On Media Coverage of Math
Edited by Mike Breen and Annette Emerson, AMS Public Awareness Officers
Art Benjamin, who was profiled in Smithsonian.
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: "Blogs for an IBL Novice" by Evelyn Lamb and "A Cheap Alternative To Pricey Journals," by Anna Haensch.
Although films like The Imitation Game and Andrew Hodges' 1983 biography depict Alan Turing as the man who singlehandedly used mathematics and computing to save the Allies from the Nazis in World War II, the truth is that others contributed to his accomplishments and at times undertook similar work simultaneously. Turing is best known for his paper on the "Turing Test" to determine whether a computer can think, for his work on the famed German Enigma machine, and for allegedly inventing the first computer--the "Turing machine." However, Polish mathematicians had cracked an early version of the Enigma by 1932, and their work was the foundation of Turing's effort to break subsequent codes. The Turing machine arose from Turing's quest to address a theorem that an algorithm composed of a finite number of instructions can compute any function to any desired precision, but another mathematician already had answered the question, and several others were working on binary machines at the same time.
See "Testing Turing's Legacy," by Tony Rothman. Discover, October 2015, pages 70-72.
--- Lisa DeKeukelaere
Professor Frank Farris provides an elementary group theory lesson couched in pretty, patterned wallpaper. Starting with the concepts of translational symmetry and mirror symmetry in a "frieze pattern" that repeats indefinitely left and right, Farris explains how a frieze pattern with one vertical mirror axis must have another set of vertical mirror axes halfway between the others. The idea that a pattern with a given set of symmetries must have all the other symmetries that arise from combining those in the set is connected with the concept of a mathematical group. Farris notes that there are only seven different types of frieze groups, based on the possible combinations of rotational, vertical, and horizontal qualities, and he introduces a notation for expressing each group as well as examples. Positing that our fondness for patterns may be an evolutionary trait that helped humans compare edible and poisonous plants, or simply an attraction to something pretty, Farris notes that the popularity of patterns is timeless. See some of Farris's work on Mathematical Imagery.
See "Patterns are math we love to look at," by Frank A. Farris. The Conversation, 22 September 2015.
--- Lisa DeKeukelaere
"Quantum computers," writes Peter Diamond, "once seen as a remote theoretical possibility, are now widely expected to work within five to 30 years. By exploiting the probabilistic rules of quantum physics, the devices could decrypt most of the world's 'secure' data, from NSA secrets to bank records to email passwords. Aware of this looming threat, cryptographers have been racing to develop 'quantum-resistant' schemes efficient enough for widespread use." In this article, Diamond introduces the reader to two of the most widely used public key encryption schemes--RSA encryption and Diffie-Hellman key exchange--and explains why these "can be broken by algorithms designed to run on future quantum computers." However, most of the article focuses on the work that has been done over the years to develop "quantum-secure" schemes based on the mathematics of lattices and on the challenge of finding the right balance between security and efficiency.
See "The Tricky Encryption that Could Stump Quantum Computers," by Peter Diamond. Wired (from Quanta magazine), 19 September 2015. Nature ran a related article: "Encryption faces quantum foe," by Chris Cesare. 10 September 2015, pages 167-168.
--- Claudia Clark
"... [T]o 25-year-old Iranian student Hamid Naderi Yeganeh, using cosines are a part of daily life--what you would expect of a mathematics major and award-winning mathlete," writes CNN reporter Chung in this article accompanied by images. Yeganeh, a student in mathematics at the University of Qom, says in the article, "At first I was interested in beautiful, symmetrical shapes. So, I started to create mathematical figures using trigonometric functions to define the endpoints of line segments. After a while, I understood I could find interesting shapes that looked like real life things, such as animals." He is now creating animations of his circle and line images (the article includes a nice video animation), and 3D sculptures of fractals. See samples of his works in an album of his works, Mathematical Concepts Illustrated by Hamid Naderi Yeganeh, on AMS's Mathematical Imagery.
Read "Next da Vinci? Math genius using formulas to create fantastical works of art," by Stephy Chung, CNN, 17 September 2015.
--- Annette Emerson (Posted 9/18/15)
Art Benjamin's love of math grew with every Martin Gardner puzzle he completed. Each problem was creative, stimulating and engaging. Unfortunately, he explains, "both the fun and the explanations are often missing from math instruction in today's schools." A proclaimed "mathemagician," Benjamin astonishes his audiences not just with his super-speedy calculations but with his ability to captivate their attention and explain topics in interesting ways. The Harvey Mudd professor admits that he "learned how to be a good teacher through [his] early experiences as a magician. My approach to teaching has always been, 'How do I make this material entertaining?'" In his new book, The Magic of Math, Benjamin hopes to do just that.
