On Media Coverage of Math
Edited by Mike Breen and Annette Emerson, AMS Public Awareness Officers
On slicing pizza, by Rachel Crowell. (Photo courtesy of Joel Haddley.)
"The news should start with mathematics, then poetry, and move down from there," from The Humans, by Matt Haig.
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: "There’s a New Prime! And It Looks Like…Wait…What?" and "Today's Post Is Brought To You By The Letter P," both by Anna Haensch.
According to this article, between 2000 and 2015, Colombia sprayed glyphosate--a toxic herbicide that affects people, crops and the environment--on fields of illegal coca. The aerial spraying was an antidrug effort supported by the U.S. government. Political strife occurred between Colombia and Ecuador over the spraying in 2008. That year, Ecuador alleged that Columbia disrespected a 2005 agreement between the two countries to avoid spraying within 10 kilometers of the Colombia-Ecuador border. However, another explanation for the presence of glyphosate in the no-spray zone was that it drifted there from other areas.
Around that time, Ecuadorian Hermann Mena, a graduate of Ecuador’s first Ph.D. program in mathematics--at the National Polytechnic School (EPN) in Quito--came back to Ecuador from a postdoc at Chemnitz University of Technology. Mena returned to his home country as an associate professor at EPN.
As a child, Mena was punished by being forced to stand in front of his class and say that he was, "no good at math." As an adult, he was determined to use a field of mathematics called optimal control to solve the Colombia-Ecuador glyphosate spraying dispute. Mena was awarded government funding to research the issue, part of which he used to build a computational cluster at EPN. He was able to develop a mathematical model and numerical simulations of the situation. However, unknowns and border control issues left Mena unable to confirm or deny the claim that Colombian planes failed to respect the agreement. In 2013, Ecuador and Colombia settled on the glyphosate issue. Colombia ceased the aerial glyphosate spraying in May 2015.
Since 2013, Mena has been an assistant professor at the University of Innsbruck in Austria, where he focuses on optimal control problems. One project he's working on is a model of El Niño, a phenomenon which causes costly damage in Ecuador. To young people in developing countries who dream of becoming mathematicians, Mena says, "[T]here is no good reason to give up." He adds, "In math, you don't need a laboratory. A computer and a few books are enough." (Photo courtesy Hermann Mena.)
See "A mathematician finds his way through adversity," by Michele Catanzaro, Science, 2 February 2016.
--- Rachel Crowell (Posted 2/9/16)
Cuneiform tablets show that the ancient Babylonians had sophisticated methods for predicting the positions of the planets in the sky. Until now, it was thought that those methods used only arithmetical computations---addition, subtraction, and multiplication. That some of the tablets showed a geometrical figure, namely a trapezoid, had remained a mystery. In 2015, Humboldt University historian Mathieu Ossendrijver discovered a tablet that had been overlooked and that offered a way to decode the meaning of the trapezoids. Ossendrijver found that the Babylonians obtained the trapezoids by making time-velocity graphs of Jupiter's motion. "By calculating the area inside the trapezoid, Babylonian astronomers could find where the planet would be in the sky," the New Scientist article says, noting that the Babylonians "looked to astrology to figure out everything from weather forecasts to the price of goods." Ossendrijver writes: "These computations predate the use of similar techniques by medieval European scholars by at least 14 centuries." The ancient Greeks also used geometrical methods in astronomy, but only to represent the positions of the heavenly bodies. The Babylonian methods that Ossendrijver uncovered are geometrical in a very different sense: "[they] describe configurations not in physical space but in an abstract mathematical space defined by time and velocity."
See "Ancient Babylonian astronomers calculated Jupiter's position from the area under a time-velocity graph," by Mathieu Ossendrijver, Science, 29 January 2016, and "Ancient maps of Jupiter's path show Babylonians' advanced maths," by Joshua Sokol, New Scientist, 28 January 2016.
