Math Digest

On Media Coverage of Math

Edited by Mike Breen and Annette Emerson, AMS Public Awareness Officers
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, Notices of the AMS)

Margot Lee Shetterly

Margot Lee Shetterly's first book, Hidden Figures, tells the stories of black female mathematicians who made important contributions to NASA.

"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: Mathematicians tour the mathematical blogosphere. PhD mathematicians Evelyn Lamb and Anna Haensch 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: "More To Math and Art Than Just Phi" by Anna Haensch, and "In Praise of People Who Tell Us How to Play with New Toys" and "Happy Birthday, Dear arXiv" by Evelyn Lamb.

On five math problems, by Rachel Crowell


Obama moving Oval Office couch
Photo: White House (Pete Souza).

In this article, Avery Thompson discusses five simple, unsolved math problems. They are:

  1. Collatz Conjecture Let n be any number. If n is even, divide n by 2. If n is odd, multiply n by 3 and add 1. Take the number that results from whichever operation you have just done and run it through the same process. Repeat these steps until you end up at 1. Mathematicians have yet to find a number that, if run through this process enough times, doesn’t end up with a result of 1.
  2. Moving Sofa Problem This problem asks the question "How large can a sofa of any shape be and still fit around a corner that has a measure of 90 degrees?" This is a two-dimensional problem (the corridor is assumed to have a width of 1).The sofa constant represents the largest two-dimensional area that can negotiate this 90-degree corner. It is currently known that the sofa constant is between 2.2195 and 2.8284, but the exact value is unknown.
  3. Perfect Cuboid Problem Let A represent the height, B the width, and C the length of a box. G is a diagonal running from one top corner of the box to the opposite bottom corner. There are three other diagonals on this box, which we’ll call D, E and F. A perfect cuboid would be a box such that A2+B2+C2 = G2 and A, B, C, D, E and F are all integers. Mathematicians haven’t found such a cuboid, but they also haven’t disproven its existence.
  4. Inscribed Square Problem Draw any closed loop such that the beginning and end meet and the loop doesn’t cross itself. It is conjectured that you should be able to draw at least one square such that each corner of the square touches the loop.
  5. Happy Ending Problem It is known that if you have a piece of paper and draw five dots on it that are not arranged in any particular way, you will be able to draw at least one convex quadrilateral using four of these dots. If you have at least nine randomly arranged dots, you’ll be able to draw a convex pentagon. To ensure that you can draw a convex hexagon, you’ll need 17 dots. The open question is, "If you want to build a convex polygon with more than six sides, how many dots will you need?" If M is the number of dots and N is the number of sides to the shape you want to draw, it is thought that the number of dots you’ll need is governed by M=1+2N-2. However, all that has been proven is that you need at least as many dots as that equation states.

See "5 Simple Math Problems No One Can Solve," by Avery Thompson. Popular Mechanics, 14 October 2016.

--- Rachel Crowell

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On envy-free cake cutting, by Rachel Crowell

Cake It is possible to divide a cake among a group of people in an "envy-free" way, according to two young computer scientists who recently published their results. Simon Mackenzie (a 27-year-old postdoctoral researcher at Carnegie Mellon University) and Haris Aziz (a 35-year-old computer scientist at the University of New South Wales and Data 61, an Australian data research group) make up the team. Envy-free cake cutting isn’t just about dividing the cake into slices that are each the same size. Envy-free cake cutting incorporates the notion of dividing a cake that has different features among people who value those features differently. This concept applies to other real-world situations where a continuous object--such as a tract of farm land--needs to be divided among people who assign different values to the varied features. For example, one person might want a tract of land that has a lot of trees but the most important feature to another person could be an abundance of wildflowers.

Since Biblical times, the rule for making such a division fair has been to let one person decide where the division should be and let the other person decide which piece of the divided object they want. In the case of a cake, one person would cut the cake and the other person would choose which piece they wanted. This works for two people but until Aziz and Mackenzie’s algorithm, it was thought that it would not be possible to develop a bounded, envy-free algorithm for dividing a cake among n people. The pair changed that by building on a procedure for envy-free cake cutting among three people that was independently devised by mathematicians John Selfridge and John Conway in 1960.

See "How to Cut Cake Fairly and Finally Eat It Too," by Erica Klarreich, Quanta Magazine, 6 October 2016.

Image: by Helena Jacoba, Creative Commons 2.0, Wikimedia .

--- Rachel Crowell (Item posted 10/19/16)

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On mathekniticians, by Claudia Clark

Curve of pursuitIn this article, writer Alex Bellos writes about the work produced by married couple Pat Ashforth and Steve Plummer, recently retired math teachers, who "have been knitting and crocheting mathematical images and objects for more than two decades." The article is filled with pictures of their colorful two- and three-dimensional creations, including afghans, hexaflexagons, polyominoes, and a cube composed of eight smaller cubes that they have named an "octopush." Each piece demonstrates a mathematical concept or proof: one afghan uses color to represent the factors (from 1 to 10) of the numbers 1 to 100; another afghan shows 3 superimposed Sudoku patterns; and a cushion cover illustrates a geometric proof of the Pythagorean theorem. "Originally," writes Bellos, "the afghans were hung in their classrooms. 'They were an invaluable as a vehicle for talking about maths,' says Ashforth." Part of the enjoyment Ashforth and Plummer derive from their work is "working out how [an idea] can be made into an afghan in a way that would be easy enough for anyone else to recreate. It is like trying to solve a puzzle and refining it to give the best possible solution." (Their patterns are available for sale.) Another source of enjoyment is seeing "the effect we have had on children, either directly by them seeing our big colourful blankets and suddenly understanding something they had previously struggled with, or because other teacher have used our ideas…to help teach maths in an unconventional way. And influencing the lives of so many (most often women) math-phobics who would not dream of becoming involved with anything mathematical in other circumstances." Image: "Curve of Pursuit," by Pat Ashforth and Steve Plummer, Woolly Thoughts.