See "From Poof to Proof: Inside the Mind of a Mathemagician," by Liz Logan, Smithsonian Magazine, 8 September 2015.
Photo courtesy of Harvey Mudd College.
When there are two routes to your destination, why does it always seem that the route you choose has more traffic? According to the author, Pradeep Mutalik, the mathematical explanation for this phenomenon is called selection bias: "The busier road has more drivers on it, so if you sample a bunch of drivers randomly, more of them will be from the more crowded road." Mutalik asks readers to consider how large an impact this has by posing the first of two questions: "Let us say the drivers of 200 cars independently and randomly make their choice between…two roads with a 50 percent probability of choosing a given road. Assume that there are no other cars on the road. How many more of the 200 cars end up on the more crowded road?" But this is not the whole story, Mutalik notes. Doesn't the fact that some of the time you find yourself on the less busy road "decrease your tendency to overestimate, or engage in upward bias, somewhat?" Here, Mutalik poses the second question: "What happens to the driver's upward bias if there are an average of 100 cars on each road? How many cars do we think he or she sees?"
See "The Road Less Traveled," by Pradeep Mutalik. Quanta Magazine, 3 September 2015. In addition to the article, the website has readers' answers to the questions.
--- Claudia Clark
In mathematics, it's people who write proofs and solve complicated problems. But today, computers are becoming sufficiently powerful to carry out proofs and even to come up with new mathematical conjectures. Two articles in New Scientist touch on the impact of computing power on today's mathematics. The first article discusses how researchers are translating highly complex proofs into a form that computers can check in a highly precise way---by confirming the rudimentary logic of each step of the proof. Among the results whose proofs have been checked in this way are the four-color theorem, the Feit-Thompson theorem, and the Kepler conjecture. Some mathematicians are going even further, by trying to revamp the very foundations of mathematics to make them more amenable to computers. Could computers then take off and create mathematics of their own---mathematics that is too complex for humans to understand? Perhaps, but most people working in this area do not think this is the point of using computers in mathematics. The article quotes Vladimir Voevodsky of the Institute for Advanced Study: "The future of mathematics is more a spiritual discipline than an applied art. One of the important functions of mathematics is the development of the human mind."
The second article, an interview with Simon Colton, mainly discusses software he wrote called HR, which is designed not to do particular calculations but rather to be creative. HR has come up with its own mathematical conjectures, including some well known to humans, such as Goldbach's Conjecture. Colton told New Scientist that computers will really be creative only when they are able to write their own software. But, he says, "writing software is one of the most difficult things that people do". Colton also wrote software called The Painting Fool, which creates portraits. He notes that mathematicians will accept a computer as being creative if it repeatedly comes up with interesting mathematical results. But art is different. "When you like a painting, you are celebrating the humanity that went into it," he says.
Read more about this theme in the Special Issue on Formal Proofs, AMS Notices, December 2008; and in the article "Voevodsky’s Univalence Axiom in Homotopy Type Theory," AMS Notices, November 2013.
See "Our number's up: Machines will do maths we'll never understand," by Jacob Aron (subscription required). New Scientist, 26 August 2015; and "The Art of Programming": Interview with Simon Colton, by Douglas Heaven. New Scientist, 29 August 2015.
--- Allyn Jackson (Posted 9/14/15)
In this Sports Illustrated article, author Emily Kaplan wants to answer the question, "Why would a mathematician delay his PhD to be an offensive lineman for the [Baltimore] Ravens?" The lineman, John Urschel, doesn't feel compelled however to explain his love of football and adds that there is nothing wrong with being good at more than one thing. Urschel has a stellar academic history from grade school--where his teacher first thought that he had "processing problems" then realized he was bored--to college at Penn State--where he had to fight athletic advisers so that he could take advanced math courses--to now, when he has earned a master's degree from Penn State and already published four papers. He is very competitive and really enjoys the physicality of football but he's not at all arrogant. Kaplan calls him "an overachiever with humility." Unfortunately, Urschel suffered a concussion during the pre-season and had to avoid football for two weeks. The most recent news is that he now feels fine and is back playing.
See "The (NFL) Mathlete," by Emily Kaplan. Sports Illustrated, 24 August 2015, page 38-43.
--- Mike Breen (Posted 9/15/15)
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