--- Allyn Jackson (Posted 2/9/16)
Finding the most-efficient packing of balls is a question mathematicians have long been interested in. But what about all the other packings, the ones that are inefficient and disordered? This article discusses a recent attempt to address that question---namely, to estimate the number of disordered packings of 128 balls in a fixed volume ("Turning intractable counting into sampling: Computing the configurational entropy of three-dimensional jammed packings", by Stefano Martiniani, K. Julian Schrenk, Jacob D. Stevenson, David J. Wales, and Daan Frenkel, Phys. Rev. E., January 25, 2016). The answer? A mind-bending 10250, much more than the 1080 atoms in the known universe. To make the estimate, the researchers thought of the balls as being inside a box, where they can be jiggled around until they jam themselves into some arrangement. From this the reserachers created an "energy landscape" representing all possible energies of the balls: "As the balls jiggle loosely in the box, they have more energy, placing them at a higher elevation in the landscape," Aron writes. "Settling down into a jammed state corresponds to the bottom of a valley, as the balls can't move into a lower energy state." The researchers modeled the energy landscape by computer, which allowed them to estimate average size of the valleys. "Since they know the size of the entire landscape, dividing by the average gives a good estimate of how many valleys, and thus jammed packings, there are---leading to the figure 10250."
See "Number of ways to arrange 128 balls exceeds atoms in universe", by Jacob Aron. New Scientist, 28 January 2016.
--- Allyn Jackson (Posted 2/9/16)
This article gives a brief overview of a three-way legal battle that is brewing over the thousands of pages of writings left behind by Alexander Grothendieck, on his death in November 2014. The combatants in the case are Grothendieck's children, the French national library, and the University of Montpellier. "Grothendieck's five children are disputing what they say is the paltry valuation of 45,000 euros [approximately US$50,000] placed on at least 30,000 pages of the documents by the Bibliothèque Nationale de France," the article says. "They are also disputing the claim of the University of Montpellier to own another 20,000 pages given to Grothendieck’s alma mater by a former pupil in 2012." Whether the papers contain mathematical work is unclear. In the last 25 years of his life, Grothendieck lived as a recluse in a village in the Pyrenees and devoted himself to thinking and writing, often about spiritual matters. He was a brilliant writer and an iconoclastic thinker, so hopes are high that his writings will contain much of interest. The article notes that wealthy universities in the United States are eyeing the Grothendieck papers with interest and "open cheque books."
See "Alexander Grothendieck: Legal battle over 'scribblings' of 20th century's 'greatest mathematician'," by John Litchfield, The Independent, 15 January 2016. Also of interest: "Who Is Alexander Grothendieck?" by Winfried Scharlau, Notices of the AMS, September 2008.
--- Allyn Jackson (Posted 1/22/16)
In his December entry to The Huffington Post, mathematician Dan Rockmore writes about two Manhattan art shows that "bring together mathematics and art in wonderful ways." The first is the Frank Stella retrospective at the Whitney Museum of American Art, and the other is a three-part show at The Nancy Hoffman Gallery. In this post, Rockmore discusses three more Manhattan exhibits, each of which can be found at The Museum of Modern Art (MoMA). The first, Endless House, Rockmore describes as "a lovely small show of architectural models that includes homes inspired by and even named for the fundamental mathematical objects the 'torus' (Preson Scott Cohen's 'Torus House') and a Möbius band (the Bos/van Berke Moebius house)." The second exhibit contains approximately 50 Jackson Pollock works from the early 1930s to the early 1950s. Rockmore writes about Pollock's "drip paintings" and the 1995 work of physicist Richard Taylor, who used the mathematics of fractal geometry to study (and authenticate) these paintings. The third is an exhibit of more than 100 sculptures created by Picasso, one of the founders of cubism. Rockmore makes a link between the turn-of-the-century discovery of special relativity--and the subsequent popularization of four dimensions--and many cubist early works, including Picasso's "Guitar."
See "Artful Geometry," by Dan Rockmore. Huffington Post, 11 January 2016.
--- Claudia Clark
The Joint Mathematics Meetings (JMM), the largest mathematics meeting in the world, were held by the American Mathematical Society (AMS) and Mathematical Association of America (MAA) on January 6-9, 2016 at the Washington State Convention Center in Seattle.
