC, USA Today, 19 April 2014; and video segment (accessible in certain browsers such as Internet Exporer) "Lumberjack vs. Mathematician" on CNBC, 21 April 2014.
The video of the CNBC tv spot has a twist at the end: the lumberjack (lowest-ranking job) asserts that his job entails math too. They use equipment that is developed and driven by computer science and individuals need to do a lot of calculations in the course of their tasks and for business purposes.
--- Annette Emerson
Maybe it was the title, "Pseudo-Mathematics and Financial Charlatanism: The Effects of Backtest Overfitting on Out-of-Sample Performance," that grabbed the attention of the Financial Times and Bloomberg News. FT's Stephen Foley writes that the authors of the article in May Notices of the AMS, David H. Bailey, Jonathan M. Borwein, Marcos López de Prado, and Qiji Jim Zhu, "make the case that the vast majority of claims being made for quantitative investment strategies are false," and "by calling it fraud, the academics command attention, and investors would be wise to beware." The Notices authors alert us that there are investment managers and advisors who don't use rigorous mathematics and "by tweaking the strategy until it neatly fits the historical data" those managers are "deliberately or negligently, misleading clients." But as Foley points out, the authors are positive about improving modeling and limiting risks. Marco Lopez de Prado offers open source software (quantresearch.info) and Bailey "suggests that a regulatory body such as Finra could step in to promote best practice in the marketing of mathematical claims."
Bloomberg's Kishan sums up the problems as 1) "Strategies that use computer models to predict future market moves are often based on selective historical data" and 2) according to the authors, "mathematicians in the 21st century have remained disappointingly silent with the regards to those in the investment community who, knowingly or not, misuse mathematical techniques such as probability theory, statistics and stochastic calculus. Our silence is consent, making us accomplices in these abuses."
See: "Ban pseudo-mathematics from investing," by Stephen Foley, Financial Times, April 16, 2014 (requires a subscription) and "Computer Models Often Use Unsound Math, Researchers Say," by Saijel Kishan, Bloomberg News, April 11, 2014. Also see "Is a Too-Perfect ETF Backtest Fraud?," by Brendan Conway, Barron's, 17 April 2014; a video "Interview with David Bailey," by Kathy Scott, Institutional Investor Journals (The Voices of Influence), 28 March 2014; and the financial-math blog by de Prado and Bailey.
--- Annette Emerson
Mathematician Skip Garibaldi studies the complicated odds of playing the lottery and shows that there is one surefire way to get rich from a lottery, by just operating your own Mega Millions jackpot--although he readily admits this is most likely illegal. Photo courtesy of Skip Garibaldi.
Digging through the records of the Florida state lottery, investigative reporter Lawrence Mower found one man in Florida had won over $700,000 in 252 lottery prizes over 6 years. A recent Phys.org article describes how a world-class mathematician helped Mower decide whether such a hefty stack of winnings over such a short time could be chalked up to unbelievably good luck or perhaps suggested foul play.
To figure out just how unlikely those odds of such an incredible winning streak would be, Mower turned to Skip Garibaldi, professor at Emory University, associate director of UCLA's Institute for Pure and Applied Mathematics, and co-author of an award-winning paper on the mathematics of playing the lottery.
Given the minuscule odds of winning any lottery prize at all, Garibaldi calculated that our lucky winner would have had to invest a minimum of $2.07 million to have even a one-in-20-trillion chance of winning 252 games and $719,051 over 6 years. His conclusion: random luck was not the only hand at play.
Garibaldi's analysis resulted in a series of police raids to remove lottery machines from suspect convenience stores, as well as an outcry from the state legislature calling for stricter lottery enforcement.
Follow Garibaldi on Twitter @skipgaribaldi.
See "'Math detective' analyzes odds for suspicious lottery wins," by Carol Clark. Phys.org, 15 April 2014.
I first got a glimpse of how complicated cancer is in high school biology, when I learned the tautological definition of an oncogene, or "cancer gene". An oncogene is any gene in which a mutation can cause cancer. Because cancer results from uncontrolled cell growth, any gene related to the process of cell division is a potential oncogene. This means there are a staggering number of oncogenes, and that every cancer is different. This is why targeted approaches--which aim to use genetic information about individual tumors to match them with drugs attacking their precise genetic features--are all the rage. In 2012, two labs in the Boston area made big news by compiling databases on the genetics of lab-grown tumor cell lines and their sensitivity to a variety of anticancer drugs ("Cancer screen yields drug clues," by Heidi Ledford, Nature News, 28 March). Promisingly, both groups suggested a new class of drugs--so-called PARP inhibitors--to treat Ewing's sarcoma, a rare bone tumor that affects mostly children and young adults.
But there are serious problems with these efforts, which go beyond the considerable methodological difficulty of defining consistently what it means for a given drug to be effective at killing a lab grown cell line ("Personalized cancer treatments suffer setback," by Erika Check Hayden, Nature News, 27 November 2013). Such library building efforts are reminiscent of the Human Genome Project, which everyone was confident would unlock the keys to human disease, until it didn't ("The failure of the genome," by Jonathan Latham, The Guardian,17 April 2011).
