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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)


Artur Avila Manjul BhargavaMartin Hairer Maryam Mirzakhani

The 2014 Fields Medalists (left to right): Artur Avila, Manjul Bhargava, Martin Hairer, and Maryam Mirzakhani.

"The news should start with mathematics, then poetry, and move down from there," from The Humans, by Matt Haig.

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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 : "Regression, Twitter, and #Ferguson," "Medaling Mathematicians."

On a 19th-century paper-and-pencil approximation to Pi, by Claudia Clark

Long before there were computers, the term "computer" referred to people who were adept at performing arithmetic operations. In this article, Hayes introduces us to "one of the finest computers of the Victorian era," William Shanks, and Shanks's work calculating the value of Pi to 707 decimal digits. You might not be surprised to find that some errors crept into Shanks' calculation--beginning at around digit 530--and it is Hayes's attempt to determine the possible reasons for these errors that makes up the bulk of the article. Hayes begins with the fact that most calculators of Shanks' era used arctan formulas (and their equivalent infinite series) for determining the value of Pi. Shanks worked with a formula discovered by mathematician John Machin in 1706 that required the evaluation of two arctan series: π/4 = 4arctan(1/5) – arctan(1/239). Hayes then explores some of the computational methods that Shanks may have used. Finally, Hayes describes the method he uses to identify, and provide a reasonable hypothesis for, three of Shanks' errors.

See "Pencil, Paper, and Pi," by Brian Hayes. American Scientist, September-October 2014, pages 342-345. Also see Hayes's Bit Player blog for additional discussion and resources.

--- Claudia Clark

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On the mathematical landscape, by Lisa DeKeukeleare

Examining Rene Thom's quote that "any mathematical pedagogy… rests on a philosophy of mathematics," columnist Ifran Muzaffar posits that while the quote may hold true for university professors, most K-12 teachers organize their instruction based on a blend of philosophies, rather than standing by a single philosophy to shape their approach to teaching. The article describes three philosophies and how each would be applied in the classroom: 1) mathematics as an objective reality to be discovered , as theorized by G.H. Hardy; 2) mathematics as a set of abstract rules and procedures to be memorized; and 3) mathematics as an iterative process of conjectures to be tested, as popularized by Karl Popper. Muzaffar recounts observing a fourth-grade teacher who adeptly used multiple techniques--without knowing about the underlying philosophical constructs--to meet the multiple demands of school mathematics.

“On the mathematical landscape,” by Irfan Muzaffar. The News on Sunday, 24 August 2014.

--- Lisa DeKeukeleare

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Study shows practicing multiplication tables definitely worth it, by Anna Haensch

Multiplying tools

At some point when we were kids, maybe 8 or 9, we stopped counting on our fingers and answers started to just…sort of appear in our brains.  As a recent article in the Detroit Free Press explains, this transition, while easier for some that for others, turns out to be a pretty good predictor of the course of a kid's mathematical life.  Youngsters who make this transition easily will likely excel, and those who don't, often face severe difficulty later in life.  A recent study funded by the NIH examines what exactly goes on the grey matter during this transition. (Image Courtesy of Jimmie, via Flickr Creative Commons.) 

The study was carried out by Professor Vinod Menon and his team at Stanford.  Menon put 28 lucky kids into a brain-scanning MRI machine and asked them to solve simple addition problems.  First they gave the kids equalities, like 2+5=8, and had them press a button to indicate "'right" or "wrong" (hint: that one's wrong). Next, the kids did the same exercise, but the researched watched them face-to-face, to see if they moved their lips or used their fingers. 

Then they did the whole thing again, nearly a year apart. Turns out, kids who relied more on their memory--signified by an active hippocampus--were much faster than the kids who showed heavy activity in their prefrontal and parietal regions, areas associated with counting. 



Hippocampus The hippocampus (left, courtesy of Wikimedia Commons) is sort of like a traffic staging area. When new memories pull in, a traffic controller directs them into a more long-term parking spot for later retrieval.  But for memories that come in and out often, they get used to the routine.  They always go to the same parking spot and eventually don't even need the help of traffic control to get there.  So for frequently accessed memories, like 2+5=7, we don't even need to rely on our hippocampus.   

What does this mean for kids learning simple arithmetic?  Practicing multiplication tables, with the end goal of rote memorization, actually helps to shape a kid's brain.  And this is particularly helpful in the long run, because kids who work too hard to understand the simple arithmetic, will often feel confused and fall behind as soon as more complicated topics are thrown into the mix. 

