** Edited by Mike Breen and Annette Emerson, AMS Public Awareness Officers
Contributors:** Mike Breen (AMS), Claudia Clark (writer and editor), Rachel Crowell (2015 AMS Media Fellow), Annette Emerson (AMS), Samantha Faria (AMS), and Allyn Jackson (Deputy Editor,

Trajectories an airplane would take if it started from the origin and tried to fly as straight as possible over randomly fluctuating geometric surfaces, courtesy of Scott Sheffield

* "The news should start with mathematics, then poetry, and move down from there,*" from

- On London's most influential mathematicians, by Annette Emerson

"The Progress 1000: London's most influential people 2016-Mathematics,"*Evening Standard*, 7 September 2016 - On Margot Lee Shetterly's
*Hidden Figures*, by Rachel Crowell

"On Being a Black Female Math Whiz During the Space Race,"*The New York Times*, 5 September 2016 - On Sophie Bryant, by Samantha Faria

"Sophie Bryant, mathematician and pioneer of education for women,"*The Irish Times*, 23 August 2016 - On Maya DiRado, by Samantha Faria

"U.S. Swim Star Maya DiRado To Delay Career, Cash In On Rio Success,"*Sports Business Daily*, 18 August 2016 - On Barry Simon, by Samantha Faria

"A Lifetime of Numbers: Question and Answer with Caltech's Amazing Barry Simon,"*Pasadena Now*, 11 August 2016; "From Mathematical Physics to Analysis: A Walk in Barry Simon's Mathematical Garden,"*Notices of the American Mathematical Society*, August 2016 - On moonshine and string theory, by Rachel Crowell

"Moonshine Master Toys With String Theory,"*Quanta Magazine*, 4 August 2016 - On randomness, by Claudia Clark

"A Unified Theory of Randomness,"*Quanta*, 2 August 2016 - On visualizing music, by Claudia Clark

"Visualizing Music Mathematically,"*Forbes*, 29 July 2016

Math Digest Archives ||
2016 ||
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. |

See also: **The AMS Blog on Math Blogs****: Mathematicians tour the mathematical blogosphere**. PhD mathematicians

**On London's most influential mathematicians, by Annette Emerso**n

The *Evening Standard* has included in its "The Progress 1000" series a piece profiling London's most influential mathematicians. They are (in the *Standard's* order): **Hannah Fry**, lecturer in the mathematics of cities, University College London (UCL), for her work researching human behavior and the math behind the railway network, and for her public outreach through books, radio, and a TED Talk; **Marcus du Sautoy**, professor of mathematics, Oxford University, for his "knack for explaining complicated number theory in accessible terms"; **Colin Hegarty**, mathematics teacher and Global Teacher prize finalist, for his "mission to make calculus cool"; **John Pullinger**, national statistician, for mobilizing "the power of information 'to help Britain make better decisions'"; **Martin Anthony**, head of mathematics, London School of Economics, for his research on Boolean theory and machine learning; **Robb McDonald**, head of mathematics, UCL, for his research and for encouraging more women to go into mathematics; **Dame Celia Hoyles**, professor of mathematics education, UCL Institute of Education, and "former government 'maths tsar'" for "sharing her enthusiasm for numbers with children and raising teachers' morale"; **David Harding**, founder and chief executive, Winton Capital Management, for his "research-driven approach to investing" and "employing maths and science whizzes to develop computer programs which lie at the heart of modern trading"; **Jenny Watson**, chair, Electoral Commission, and chief counting officer, for launching "a public awareness campaign in May to increase voter registration"; **Paul Johnson**, director, Institute for Fiscal Studies, for explaining dubious economic claims of politicians to the general public; **Robert Chote**, chairman, Office for Budget Responsibility, for overseeing public finances at the OBR; **Anne-Marie Imafidon**, co-founder, Stemettes, for inspiring girls to study STEM subjects; **Alex Bellos**, writer and broadcaster, for his best-selling popular science books and math coloring book; and **Simon Tavaré**, president, London Mathematical Society, for "promoting maths to a wider audience" and his work on the effects of genome alterations on cancer.

Congratulations to these mathematical scientists for their contributions, and congratulations to the *Evening Standard* for drawing attention to them.

See "The Progress 1000: London's most influential people 2016--Mathematics," *Evening Standard*, 7 September 2016.