Perhaps the biggest discovery to come out of the HGP is how little (traditional, Epigenetics) genetics really contributes to human biology. This is why Robert Gatenby, founder of the Integrated Mathematical Oncology (IMO) group at Tampa's Moffitt Cancer Center, isn't interested in genes. Not only is every cancer different, he points out, but every cell in every cancer is different. A cancer is not a homogeneous blob, composed of a single cell type turned rogue by a single mutation. Rather, a cancer is a population of cells, which are good not only at rapid growth and division, but also--exactly because they divide and grow rapidly--at evolution. In the best-case scenario, this means gene-targeted drugs may be effective for only a limited time. In the worst-case scenario, gene-targeted therapies may sculpt a tumor's population in unforseen ways, turning a benign mix of cells into a dangerous army of drug-resistant warriors. So many patients go through multiple rounds of treatments, in which promising initial results eventually give way to cancer's return. Gatenby's team, which consists of a handful of mathematicians with little medical or biological experience, is pushing the radical idea that perhaps the best solution to cancer is a stalemate--a combination of treatments designed not to kill the cancer, but to keep its host alive, by prodding the tumor to evolve into a less volatile form. The mathematicians of the IMO use a mixture of evolutionary theory, game theory, and dynamical systems to understand each cancer as its own microscopic ecosystem, or weather system (see previous coverage of "Medical Math: Mathematicians doing cancer research," by Amy Keller, Florida Trend, 6 May 2013). "What we’d love to do," says Gatenby, "is have everybody’s own little hurricane model for their cancer." Of course, this puts the researchers at odds with many of their medical colleagues, and the "vast industry that's developed over molecular data". But opposition is a position their iconoclastic leader is comfortable in. Says Gatenby, "I never met a dogma I didn't hate."
See "The cancer equation: Mathematically modelling the cure," by Alex Nazaryan, The Independent, April 8 2014.
--- Ben Polletta
In this interview, Colbert interviews University of California, Berkeley mathematics professor Edward Frenkel, whose new book, Love and Math, The Heart of Hidden Reality, was published last October. Not surprisingly, Colbert begins the interview by admitting that he hated math. In good-natured fashion, Frenkel points out the fact that it has become quite acceptable for people in the United States to make this claim, as opposed to making a similar claim about art or reading. Frenkel thinks that when people say "I hate math," it's not their fault: they are really saying that they don't like math because of the way it was taught to them. For example, if students had an art class in which they only learned how to paint fences, and never saw the works of the great masters, they might say later on that they hate art because they were bad at painting fences. When Colbert asks if it isn’t necessary to "grow the math eyeballs to see the equations as beautiful," Frenkel says that that is the mathematician's job, and he gives a humorous example, told to him by one of his teachers, of the importance of presenting mathematical ideas so that the student gets it. (Photo: Frenkel giving an Invited Address at the 2012 Joint Mathematics Meetings. Photo by E. David Luria.)
See: "The Colbert Report, interview with Ed Frenkel by Stephen Colbert. Comedy Central, 7 April 2014.
--- Claudia Clark
As attention and expectations grow for making great leaps in our understanding of the world by examining "big data," NYU psychology professor Gary Marcus details nine reasons big data isn't the panacea it seems to be. Marcus notes that although powerful computational capabilities and widespread availability of large data sets allow for easier identification of correlations, many such correlations are meaningless, and big data is a tool—rather than a substitution—for the scientific conclusions human researchers draw. Marcus highlights that analysis of big data can be gamed, for example by websites that engineer themselves to rank highly on a Google search, or simply turn out to be less accurate than initially assessed. He also notes that analysis of big data may provide seemingly precise answers to imprecise questions, and may overshadow—by virtue of its hype—more significant scientific achievements human researchers have made.
See: "Eight (No, Nine!) Problems With Big Data," by Gary Marcus and Ernest Davis, New York Times Op-Ed, 6 April 2014, and "The Parable of Google Flu: Traps in Big Data Analysis," by David Lazer, Ryan Kennedy, Gary King, and Alessandro Vespignani, published in Science, 14 March 2014.
--- Lisa DeKeukelaere
April was Mathematics Awareness Month. For the University of Kansas in Lawrence, Kansas, several members of the mathematics faculty began the month with a trip to Lawrence City Hall where this is announced, followed throughout the month by math competitions and workshops for students of various ages, an awards ceremony, a banquet, and an undergraduate mathematics colloquium. For this article, local reporter Chad Lawhorn spoke with several KU mathematics professors, including Bozenna Pasik-Duncan (pictured at left) and Margaret Bayer, who shared some of their thoughts about the beauty of mathematics and ways to get people in general (and students in particular) to appreciate mathematics. According to Lawhorn, several of the professors think that changing how math is taught to young children would be helpful. Pasik-Duncan asserted that young students will find math more interesting and easier to understand if they are shown how math solves real-world problems. At the same time, Bayer thinks that "because of the emphasis on assessment tests in schools, teachers don't have much freedom to emphasize the interesting and fun things in math." (Photo by Cody Clifton.)
See the article: "Lawhorn’s Lawrence: The beauty of math," by Chad Lawhorn. Lawrence Journal-World.com, 5 April 2014.
--- Claudia Clark
This excerpt from Amir Alexander's new book "Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World" describes the faith-based debate between Bonaventura Cavalieri, the Italian mathematician who pioneered the idea of integral calculus, and Paul Guldin, a skeptical Swiss scholar. In a revolutionary paper published in 1635, Cavalieri posited that any plane is composed of an infinite number of parallel lines, and any solid is composed of an infinite number of planes. Cavalieri approached mathematics from the perspective that one could assume the underlying structure of the world and investigate starting from these assumptions, counter to the common belief at the time—known as Jesuit mathematics—that all proofs should begin with a rigorous construction of figures using rulers and compasses. Guldin a Jesuit mathematician, attacked Cavalieri's assumptions and lack of a constructed order, and Cavalieri's response underscored the two scholars' philosophical differences.
See: "The Secret Spiritual History of Calculus," by Amir Alexander. Scientific American, April 2014, pp. 82-85.
--- Lisa DeKeukelaere
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