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, Notices of the AMS)
Can simple non-abelian groups model brain cell processes?
Image from YouTube, CC BY-SA.
"The news should start with mathematics, then poetry, and move down from there," from The Humans, by Matt Haig.
Math Digest Archives ||
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 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: "The Ramanujan Movie," by Anna Haensch, and "Beyond Euro-American Mathematics," by Evelyn Lamb.
"Ramanujan indeed had preternatural insights into infinity: he was a consummate bridge builder between the finite and the infinite, finding ways to represent numbers in the form of infinite series, infinite sums and products, infinite integrals, and infinite continued fractions, an area in which, in the words of Hardy, his mastery was 'beyond that of any mathematician in the world.'" Article author Mutalik goes on to explore some simple infinite forms with some puzzles inspired by Ramanujan and "using nothing more than middle school algebra." One puzzle sets out to prove an equation involving an infinite nested radical, another uses basic algebra to prove that the famous golden ratio, phi, is equal to the infinite continued fraction illustrated in the article, and the third is a word problem with a background story involving Ramanujan: "A certain street has between 50 and 500 houses in a row, numbered 1, 2, 3, 4, … consecutively. There is a certain house on the street such that the sum of all the house numbers to the left side of it is equal to the sum of all the house numbers to its right. Find the number of this house."
Mutalik also poses, "What if Ramanujan had modern calculating tools?," "Where do you think Ramanujan’s results came from?," and "How would 21st-century mathematics be different had Ramanujan lived a life of normal length?" the authjor invites solutions in the comments section after the article.
See "Three Puzzles Inspired by Ramanujan," by Pradeep Mutalik, Quanta Magazine, 14 July 2016.
--- Annette Emerson
In 2014, Artur Avila became the first Latin American to win the Fields Medal. He received it for his contributions to the field of dynamical systems. This article calls him, "an evangelical of sorts," because he is, "an example, an inspiration and a role model for the young people living in places with no history in the field of mathematics." Avila is Director of Research at the (CNRS) Centre National de la Recherche Scientifique in Paris. He studies chaotic systems. Avila told VICE, "Mathematicians find pleasure, one that is almost artisanal, in getting our hands dirty with abstract dirt."
He noted that many non-mathematicians perceive math as something that is stagnant. They do not see math the way he sees it--as a changing discipline that is a necessary part of growing and evolving societies.
Avila started his master's degree at the Brazilian Institute for Pure and Applied Math (IMPA) while he was still attending São Bento, a conservative school that forced students to complete courses in religion. He rebelled against those courses by intentionally flunking them. During that time, Avila was socially isolated. He spent his free time focused on mathematics, which led to him earning a doctoral degree by age 21. When Avila was younger, he solved a problem in the interval exchange field with the help of a mentor. The problem had been unsolved for over thirty years.
Avila told Vice that he hasn't decided what he will focus on next, but that he tends to work on several research projects at the same time, "each at its own pace."
See "The Brazilian Genius Trying to Get Non-Mathematicians Interested in Maths," by Mattias Max, Translation by Thiago "Índio" Silva. Vice, 4 July 2015. (The article originally appeared on VICE Brasil and was republished on 4 July in Vice UK.)
--- Rachel Crowell (Posted 7/18/16)
A team in the City University of New York system studied the effectiveness of remedial math courses, which are the "single largest academic block to college graduation in the United States," according to the study's lead author Alexandra W. Logue. About 900 entering students who needed remedial math were randomly assigned to one of three courses: a non-credit remedial algebra course, a remedial algebra course with workshops for extra help, and a college-level statistics course that also had workshops. More than half passed the statistics course, a little less than half passed the remedial course with workshops, and about 40% passed the course without workshops. The results don't seem too surprising--having a workshop that offers help ought to increase pass rates--and it's not obvious that pass rates in algebra are the same as the rates for statistics, but the leaders of the study hope that the results will show colleges and universities that there are other options for students besides remediation. As for long-term benefits, the study found that 57% of the group who took the statistics course had satisfied the school's quantitative general education requirement by their third semester, compared with 16% of those who took remedial algebra. The study was published in Educational Evaluation and Policy Analysis.
See "Study casts doubt on value of remedial math for college," by Nick Anderson. The Washington Post, 23 June 2016.