*--- Annette Emerson* (Posted 9/16/16)

**On Margot Lee Shetterly's Hidden Figures, by Rachel Crowell**

Margot Lee Shetterly's (left) first book, *Hidden Figures*, tells the stories of black female mathematicians who made important contributions to NASA's mission before measures were taken to desegregate NASA in 1958. A movie version of the story is scheduled to be released at the end of this year. Taraji P. Henson, Octavia Spencer, and Janelle Monáe star in the movie.

According to this article, the job title of these influential women was, "colored computers." Among the women discussed in the book are **Christine Darden** and **Katherine Johnson**. Darden, who is 73, became a leader in engineering research of sonic booms before retiring from NASA. Johnson, who is 98, was responsible for calculating trajectories of rockets for the Mercury and Apollo missions. She and her husband of 57 years--James A. Johnson--live together in a retirement home.

Shetterly's father was a scientist at NASA. As a youngster, she knew female mathematicians and scientists who worked for NASA, including one of her Sunday school teachers. Shetterly was inspired to write the book after a conversation she had with her husband (Aran Shetterly) and her father. *Photo*: Aran Shetterly.

See "On Being a Black Female Math Whiz During the Space Race," by Cara Buckley, *The New York Times*, 5 September 2016.

--- *Rachel Crowell * (Posted (9/16/16)

[Editor's note: For more on the film, see “This movie about black female mathematicians looks glorious,” by Lili Loofbourow, *The Week*, 15 August 2016; “The African-American women behind NASA's rocket launches,” by Jan Crawford, *CBS This Morning*, 7 September 2016; “The Forgotten Black Women Mathematicians Who Helped Send Astronauts to Space,” by Maya Wei-Haas, *Smithsonian*, 8 September 2016.]

**On Sophie Bryant, by Samantha Faria**

Born in 1850, Sophie Bryant was raised in a home that valued education: her father was a mathematician, a fellow of Trinity College Dublin and later Chair of Geometry at the University of London. Unsurprisingly, Bryant won a science scholarship for college and later began teaching other young women. Although married at an early age, her husband passed away after only a year of marriage. Rather than remarry, she spent her life committed to education and published books on a variety of subjects, including Irish history, religion, education, women’s rights, and philosophy. She was the third woman elected to the London Mathematical Society. Sadly, in 1922 her life was cut short during a “walking holiday” in France.

See "Sophie Bryant, mathematician and pioneer of education for women," by Rosita Boland, *The Irish Times*, 23 August 2016.

*---Samantha Faria *(Posted 9/22/16)

**On Maya DiRado, by Samantha Faria**

Maya Dirado has been known in the competitive swimming circuit for years but since the Rio Olympics she's now a household name. Her speed, effort and fortitude helped her bring home four Olympic medals: two gold, one silver and a bronze. Unlike some athletes who are driven by a single goal, Dirado has spent her life perfecting whatever it is that she is working on. This internal effort led her to a perfect math score on the SATs (and the PSATS), a degree in management science and engineering from Stanford, and an upcoming career as a business analyst. She once said, "It's about going to practice every day and trying as hard as you can... If you do that, it will give you the results." It seems as though she has applied this strategy to every area of her life.

See "U.S. Swim Star Maya DiRado To Delay Career, Cash In On Rio Success," by Ben Fischer, *Sports Business Daily*, August 18, 2016; "Meet Maya DiRado, the 'late-blooming' phenom who could star for U.S. in Rio," by Pat Forde, *Yahoo Sports*, June 21, 2016; and "Stanford-bound Dirado, best all-around swimmer in region's history, in last NCS meet," Eric Branch, The Press Democrat, May 21, 2010.

*--- Samantha Faria*

**On Barry Simon, by Samantha Faria**

Although gifted as a child, a career as a mathematician was not necessarily Barry Simon's goal. Simon says his "biggest influence was his high school physics teacher." Through hard work, curiosity, and a deepening interest, he has been able to work successfully in both math and physics. Known as one of the founders of modern mathematical physics, Simon was awarded the 2016 Leroy Steele Prize for Lifetime Achievement. Accordingly, he has a long list of contributions and accomplishments under his belt in both of these fields. At 70 years old, Barry Simon is not slowing down. Despite his recent retirement from academia, he has three books in development, various research projects underway, and has begun an online "Selecta" where he annotates his papers with important notes.

See "A Lifetime of Numbers: Question and Answer with Caltech's Amazing Barry Simon," by Whitney Clavin, *Pasadena Now*, 11 August 2016; "From Mathematical Physics to Analysis: A Walk in Barry Simon's Mathematical Garden," by Fritz Gesztesy, *Notices of the American Mathematical Society*, August 2016.

