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)
Meet 28-year old mathematician Peter Scholze. Photo by G. Bergman.
"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: "Beware of Counterintuitive Results: Police Shooting Edition," by Anna Haensch, and "Picture This!," by Evelyn Lamb.
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
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
According to this article, in 2015, when the Umbral Moonshine Conjecture was proven, this 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 K3 surface. Article author Natalie Wolchover describes K3 surfaces as, "possible toy models of real space-time."
Cheng and other string theorists hope that by probing the properties of the K3 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 of the inside of 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
This article describes Jim Papadopoulos's obsession with bikes, which goes beyond riding them and even his previous competition in recreational races. Papadopoulos, 62, is an assistant teaching professor of mechanical and industrial engineering at Northeastern University. (Photo courtesy Northeastern University.)
For decades, Papadopoulos has been trying to use mathematics to explain how bicycles work. He pursued this interest in greater depth when he was hired as a postdoc at Cornell by his friend Andy Ruina. The Cornell Bicycle Research Project was formed, a project that garnered support from bicycle companies to study different aspects of bicycle performance. Papadopoulos set forth with the goal of writing equations that describe the stability of certain bikes over others. According to the article, he found that, "No single variable... could account for self-stability," of bicycles.
The Bicycle Research Project came to a halt when Ruina couldn't support Papadopoulos's work any longer, and Papadopoulos couldn't raise enough support from bicycle companies. Papadopoulos was first-author on one paper related to the mathematics behind bicycles before he held teaching and industry jobs. Then in 2003, Ruina called him. Arend Schwab of Delft University of Technology in the Netherlands was visiting Ruina's lab at Cornell and wanted to revitalize the research on bike stability. With Schwab's collaboration, Papadopoulos and Ruina unearthed answers to the long-held question of why bikes can move forward with stability, without a rider, findings that were published in the Royal Society and Science. The three researchers, along with Jaap Meijaard, who is now an engineer at University of Twente in the Netherlands, also published a set of bicycle equations in the Proceedings of the Royal Society of London A that agreed with Papadopoulos's previously derived but unpublished equations.
Video: TMS bicycle, Andy Ruina explains how bicycles balance.
Now at Northeastern University, Papadopoulos has moved on to studying a new problem: what causes some bikes to wobble at high speeds and what modifications can be made to bicycles to remedy the wobble.
See "The bicycle problem that nearly broke mathematics," by Brendan Borrell, Nature, 20 July 2016.
--- Rachel Crowell (Posted 8/11/16)
The U.S. International Mathematical Olympiad (IMO) team won first place in the IMO for the second straight year. Korea finished seven points behind the U.S. and China was third. All six U.S. team members earned gold medals in the competition. In an article in The Washington Post, Valerie Strauss talks with U.S. coach Po-Shen Loh, Carnegie Mellon University, about the team and the competition. The online article links to a video about the MAA's summer program for the team and other top scorers in the American Mathematics Competition, and includes three of the six problems from the 2016 IMO exam. The competition took place in Hong Kong. Next year's IMO will take place in Rio de Janeiro, July 12-24. Three of the U.S. team members, Ankan, Michael, and Ashwin, are former Who Wants to Be a Mathematician contestants. (Photo, left to right: Ankan Bhattacharya, Allen Liu, Ashwin Sah, Michael Kural, Yuan Yao, Junyao Peng; courtesy of the Mathematical Association of America/Carnegie Mellon University.)
See "U.S. students win prestigious International Math Olympiad — for second straight year," by Valerie Strauss, The Washington Post, 18 July 2016.