--- Mike Breen (Posted 6/30/16)
Mutalik offers three puzzles to "test whether the concept of infinity has purchase in the physical world." He writes that "the infinity assumption can give qualitative answers that are not quite correct in the real world," and he presents the puzzles to demonstrate that "better or at least more useful answers can be obtained if we just stick to very large or very small quantities." He poses: 1. Can a number that is finite but very large substitute for infinity?, 2. What if there are physical limits to the smallest measurable amount of space?, and 3. How sharp is a geometric focus in the real world? This last puzzle is demonstrated in this video by Alex Bellos, who creates an elliptical billiard table to demonstrate how a ball will always go in a pocket if hit from a specific point to anywhere on the edge of the table. Mutalik concludes, "I hope these questions give you new insights about the contrast between infinity in mathematics and the physical world."
See "Is Infinity Real?," by Pradeep Mutalik, Quanta Magazine, 16 June 2016.
--- Annette Emerson
Given a collection of points in the plane, the corresponding Voronoi diagram provides a visual way to indicate which regions of the plane are closest to the points in the collection. More precisely, the Voronoi diagram divides the plane into regions such that each region contains a) one point, say X, from the collection, and b) all other points that are closer to X than to other points in the collection. The Delaunay triangulation, the dual of the Voronoi diagram, is constructed as follows. If Voronoi regions for the points X and Y share an edge, connect X and Y by an edge; doing this for all points in the collection gives the Delaunay triangulation. This article explains in nontechnical language what Voronoi diagrams and Delaunay triangulations are. At the end of the article, the author mentions some applications. (Image: U.S. airport Voronoi diagram (http://bl.ocks.org/mbostock/4360892) GNU General Public License, v. 3.)
See "Delaunay Triangulations: How Mathematicians Connect The Dots, by Kevin Knudson, Forbes, 13 June 2016.
--- Allyn Jackson
Much attention has been given recently to Katherine Johnson and her role at NASA as an early female African American mathematician. An upcoming feature film, "Hidden Figures," showcases the accomplishments of Johnson and six other pioneering women mathematicians. Unfortunately, Dr. Evelyn Boyd Granville was not one of the women included. This article shines a light on Granville and her contributions to the Space Race. Her work focused on orbit computations and computer procedures for multiple space related projects, including Project Apollo, which led to a successful moon landing. "Fortunately for me as I was growing up, I never heard the theory that females aren’t equipped mentally to succeed in mathematics... Our parents and teachers preached over and over again that education is the vehicle to a productive life," Granville once wrote. She followed her parents advice and became the second African American woman to earn a PhD in mathematics. Later on in her career she guided two of her students to doctoral degrees of their own. One of whom was honored by the Association for Women in Mathematics by having an award named for her, the Etta Z. Falconer Lecture.
See "Unsung: Dr. Evelyn Boyd Granville," by Sibrina Nichelle Collins, Undark, June 13, 2016.
--- Samantha Faria (Posted 6/21/16)
After starring in a very successful television show, Danica McKellar was interested in transitioning to something new, something away from Hollywood. She headed to UCLA intending to major in film studies and focus on finding out who she was now that her show had ended. Despite earning a 5, the top score, on her advanced placement calculus exam, McKellar still felt insecure with her mathematical aptitude. Her outlook changed, though, after doing exceptionally well on her first college math test. Instead of always being recognized as Winnie Cooper, her former tv show character, McKellar was now getting attention for her math abilities. This achievement changed her identity, she realized that she could be "smart and capable and valuable for something that had nothing to do with Hollywood."
McKellar was recently featured in NOVA’s Secret Life of Scientists and Engineers. In the video she tells the story of her mathematical journey. Now in to its fifth season, many different types of scientists and engineers share their own experiences, including accomplished mathematician, Maria Klawe.
See "Danica McKellar's Inspiring Journey From Winnie Cooper to Mathematician," Yahoo News, 7 June 2016 and NOVA's Secret Life of Scientists and Engineers.
--- Samantha Faria (Posted 6/21/16)
In the Fluid Dynamics of Disease Transmission Laboratory at MIT, Lydia Bourouiba, Esther and Harold E. Edgerton Assistant Professor, literally gives people something to sneeze at. According to this article, she uses an instrument to tickle the noses of study participants so she can record video of their sneezes. She then analyzes the video to learn more about certain aspects of sneezes, such as how big the droplets that come out of a person's mouth are, how fast the droplets travel, and the pattern in which they travel.The goal of Bourouiba's work is to provide a foundation in math and physics for epidemiology and public health, especially when it comes to decision-making. She told Cori Lok of Nature that when it comes to decisions in these areas, "we want to be giving recommendations that are based on science that has been tested in the lab."