*Who Wants to Be a Mathematician (WWTBAM) competition coverage
--- Rachel Crowell (posted 2/1/16)
(Photo courtesy of Joel Haddley.)
Imagine serving homemade pizza to a group of children with strong preferences about crust and toppings. All children in the group will be aware of the amount of pizza given to each child. You wonder: Is there a way you can slice the pizza that will result in equal-sized pieces with different properties based on what each child wants? Yes (an example is pictured above). A recent article in New Scientist describes how mathematics--specifically monohedral disk tiling--can help you tackle this problem in a few simple steps, as shown in the chart below:
First, you must decide on an odd number of sides that you want each of your pieces of pizza to have. The curved pieces are described by the number of sides they have. For example, if you want to cut the pizza into five-sided slices, your slices with be 5-gons. This pattern continues. Joel Haddley told New Scientist, "Mathematically there is no limit whatsoever" to the number of sides your slices can have, but the logistics of exceeding 9-gon slices may be challenging.
Once you have decided on the number of sides for your pieces, the next step is to grab your already-cooked pizza and start slicing. Starting at one side of the pizza, cut in a curved pattern to the opposite side of the pizza. Starting from another side of the pizza, make another cut to the side of the pizza opposite the side where you started your second cut. Repeat this step until the number of curved cuts you have made is equal to the number of sides you want your slices to have. For example, if you want 7-gon slices, make seven such cuts. Next, divide each slice in half. The resulting number of identically-shaped slices will be four times the number of sides your slices have. For example, if you cut a pizza into 7-gon slices using this method, you will end up with 28 identically-shaped pieces. If you want to make the pizza-consumption experience even more thrilling for your young guests, you can create eccentrically-shaped pieces by slicing a wedge out of one corner of each shape.
Haddley told New Scientist that while he has used the results of his work with colleague Stephen Worsley to slice real pizzas, he is unsure if there are other applications of their results. For now, we can all at least rest assured that there are ways to divide a pizza equally among people who want their slices to have different properties.
I dare you to try this interesting technique the next time it’s your turn to slice a pizza.
See "Mathematicians invent new way to slice pizza into exotic shapes," by Jacob Aron. New Scientist, 8 January 2016. Read Haddley and Worsley’s publication “Infinite families of monohedral disk tilings.”
--- Rachel Crowell (posted 1/21/16)
It is not uncommon for teachers to begin the school year with a mathematics test, presumably to learn more about what the students already know, but this method is not used in English or history class. Students learn best in an environment where, "they feel free to try ideas, fail, and revise their thinking." By testing students so often, with short, closed questions, they do not get to try out various ideas and are often most worried about their grade. Students need to be quick with their answers yet mathematicians most often think "carefully and deeply" and understand that it can take years to arrive at a solution. "When educators teach real mathematics--a growth subject of depth and connections--the opportunities for learning increase and classrooms become filled with happy, excited, and engaged math students."
See "The Math-Class Paradox," by Jo Boaler. The Atlantic, 31 December 2015. You may also like a short video of 2016 Who Wants to Be a Mathematician champ Ankan Bhattacharya comparing most math instruction with teaching art by using painting by numbers.
--- Samantha Faria (Posted 1/22/16)
If you're going to be in London between now and the end of March, you'll want to stop by the Science Museum to see an exhibit honoring the life and mathematical work of Ada Lovelace on the bicentenary of her birth. In addition to being the daughter of the famous poet Lord Byron, she was, Robinson writes, "the first person to discuss the concept of programming a computer: In the 1840s, she issued an extensive and farsighted commentary on a calculating machine known as the Analytical Engine, created by the mathematician and inventor Charles Babbage." The exhibit contains Babbage's Difference Engine and Analytical Engine, as well as a model of a Jacquard loom: a type of loom, invented in 1805, that used punch cards to automate the process of weaving. Also on display are two portraits of Lovelace, as well as "originals of her letters from the collections of the British Library and the Bodleian Library...which allows the visitor to follow the progress of her work and her interactions with Babbage, Michael Faraday, and others."
See "The enchantress of numbers," by Andrew Robinson. Science, 11 December 2015, page 1323.
--- Claudia Clark
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