*--- Samantha Faria*

**On moonshine and string theory, by Rachel Crowell**

The proof of the Umbral Moonshine Conjecture in 2015 showed that 23 moonshines--structural connections between symmetry groups and mock modular forms--exist. Mock modular forms are a class of fundamental objects in number theory.

Miranda Cheng, an assistant professor at the University of Amsterdam on leave from the National Center for Scientific Research in France, is developing K3 string theory. The theory is important to understanding umbral moonshines. This is a version of string theory in which the geometry of space-time is that of a K_{3} surface. Article author Natalie Wolchover describes K_{3} surfaces as, "possible toy models of real space-time."

Cheng and other string theorists hope that by probing the properties of the K_{3} model using what they know about the 23 moonshines, they will be able to understand the physics of aspects of real life that can’t be observed directly, such as that inside black holes. One mystery she would like to try to solve is the information paradox--or the question of how quantum information is affected when it enters a black hole. Cheng says her research is, "on the boundary between physics and mathematics." She discusses this further in the video below.

See "Moonshine Master Toys With String Theory," by Natalie Wolchover, *Quanta Magazine*, 4 August 2016.

*--- Rachel Cowell*

**On randomness, by Claudia Clark **

In this article, writer Kevin Hartnett discusses the work done over the past few years by MIT professor of mathematics **Scott Sheffield** and University of Cambridge professor **Jason Miller**, who "have shown that random [two-dimensional surfaces] can be categorized into various classes, that these classes have distinct properties of their own, and that some kinds of random objects have surprisingly clear connections with other kinds of random objects." Hartnett begins the article by having the reader visualize random two-dimensional geometries by considering the trajectory that would be made by a plane flying over increasingly random fluctuating surfaces: the path becomes "nearly incoherent"…but not incomprehensible, he adds. "In random geometry, if you know the location of some points, you can (at best) assign probabilities to the location of subsequent points. And just like a loaded set of dice is still random, but random in a different way than a fair set of dice, it's possible to have different probability measures for generating the coordinate values of points on random surfaces." Hartnett continues: "What mathematicians have found--and hope to continue to find--is that certain probability measures on random geometries are special, and tend to arise in many different contexts." The random walk was "the first kind of random shape to be understood in this way," Hartnett writes. Decades later, two complementary perspectives developed in parallel to study two-dimensional random surfaces: Liouville quantum gravity (LQG) and the Brownian map. LGQ "gave physicists a way of defining a surface's angles so that they could calculate the surface area." On the other hand, the Brownian map "has a structure that allows researchers to calculate the distances between points." And in 2013, Sheffield and Miller "set out to prove that these two models described fundamentally the same thing."

*Image* courtesy of Scott Sheffield. Each ray represents the trajectory an airplane would take if it started from the origin and tried to fly as straight as possible over a randomly fluctuating geometric surface.

See "A Unified Theory of Randomness," by Kevin Hartnett. *Quanta*, 2 August 2016.

*--- Claudia Clark*

**On visualizing music, by Claudia Clark**

In this article, University of Florida professor of mathematics **Kevin Knudson** explains to the general reader how a piece of music can be described and visualized using mathematics. He starts by noting that a typical pop song has distinct parts, like verses and a chorus, each of which has certain chord progressions. In addition, various instruments, including voices, are used at different times. But to "see" a song mathematically, Knudson describes one method, which was presented by Duke University PhD student **Chris Tralie** and mathematics professor **Paul Bendich** in their 2015 paper, "Cover Song Identification with Timbral Shape Sequences." He explains how the authors analyze songs--which are, after all, simply waves--using "some commonly used features in music analysis called 'timbral features,' the 'Mel-Frequency Cepstral Coefficients,' and a feature set called 'chroma' which gives information about notes and chord." These features can be measured along small pieces of the graph, ultimately resulting in a "cloud of points in a 59-dimensional Euclidean space." Then, the authors use topological data analysis to "develop some novel methods for organizing a point cloud into clusters based on [the] local dimension," notes Knudson. "Finally, to visualize, you project the data into 3-dimensional space using the first three principal components of the data" (which involves principle component analysis).

*Image*: Principal Component Analysis of an eight-beat block from the hook of Robert Palmer's "Addicted To Love" with a window size of .05 seconds; cool colors indicate windows towards the beginning of the block, and hot colors indicate windows towards the end, courtesy of Christopher J. Tralie and Paul Bendich.

See "Visualizing Music Mathematically," by Kevin Knudson. *Forbes*, 29 July 2016.

*--- Claudia Clark*

Math Digest Archives ||
2016 ||
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. |