In the past, Bourouiba's research focused on determining droplet size distributions during coughs and sneezes. She took videos of coughs and sneezes from healthy study participants and found that droplets came out of people's mouths in what Lok calls a "turbulent, buoyant cloud." Bourouiba found that bigger droplets can travel eight meters if they originate from a sneeze and six meters if they come from a cough. These findings suggest that if a healthy person is on the other side of a room from a sick person who is coughing or sneezing, airborne fluids from the sick person may still reach the healthy person.
Bourouiba has only studied video of the coughs and sneezes of healthy people, but that is about to change. Her team is getting ready to move into a new lab with a biosafety level 2+ containment room. In this lab, she will be able to study the coughs and sneezes of people with colds and the flu. Ultimately, Bourouiba wants to create a mathematical model based on her data that could be used by public-health officials to determine the ways certain diseases spread, whether the diseases contaminate the air or surfaces, and ways to minimize risks of disease spread in hospitals. (Image: Prof. L. Bourouiba, MIT.)
--- Rachel Crowell (Posted 6/30/16)
According to this article, in the game Set, if a player can find three cards out of a group of 12 that have certain attributes, then the player has a set. Each of the 81 cards in a deck has an image that has a color (red, green, or purple), shape (oval, diamond, or squiggle), shade (solid, striped, or outlined) and number of objects (one, two, or three). If a player finds three cards for which all of the images are identical or three cards for which the images don't have any attributes in common, then the player has a set. If a player can't find a set within the 12 cards that are in play, then three more cards are added. This pattern continues until a player finds at least one set. If you are wondering just how many cards players need in order for them to be guaranteed at least one set in the game, a 1971 result from mathematician Giuseppe Pellegrino provides the answer: 21.
But what if there were a different version of the game that included more cards in the deck, with more options for the properties on each card? What if each card had more than four attributes, or there were more than three options for each attribute? In May, three mathematicians published a proof that can be used to solve the same problem for a collection of cards where there are four options for each of the four attributes on a card. Mathematicians Ernie Croot of the Georgia Institute of Technology, Vsevolod Lev of the University of Haifa, Oranim, in Israel and Péter Pál Pach of the Budapest University of Technology and Economics in Hungary used a method based on finding polynomials that evaluate to zero at certain points in a collection.
Jordan Ellenberg (pictured), a mathematician at the University of Wisconsin, Madison and Dion Gijswijt, a mathematician at the Delft University of Technology in the Netherlands, independently published papers that generalized Croot, Lev, and Pach's result. The proofs that Ellenberg and Gijswijt published can be used to show that for a collection of cards each with n attributes, the largest collection of cards which will not contain a set will be at most (2.756/3)n as large as the entire deck of cards. Ellenberg and Gijswijt also based their proofs on the polynomial method. Terence Tao, a mathematician at the University of California, Los Angeles, and a winner of the Fields Medal, told Erica Klarreich of Quanta Magazine that the polynomial method creates, "beautiful short proofs," and the method is, "sort of magical." (Photo: Mats Rudels.)
See "Simple Set Game Proof Stuns Mathematicians," by Erica Klarreich. Quanta, 31 May 2016.
--- Rachel Crowell (Posted 6/13/16)
On the occasion of the NCAA tennis championships held at the University of Tulsa's Michael D. Case Tennis Center, sports writer Kelly Hines introduces the reader to a key player at the event: Brian Garman, a University of Tampa professor of mathematics who has been managing the scheduling for the NCAA tennis championships for the past 30 years. "Known as a living legend in the sport," Hines writes, "Brian Garman is a former tennis umpire who saw a need for better scheduling at juniors events. He came up with a formula called the Garman System that takes into account the number of courts that are available and the average time it takes to conclude a match." Garman explains that "the way the matches are distributed is linear…Because of that, I could then make a prediction on any number of courts." This system was adopted by the NCAA in 1984, eventually spread worldwide, and is used at all levels except professional.
See "NCAA Tennis: Meet the 71-year-old mathematician who keeps the championships running on schedule," by Kelly Hines. Tulsa World, 26 May 2016.