--- Mike Breen
"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)
At the age of 14, he was teaching himself college-level math. At 16, he was teaching himself the mathematics necessary to understand Andrew Wiles's proof of Fermat's Last Theorem. In college, he began studying arithmetic geometry, and, as a graduate student, he wrote a 37-page paper that redid "a 288-page book dedicated to a single impenetrable proof in number theory." Meet 28-year old mathematician Peter Scholze, a professor of mathematics at the University of Bonn in Germany, who has since "risen to eminence in the broader mathematics community," according to profile writer Erica Klarreich. "Scholze's key innovation--a class of fractal structures he calls perfectoid spaces--is only a few years old, but it already has far-reaching ramifications in the field of arithmetic geometry, where number theory and geometry come together." And it's this "unnerving ability to see deep into the nature of mathematics" that colleagues find particularly remarkable: "Unlike many mathematicians," Klarreich notes, "he often starts not with a particular problem he wants to solve, but with some elusive concept that he wants to understand for its own sake. But then, the structures he creates 'turn out to have applications in a million other directions that weren't predicted at the time, just because they were the right objects to think about,'" according to number theorist and collaborator Ana Caraiani. (Photo: Peter Scholze, recipient of the 2015 AMS Frank Nelson Cole Prize in Algebra and European Mathematical Society Prize at 7ECM. Photo by G. Bergman.
See "The Oracle of Arithmetic," by Erica Klarreich, Quanta Magazine, 28 June 2016.
--- Claudia Clark
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)
This article is an interview with Steven Strogatz, a professor of applied mathematics at Cornell University. Strogatz is first asked about where his interests in chaos theory lie: "In broad terms, the question of how order emerges out of chaos.... And I love the idea that things can organize themselves.... All this kind of unfolding of structure and organization all around us and inside of us, to me, is inspiring and baffling." This leads him to discuss what has been learned about the best strategies to use to win the Prisoner's Dilemma game. He then responds at length to the statement: "Many people say math is boring." Strogatz thinks that "much of school is about... teaching kids the answers to questions they're not asking," and he feels "bad about that because teachers are stuck: they're supposed to do what they are doing.... But math is especially tough because there is a lot of jargon, a lot of unfamiliar ideas [and] people do have to concentrate." However, "many people do like using their minds to solve logic puzzles or crossword puzzles or brain teasers.... And even though math can be difficult, so what? A lot of things can be difficult." He hopes "that bright or creative people go into teaching and are rewarded for doing it." Other topics of discussion include what it means to say that a proof is "elegant"; how describing math as "beautiful" may alienate the average person, who may not have that experience, but still feel satisfied when they work out a math problem; how some of the math that we take for granted today would have been impossible for the best mathematical minds in earlier times; and a description of a math course for liberal arts students, developed at Westfield State, that he enjoys teaching.
See "An Ivy League professor explains chaos theory, the prisoner's dilemma, and why math isn't really boring," by Elena Holodny, Business Insider, 8 June 2016.
--- Claudia Clark
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)
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.
Our experience of reality is built upon on information taken in by our senses woven together with our expectations based on past experiences. In the words of computational neuroscientist Peggy Seriès, "The brain is a guessing machine, trying at each moment of time to guess what is out there." She and other neuroscientists suspect that "guessing gone seriously awry may play a part in mental illnesses such as schizophrenia, autism and even anxiety disorders," writes article author Laura Sanders. Practitioners in the young field of computational psychiatry apply mathematical theories to such mental disorders in order to provide new insights. "Scientists hope that a deeper description of mental illnesses may lead to clearer ways to identify a disorder, chart how well treatments work and even improve therapies." In this article, Sanders describes some of the work researchers are doing applying Bayes's theorem--which describes the probability of an event based on related probabilities--to schizophrenia, autism, and anxiety disorders. "Experiments guided by Bayesian math reveal that the guessing process differs in people with some disorders," Sanders notes. "People with schizophrenia, for instance, can have trouble tying together their expectations with what their senses detect. And people with autism and high anxiety don't flexibly update their expectations about the world, some lab experiments suggest. That missed step can muddy their decision-making abilities."
See "Bayesian reasoning implicated in some mental disorders," by Laura Sanders, Science News, 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.