So bust out those flashcards and fire up that hippocampus.  Your future self will thank you.  



See: "Brain scans show how kids' math skills grow," by Lauran Neergaard, Detroit Free Press, 19 August 2014.

--- Anna Haensch (Posted 8/26/14)

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Take my peer review... please, by Ben Pittman-Polletta

Thomas Hales

Being asked to review a 50 page paper can be a frightening proposition, and debugging someone else's code can be a nightmare. Imagine the horror, then, of being asked to review Thomas Hales' computer-assisted proof of the Kepler conjecture, over 300 pages long and depending on approximately 40,000 lines of custom code ("Mathematical proofs getting harder to verify," by Roxanne Khamsi, New Scientist, 19 February 2006). The reviewers charged with this task by the Annals of Mathematics spent five years vetting the proof. "After a year they came back to me and said that they were 99% sure that the proof was correct," says Hales in the above article. To eliminate this uncertainty, the reviewers continued their evaluation. "After four years they came back to me and said they were still 99% sure that the proof was correct, but this time they said were they exhausted from checking the proof." (Image: Thomas Hales talking about sphere packing at the 2010 Arnold Ross Lecture in Pittsburgh.)

The Kepler conjecture asserts that no sphere packing (i.e., arrangement of spheres in three dimensions) can be denser (i.e., have a larger ratio of sphere to empty space) than the "greengrocer's" or hexagonal lattice packing. Hales' original proof comes in six chapters, and is frankly bewildering. As far as I can tell, it involves finding the minimum value of a function of 150 variables over a set of ~50,000 sphere configurations, each of which represents some neighborhood of a compact topological space, the points of which represent sphere packings ("A Formulation of the Kepler Conjecture," by Thomas C. Hales and Samuel P. Ferguson, a chapter from The Kepler Conjecture, Springer, 2011, available for a fee). With the help of graduate student Samuel Ferguson (who seems to have disappeared from at least the internet after his graduation from the University of Michigan in 2007), Hales spent six years solving around 100,000 linear programming problems to complete his computer-assisted proof.

When Hales was met with the reasonable doubts of his reviewers, he began the FlysPecK Project -- an attempt to provide a Formal Proof of the Kepler conjecture -- and made the natural choice of computer-assisted peer review for a computer-assisted proof. Flyspeck consists of three parts: a classification of the so-called tame graphs, which "enumerates the combinatorial structures of potential counterexamples to the Kepler conjecture"; a "conjunction of several hundred nonlinear inequalities," which I can only assume are related to the minimization of the function described above, and which were broken into 23,000 pieces and checked in parallel on 32 cores; and a formalization of the proof, combining the above two pieces. The automated proof checkers utilize two "kernels of logic" that have themselves been rigorously checked. "This technology cuts the mathematical referees out of the verification process," says Hales. "Their opinion about the correctness of the proof no longer matters."

Whether the rest of the mathematical community is any more likely to trust automatic proof checkers than computer-assisted proofs -- not to mention the automatic theorem generators that have recently come into existence and gone into business ("Mathematical immortality? Name that theorem," by Jacob Aron, New Scientist, 3 December 2010) -- remains to be seen. In the meantime, we can take comfort in Wikipedia's list of long proofs. While a cursory glance suggests that proofs have gotten longer over the years, a second look suggests that the long proofs of the past have been made vastly shorter by advances in our collective mathematical sophistication. Perhaps the long proofs of today, even those mostly built and checked by computers ("Wikipedia-size maths proof too big for humans to check," by Jacob Aron, New Scientist, 17 February 2014), await only time and the slow accumulation of mathematical insight to be cut down to size. As for Hales, he's no longer holding his breath. "An enormous burden has been lifted from my shoulders," he says. "I suddenly feel ten years younger!"

See "Proof confirmed of 400-year-old fruit-stacking problem," by Jacob Aron. New Scientist, 12 August 2014.

