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Tony PhillipsTony Phillips' Take on Math in the Media
A monthly survey of math news

This month's topics:

"They're No. 1: U.S. Wins Math Olympiad"

For First Time In 21 Years" was NPR's take on the U.S. team's victory (All Things Considered, July 18, 2015). From the transcript of the item, compiled by NPR staff: "In one of this year's most intense international competitions, the United States has come out as best in the world--and this time, we're not talking about soccer." The olympiad involves six problems over the course of two days. NPR quotes Po-Shen Loh, Team USA's head coach: "If you can even solve one question, you're a bit of a genius." Loh has a problem of his own, the lack of women on the U.S. team. They quote him: "That is actually something that one hopes will change. ... It could be that maybe the way math is sold, in some sense, is one in which it's just a bunch of formulas to memorize. I think if we are able to communicate to the greater American public that mathematics is not just about memorizing a bunch of formulas, but in fact is as creative as the humanities and arts, quite possibly you might be able to upend the culture difference."

The U.S. students' triumph did not make the New York Times, but the Washington Post came through (by Michael E. Miller, July 18, 2015) with "Winning Formula: USA tops International Math Olympiad for first time in 21 years." Miller also uses a sports analogy: "In 1980, the United States hockey team pulled off one of the greatest upsets in Olympic history, beating a powerhouse Soviet squad, 4-3, on its way to winning the gold medal. The game would go down in history as 'The Miracle on Ice.' Thirty-five years later, America pulled off another stunning upset this week." As he reports, "The U.S. edged out China by four points, 185-181. South Korea took third place."

Post printed one of the problems from the test (No. 6, presumably the hardest), as did The Guardian, which reported ("US triumphs in 'hardest ever' maths Olympiad," by Alex Bellos, July 15, 2015) that the British team was 'pleased as punch' with their 4 silver medals and 22nd place overall.

New pentagonal tiling in The Guardian

The discovery, by a team at the University of Washington at Bothell, of a new pentagonal shape that can tile the plane, was reported in The Guardian (August 11, 2015, article by Alex Bellos) under the title "Attack on the pentagon results in discovery of new mathematical tile." Bellos' subtitle is "Joy as mathematicians discover a new type of pentagon that can cover the plane leaving no gaps and with no overlaps. It becomes only the 15th type of pentagon known that can do this, and the first discovered in 30 years." He sketches the history of the problem: it is known that the regular pentagon cannot tile the plane by itself; but 5 classes of irregular, convex pentagons that could tile were established in 1918; the number grew to 8 in 1968, 9 in 1975, 13 in the next few years and 14 in 1985. "But then the hunt went cold. Until last month, when Casey Mann, Jennifer McLoud and David Von Derau of the University of Washington Bothell announced last week that they had discovered this little beauty:"

pentagon

The new pentagon. $~~A=60^{\circ},~B=135^{\circ}, ~C=105^{\circ}, ~D=90^{\circ}, ~E=150^{\circ}$; $a=1$, $~b=1/2$, $~c=1/(\sqrt{2}(\sqrt{3}-1))$, $~d=1/2$, $~e=1/2$.

Bellos quotes Mann: "We discovered the tile using using a computer to exhaustively search through a large but finite set of possibilities."

tiling

How copies of the pentagon and their mirror images fit together to tile the plane. Image courtesy of Casey Mann.

Bellos explains: "Pentagons remain the area of most mathematical interest when it comes to tilings since it is the only of the '-gons' that is not yet totally understood. ... [A]ll triangles and quadrilaterals tile the plane. It was proved in 1963 that there are exactly three types of convex hexagon that tile the plane. And no convex heptagon, octagon, or anything else-gon tiles the plane. But full classification of the pentagons is still an open area of research." Mann: "I am too cautious to make predictions about whether or not more pentagon types will be found, but we have found no evidence preventing more from being found and are hopeful that we will see a few more."