See "Meet the mathekniticians - and their amazing woolly maths creations," by Alex Bellos. The Guardian, 3 October 2016.

--- Claudia Clark

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On math and credit scores, by Claudia Clark

Cathy O'Neil

In this article, adapted from her recently published book of the same name, mathematician and former Wall Street "quant" Cathy O'Neil takes a sober look at what she calls WMDs, or Weapons of Math Destruction: the models and algorithms that have unintentionally "encoded human prejudice, misunderstanding and bias into the software systems that increasingly manage our lives." Take, for example, the means by which people are determined to be creditworthy. Before Earl Isaac and Bill Fair came up with a model for assessing risk, called Fair, Issac, and Corporation (FICO), a person's eligibility for credit was determined by another human being, with his or her own conscious or unconscious biases. A person's FICO score, on the other hand, "was fed by a formula that looked only at a borrower's finances--mostly his or her debt load or bill-paying record." O'Neil notes that "these scores have lots of commendable, non-WMD attributes," including a clear feedback loop and relative transparency. Now, however, "the use of scoring has proliferated wildly" and many of the models used to predict our creditworthiness are "arbitrary, unaccountable, unregulated and often unfair." O'Neil also argues that using credit scores in making decisions about employment is unfair: "Framing debt as a moral issue is a mistake. Plenty of hardworking and trustworthy people lose jobs every day as companies fail, cut costs, or move jobs offshore." And, even with the Affordable Care Act, she points out, the loss of employment often means the loss of health insurance. "'The more data, the better' is the guiding principle of the Information Age," O'Neil concludes. "Yet in the name of fairness, some of this data should remain uncrunched."

See "Weapons of Math Destruction," by Cathy O'Neil. Discover, October 2016, pages 50-55, and also "'Weapons Of Math Destruction' Outlines Dangers Of Relying On Data Analytics," Interview of Cathy O’Neil by Kelly McEvers. NPR’s All Things Considered, 12 September 2016.

--- Claudia Clark

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On modeling crime, by Claudia Clark

Andrea BertozziIn this article, Fenella Saunders interviews mathematician Andrea Bertozzi and sociologist P. Jeffrey Brantingham about the software they have developed to help police departments determine where crime is likely to occur in the very near future, and therefore where departments should increase patrols. This practice, known as predictive policing, applies algorithms to large amounts of data, looking for patterns of specific criminal events and their locations. "We're using statistical methods, and these methods work very well when you have a large population where you've got a number of different interacting players in the process: for example, residential burglaries, criminals interacting with the environment," Bertozzi explains. "Then we look at how one event might trigger another event. To date, we've mainly focused on crimes of opportunity and ones that happen fairly frequently." (Among some of the models they've "tapped into" are those related to earthquakes and the subsequent aftershocks that are triggered.) According to Brantingham, the advantage of using a predictive algorithm is not in identifying, say, the top three "hot spots" for crime in a community: police departments already have a very good idea where these are. But "if you get down to hot spots 18, 19, 20, you're making it up. The algorithm doesn't have that same limitation. It can look at every single event in the context of the complete history in space and time, and make a much more accurate call about, 'This is hot spot 17 today,' or 'This is hot spot 12 today. In this context the algorithm has an advantage of being able to manage a much larger volume of data to pinpoint that risk."

Watch the entire interview and see "First Person: Andrea L. Bertozzi and P. Jeffrey Brantingham," by Fenella Saunders, American Scientist, September-October 2016, and hear a podcast interview with Bertozzi.

--- Claudia Clark

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On vision and mathematical processing, by Rachel Crowell

Brain PET scan

According to this article, researchers at Johns Hopkins wanted to know how visual experience influences the way people conceptualize numbers, so they studied the brain activity of congenitally blind and sighted people. From a 2013 study conducted by researchers at Stanford School of Medicine, it is known that people owe their processing of numbers to a cluster of specialized nerve cells in their brains. However, the researchers at Johns Hopkins discovered something further: When people who are congenitally blind perform math calculations, they make use of an area of their brains that sighted individuals use only for vision. What’s more, activity in this region of the brain increased in proportion to the difficulty of math problems congenitally blind participants were given.

Shipra Kanjlia is a graduate student in psychological and brain sciences at Johns Hopkins University. Kanjlia was the lead author on the study. She and her colleagues published the study in the Proceedings of the National Academy of the Sciences.

The results of the study leave an important question for future work: Do blind people have an advantage over sighted people when it comes to learning math? However, the results of the study challenge the idea that math is an innately visual process. (Photo: Jens Maus/Wikimedia Commons)

See "What Math Looks Like in the Mind," by Adrienne LaFrance, The Atlantic, 19 September 2016.

--- Rachel Crowell

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On London's most influential mathematicians, by Annette Emerson

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)

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

Margot Lee ShetterlyMargot 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.]

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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)

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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

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