--- Claudia Clark
In this article, Chrystopher Nehaniv, a professor of mathematical and evolutionary computer science at the University of Hertfordshire (UK), describes the international effort with which he has been involved: exploring whether simple non-abelian groups (SNAGs) can be used to model complex processes in living cells. "We have for the first time shown that there are SNAGs hidden in common biological networks," he reports. "To do this, we analysed the internal workings of cells (their gene regulation and metabolism) using mathematics, computers and models from systems biology. We found that SNAG symmetries accurately describe potential activities in the genetic regulatory network that controls a cell's response to certain kinds of stress--such as radiation and DNA damage." It turns out that this genetic network involves the smallest simple non-abelian group, A5, which describes the symmetries of the icosahedron and the dodecahedron. "The 60 symmetries in this case are the result of particular sequences of manipulations by the cell's genetic regulatory network to transform ensembles of proteins into other forms," Nehaniv explains. "For example, when a set of five concentration levels of proteins is manipulated, it can be transformed to another set. When this is done many times, it can break some of the proteins down, join some together or synthesise new types of proteins. But after a specific number of manipulations the original five concentration levels of proteins will eventually return." Nehaniv is hopeful about the potential use of SNAG-based computations in non-living organisms as well: "In the future, new kinds of computers and software systems may deploy resources the way some living organisms do, in robust adaptive responses."
Image: Simulating the human brain is proving tricky. But could mathematics based on symmetries help? youtube, CC BY-SA
See "How the hidden mathematics of living cells could help us decipher the brain ," by Chrystopher Nehaniv. The Conversation, 20 May 2016 and the research article, "Symmetry structure in discrete models of biochemical systems: natural subsystems and the weak control hierarchy in a new model of computation driven by interactions," Philosophical Transactions A. For more information about math and the brain, listen to the Mathematical Moment podcast of Van Weeden talking about his use of math in researching the brain's communications pathways.
--- Claudia Clark
In a recent position paper, the National Council of Teachers of Mathematics (NCTM) wrote that "calculators promote the higher-order thinking and reasoning needed for problem solving and help students learn arithmetic operations, algorithms and numerical relationships." Yet, a divide exists over whether calculators help or hinder learning. This may be because "people haven't figured out what math is. Is it calculations or is it the thinking that goes in to producing calculations," explained Barbara Reys, an expert on math education. Experts agree that teachers must be trained in using calculators in the classroom and "know when and how to incorporate them into lessons." Despite the fact that the NCTM encourages the use of calculators by every student in every grade, research shows that their use varies wildly.
See "Calculators in Class: Use Them or Lose Them?" by Jo Craven McGinty, The Wall Street Journal, May 23, 2016.
In this episode of the weekly radio program Science Friday, host Ira Flatow interviews mathematician Ken Ono, professor of math and computer science at Emory University, about the great Indian mathematician, Srinivasa Ramanujan. Ono was an advisor to the just-released film about Ramanujan, The Man Who Knew Infinity, as well as the author of a memoir, My Search for Ramanujan: How I Learned to Count. During the interview, Ono discusses how Ramanujan taught himself mathematics and did mathematical work, as well as the important and unique relationship Ramanujan had with G. H. Hardy. Ono also describes the tremendous impact that Ramanujan's life and work had on him personally, inspiring him with his struggles as well as his creativity and passion for mathematics, and serving as a bridge between himself and his eminent mathematician father. When asked how he would compare Ramanujan to other mathematicians, Ono describes him as "an incomplete prophet. He died young. He left behind three notebooks that we've been mining 100 years after his death…and we are still learning about the full potential of his ideas. So as an anticipator of the future, as someone whose ideas mean a lot for the future of science, I'm not sure Ramanujan has an equal." Ono would like to see Ramanujan become a household name: "Of course, to mathematicians like me he matters. But what he symbolizes is much greater. What he symbolizes is that greatness can be found in the most unforgiving of circumstances and it's the responsibility of teachers and mentors alike to first recognize that talent, and then find a way to nurture it…Science usually proceeds by the work of thousands, slowly adding to a body of work. But, …every once in a while, some people come along and they propel knowledge further. They are rare. And that's what we have in Ramanujan."
See "Finding Ramanujan: Interview with Ken Ono," by Ira Flatow. Science Friday, 13 May 2016.
--- Claudia Clark
Math Digest Archives ||
1997 || 1996 || 1995
Click here for a list of links to web pages of publications covered in the Digest.