Bellos: "For the time being, however, the choice of pentagonal tile types for your bathroom wall are these:" and he shows all 15 possibilities, including the latest. Forbes also picks up this useful aspect of the discovery: "A New Way To Tile Your Floor (If You Like Pentagons)," by Kevin Knudson, August 6, 2015. Knudson briefly surveys the history, and then: "Why should we care? Packing problems have important applications, and tilings are 2-dimensional packings of the plane. ... Or, maybe we just like pretty patterns, and now we have another shape we can use to tile a floor." A similar take from Brian Nelson for Mother Nature Network, August 20, 2015: "Breakthrough mathematics discovery could forever change how your bathroom is tiled."

The media excitement over this somewhat esoteric discovery prompted an analysis by Laura Dattaro in the Columbia Journalism Review (August 26, 2015): "Math doesn't get the media attention it deserves." Dattaro writes: "Unlike developments in other fields, discoveries in mathematics rarely make it beyond academic journals and special-interest blogs. Even among the dedicated science press, which regularly covers opaque fields like cosmology, pure math stories can be hard to find." She spoke with Lisa Grossman, the physical sciences news editor at New Scientist, Kristin Ozelli, senior editor at Scientific American Mind and Kevin Hartnett, who writes the Boston Globe "Brainiac" column. The consensus is that the inscrutable vocabulary of mathematics, as much as anything else, makes the subject hard to present. "Simply finding a story can prove more complicated than in, say, physics, wherein a published paper might at least use a recognizable phrase like 'black holes.'" Another problem, in Ozelli's words: "Compared to other fields, developments in math don't always have the same immediate relevancy to the real world. It can be harder to answer that question of, Why do readers need to know that now? A lot of math is fun or beautiful or interesting, but not immediately practical." One possible hook: "Many of the most successful math stories have been features that arrive at math's inner workings through the lives of its enigmatic practitioners." Dattaro mentions the New Yorker's 1992 profile of the Chudnovsky brothers, the recent New York Times Magazine piece on Terry Tao (see below) and A Beautiful Mind, Sylvia Nasar's very successful biography of John Nash. She quotes Hartnett: "People are intrigued by mathematicians."

Terence Tao in The New York Times Magazine

Gareth Cook's "The Singular Mind of Terry Tao," which ran in the magazine on July 24, 2015, is a piece of exceptionally good scientific journalism. Following the strategy noticed by Laura Dattaro (see above), Cook uses the human interest generated by a compelling life story (Australian child prodigy with savvy parents grows up to be an unusually unpeculiar world-class mathematician with talented and well-adjusted kids of his own) to keep his readers' attention while he delivers a substantial amount of information about some of the problems Tao works on--in particular, the twin primes conjecture and the stability of solutions to the Navier-Stokes equations--and about mathematics, and the life of a mathematician, in general. Here are two samples:

  • The primes are elementary and, at the same time, mysterious. They are a result of simple logic, yet they seem to appear at random on the number line; you never know when the next one will occur. They are at once orderly and disorderly. ... From counting, you can develop the concept of number, and then, quite naturally, the basic operations of arithmetic: addition, subtraction, multiplication and division. That is all you need to spot the primes--though, eerily, scientists have uncovered deep connections between primes and quantum mechanics that remain unexplained. Imagine that there is an advanced civilization of aliens around some distant star: They surely do not speak English, they may or may not have developed television, but we can be almost certain that their mathematicians have discovered the primes and puzzled over them.
  • The true work of the mathematician is not experienced until the later parts of graduate school, when the student is challenged to create knowledge in the form of a novel proof. It is common to fill page after page with an attempt, the seasons turning, only to arrive precisely where you began, empty-handed - or to realize that a subtle flaw of logic doomed the whole enterprise from its outset. The steady state of mathematical research is to be completely stuck. It is a process that Charles Fefferman of Princeton, himself a onetime math prodigy turned Fields medalist, likens to "playing chess with the devil." The rules of the devil's game are special, though: The devil is vastly superior at chess, but, Fefferman explained, you may take back as many moves as you like, and the devil may not. You play a first game, and, of course, "he crushes you." So you take back moves and try something different, and he crushes you again, "in much the same way." If you are sufficiently wily, you will eventually discover a move that forces the devil to shift strategy; you still lose, but--aha!--you have your first clue.

 

Tony Phillips
Stony Brook University
tony at math.sunysb.edu