--- Ben Pittman-Polletta (Posted 8/22/14)

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Coverage of the 2014 Fields Medals, by Allyn Jackson

Artur Avila Manjul Bhargava

"Top Math Prize Has Its First Female Winner", by Kenneth Chang. New York Times, 12 August 2014.
"Maryam Mirzakhani Named the First Female Fields Medalist"
, by Mary Grace Garis. Elle, 12 August 2014.
"Top Mathematics Prize Awarded to a Woman for First Time", by Alex Bellos. Time, 12 August 2014.
"Iranian woman wins maths' top prize, the Fields medal"
, by Dana Mackenzie. New Scientist, 12 August 2014.
"Fields Medal won by woman for first time", by Núria Radó-Trilla. Times Higher Education, 13 August 2014.
"First female winner for Fields maths medal"
, by Jonathan Webb. BBC News, 12 August 2014.
"These 4 People Just Won The Most Prestigious Award In Mathematics"
, by Andy Kiersz. Business Insider, 12 August 2014.
"Fields Medals 2014: prizes for maths work that few of us can grasp", by Alex Bellos. Guardian, 13 August 2014.
"Stanford professor becomes the first woman to win the Fields Medal - the highest honor in mathematics"
, by Lauren Lumsden. Daily Mail, 13 August 2014.
"After 78 Years, A First: Math Prize Celebrates Work Of A Woman", by Geoff Brumfiel. National Public Radio, 13 August 2014.
Photos: Artur Avila (left) and Manjul Bhargava (right).



Martin Hairer Maryam Mirzakhani

"Fields-Medaille an Iranerin Maryam Mirzakhani: Das gab es noch niemals zuvor. Eine Frau hat die höchste Auszeichnung für Mathematik erhalten, die Fields-Medaille (Fields Medal to Maryam Mirzakhani: This has never happened before. A woman has received the top honor in mathematics, the Fields Medal)", by Manfred Lindinger. Frankfurter Allgemeine Zeitung, 13 August 2014.
"Stanford math professor becomes first woman to receive prestigious Fields Medal", by Catherine Garcia. The Week, 13 August 2014.
"Sanskrit, music and mathematics: Manjul Bhargava wins Fields Medal, considered Nobel Prize for maths", by Bibhu Ranjan Mishra. Business Standard, 14 August 2014.
"Curiosity key to learning mathematics", by Chung Hyun-chae. Korea Times, 20 August 2014.
"Kenilworth professor awarded 'Nobel Prize of the maths world'". Kenilworth Weekly News, 20 August 2014.
"Maryam Mirzakhani: the right woman at the right time", by Caroline Series. Times Higher Education, 21 August 2014.
Left: Martin Hairer, right: Maryam Mirzakhani.


Above are links to a sampling of the worldwide coverage of the 2014 Fields Medals, which were presented on August 13 at the International Congress of Mathematicians (ICM) in Seoul. Though often called the "Nobel Prize" of mathematics (there is no Nobel in mathematics), the Fields Medal differs from the Nobel Prize: The medal is given every four years and, instead of honoring a career-long body of work, it is presented to young (under 40 years of age) mathematicians as an encouragement to further achievements. [See a summary of an article about the Fields Medal's label as the "Nobel" of mathematics.]

Since its establishment in 1936, the Fields Medal had never gone to a woman, until this year. Naturally, most of the coverage centered on the first-ever woman Fields Medalist, Maryam Mirzakhani. The article by Caroline Series, a distinguished British mathematician, provides insights on why it took so long for the Fields Medal to be awarded to a woman. "[T]he generation of women born after the Second World War and currently reaching retirement is really the first in which aspiring mathematicians have been able to pursue their chosen career without institutional obstacles in their path," she writes. "Combine this history with the level of concentration that is needed in those precious twenties and thirties---the years in which most of us want to be building a family, the years of juggling the demands of two careers in a discipline that may require relocating anywhere in the world, perhaps with a husband, who may, or may not, consider his wife's career as important as his own. It then becomes a little clearer why it is that women have lacked the support networks, the role models and the contacts that most people need to get to the very top."

Other firsts in this crop of Fields Medals: Mirzakhani is the first Iranian Fields Medalist, Artur Avila the first Brazilian, Manjul Bhargava the first of Indian origin, and Martin Hairer the first Austrian. The International Mathematical Union, which awards the Fields Medals, works hard to nurture and support mathematical development the world over. The Time magazine story quoted IMU President Ingrid Daubechies: "At the IMU we believe that mathematical talent is spread randomly and uniformly over the Earth---it is just opportunity that is not. We hope very much that by making more opportunities available---for women, or people from developing countries---we will see more of them at the very top, not just in the rank and file."

Because Mirzakhani dominated the coverage, the other IMU honors presented at the ICM received less attention: The Nevanlinna Prize went to Subhash Khot, the Gauss Prize went to Stanley Osher, and the first-ever Leelavati Prize went to Adrian Paenza.

Don't miss the outstanding articles on the work of the Fields Medalists that appear in Quanta magazine.

--- Allyn Jackson

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On fonts from puzzles, by Claudia Clark

In this article, Rosen tells the story behind a few of the fonts designed by the father-son team of Martin and Erik Demaine, an artist-in-residence and a professor in computer science, respectively, at MIT. Perhaps more well known for their work with geometric folding, the two have applied mathematics and computational geometry to design a number of fonts. The idea for the "conveyor belt" font--imagine letters formed from thumb tacks and elastic bands--occurred during a break the Demaines and a colleague were taking from working on the following question: Can a single 2-D conveyor belt be stretched around a set of wheels such that the belt is taut and touches every wheel without crossing itself? The "glass-squashing" font resulted from their interest in glass blowing: clear disks and blue glass sticks can be arranged in such a way that, when heated and pressed together horizontally, the blue glass sticks form letters. Both are called puzzle fonts because, in one form, the letters are difficult to discern. Visit their website to play with these and other fonts.

See "Father-son mathematicians fold math into fonts," by Meghan Rosen. Science News, 10 August 2014.

--- Claudia Clark

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Background on the Fields Medal, by Lisa DeKeukelaere

In preparation for the mid-August announcement of the 2014 Fields Medal winner, this article (published in early August) examines the history of the Medal and the intersection between mathematics and politics. Debunking the myth that Alfred Nobel neglected to create a mathematics prize to spite a Swedish mathematician rival, the article explains that mathematics simply was not important to Nobel, and Canadian mathematician John Charles Fields created the award in 1950 to unite the divided scientific community following World War II. The Medal did not gain widespread recognition--or the "Nobel of mathematics" tag line--until the 1960s, when media outlets championed the award to help Medal recipient Stephen Smale evade censure for alleged anti-Communist activities. Math and politics continue to be intertwined, as mathematicians consider the implications of military funding and working for the NSA, but the author argues that acknowledging this overlap bolsters the meaning and promise of mathematics.

See "How Math Got Its 'Nobel'," by Michael J. Barany. The New York Times, 8 August 2014 and coverage of the 2014 Fields Medals winners, above, and in Tony's Take.

--- Lisa DeKeukelaere

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On a Google Doodle saluting John Venn, by Mike Breen

Sketch along the way to the DoodleIt's perhaps not quite media coverage, but definitely worthy of mention. August 4 was the 180th birthday of mathematician and logician John Venn, of Venn diagram fame. Google saluted him with a very clever animated Doodle, which you can still see in the Doodle archive. The site also has an interview with the Doodle's creators as well as images, such as the one at left, that show their thought process as they developed the Doodle.

--- Mike Breen


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The sheep of Wall Street, by Anna Haensch

I will begin by confessing that Leonardo DiCaprio, all decked out in a crisp white Polo and Ray-Bans, angrily throwing $100 bills off the side of his ginormous yacht is pretty in-line with how I picture big-shot Wall Street types.  But a profile of successful Wall Street trader and financial entrepreneur Elie Galam on cnn.com paints a much different picture -- that of a quiet math nerd, more concerned with probability theory than parties and yachts. 

Galam is part of a new breed of Wall Street denizens called quantitative analysts, or more colloquially, "quants."  This means he spends his days using complex mathematical concepts to try and understand financial markets. Because of the number-crunchy nature of this work, many math types are finding themselves increasingly at home in the world of finance. 

And statistics suggest that it's a great job and likely to boom in popularity over the next decade.  The number of quants is expected to grow by 41% from 2010 to 2020, and according to the Federal Bureau of Labor Statistics, the mean annual salary for a quant is $91,620--a veritable fortune to a poor grad student. 

For Galam, Wall Street came calling and plucked him out of graduate school after only one year, but for other mathematicians considering making the transition, Cathy O'Neill wrote this great article for Notices summing up her experience moving from the ivory tower to Wall Street. 

See "Math nerds are taking over Wall Street," by Jesse Solomon. CNN.com, 26 July 2014.

--- Anna Haensch (posted 8/12/14)

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Click here for a list of links to web pages of publications covered in the Digest.