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"Like a good magic trick, a clever puzzle can inspire awe, reveal mathematical truths and prompt important questions...." Celebrate Martin Gardner this month. Image: "Martin Gardner - Master Puzzler," by Bruce Torrence (Randolph-Macon College, Ashland, VA).

 

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Tony Phillips Tony Phillips' Take on Math in the Media
A monthly survey of math news
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This month's topics:

The Best Language for Math?

"The Best Language for Math" ran in the Wall Street Journal, September 9, 2014. The article, by Sue Shellenbarger, was subtitled "Confusing English Number Words Are Linked to Weaker Skills." The concept is not absurd: children who have to master eleven, twelve, thirteen, fourteen, ... as opposed to ten-one, ten-two, ten-three, ten-four, ... and to distinguish seventeen from seventy instead of ten-seven from seven-ten (to compare English number-words to the literal meaning of their Chinese equivalents) should, it seems, have some extra trouble in beginning their arithmetic. And so we read "Chinese, Japanese, Korean and Turkish use simpler number words and express math concepts more clearly than English, making it easier for small children to learn counting and arithmetic, research shows."

The research actually shows a more complex picture, as Shellenbarger acknowledges. One line of study that she cites is a review of work in the area by Ng and Rao (Hong Kong). Their abstract reads in part: "The review (a) provides equivocal findings about the extent to which number words in the Chinese language afford benefits for mathematics learning; (b) indicates that cultural and contextual factors are gaining prominence in accounting for the superior performance of East Asian students in cross-national studies; and (c) yields emerging evidence from neuroscience that highlights interrelationships among language, cultural beliefs, and mathematics learning."

Shellenbarger also cites as evidence for "The negative impact of English" a 2014 study by Jo-Anne Lefevre, Oziem Canyaka and Kristina Dunbar (Carleton University, Ottawa; see their Count Me In website), which compared 59 English-speaking Canadian children from Ottawa with 88 Turkish children from Istanbul, ranging in age from 3 to 4 1/2 years. "The Turkish children had received less instruction in numbers and counting than the Canadians. Yet the Turkish children improved their counting skills more after practicing in the lab with a numbered board game." The acticle is more nuanced. "All of the Turkish-speaking children in the number game condition showed some improvement in their rote counting skills whereas almost half of the English-speaking children did not. Despite the advantage of the regular number naming system, however, the Turkish-speaking children had lower scores than the English-speaking children on other early numeracy tasks. These results support the view that both the characteristics of the number language and factors such as children's numeracy-related experiences must be considered when comparing children's early numeracy skills across language groups."

What to do? Shellenbarger gives a list of video math games that "can help offset linguistic disadvantages" for English-speaking toddlers facing mathematics.

Gauss and the Art of Pizza Eating

Wired hosts Aatish Bhatia's "Empirical Zeal" blog, where one can read "How a 19th Century Math Genius Taught Us the Best Way to Hold a Pizza Slice," posted on September 5, 2014.

pizza

The wrong and the right way to hold a slice of pizza. Adapted from a photograph by Aatish Bhatiya.

"We've all been there. You pick up a slice of pizza and you're about to take a bite, but it flops over and dangles limply from your fingers instead. ... But there's no need to despair, for years of pizza eating experience have taught you how to deal with this situation. Just fold the pizza slice into a U shape (aka the fold hold). This keeps the slice from flopping over, and you can proceed to enjoy your meal.... Behind this pizza trick lies a powerful mathematical result about curved surfaces, one that's so startling that its discoverer, the mathematical genius Carl Friedrich Gauss, named it Theorema Egregium, Latin for excellent or remarkable theorem." Bhatiya goes on to explain the theorem (he uses ants walking on the surfaces). "What does any of this have to do with pizza? Well, the pizza slice was flat before you picked it up (in math speak, it has zero Gaussian curvature). Gauss's remarkable theorem assures us that one direction of the slice must always remain flat - no matter how you bend it, the pizza must retain a trace of its original flatness. ... [B]y folding the pizza slice sideways, you're forcing it to become flat in the other direction - the one that points towards your mouth. Theorema egregium, indeed." And he goes on: "Once you recognize this idea, you start seeing it everywhere." Many nice examples follow.

Artur Avila in O Globo

Last month we read the French crowing about Artur Avila's Fields Medal. But it was much more significant in Brazil, where his was the very first. On September 4, 2014, O Globo ran "The winner of the mathematical 'Nobel' meets with President Dilma," with a nice photograph of Artur in the Palácio da Alvorada sitting next to Brazilian President Dilma Rousseff. The reporter, Filipe Matoso, tells us that they spoke for 45 minutes. Afterwards, Avila was asked about the usefulness of Math Olympiads. "Olympiads are one way, not the only one, that works well in Brazil and also in other countries, of detecting talent and motivating youngsters to do mathematics. The kind of problems used on the tests is, I would say, much more interesting than what gets presented in schools. In school the student only has contact with the arid part of mathematics, with rules and formulas everywhere. This the computer is right there and can do. The mathematician does things that the computer doesn't do, the creative and non-repetitive part." The article continues with remarks from the Minister of Education, who was also present at the meeting.

A much more wide-ranging interview was posted on O Globo's Lá Fora blog by Fernando Eichenberg, the newspaper's correspondent in Paris. "Equações de um gênio da matemática" ("Equations of a mathematical genius," August 14, 2014; features two photographs of Artur across the river from Notre Dame, shirtless and looking quite buff). Among many topics, the meaning of the prize for Brazil: "It's symbolically important. It's a big international prize and it certifies that high-level science is being done in the country. And this didn't just happen, it has been in the works for years. I got my education at IMPA a while ago; my Ph.D. is from 2001. There were already high-quality people who had been students of very high-quality people. There's a whole history." [My translations -TP]

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

Math Digest Math Digest
On Media Coverage of Math

Math Digest includes posts throughout each month by Anna Haensch (Drexel University) and Ben Pittman-Polletta (Boston University). These early-career mathematicians provide their unique insights (and occasionally videos, interviews and podcasts) on math-related topics recently covered by the media.

Recently posted:

"What comes next?" Sloane's database of sequences delivers an answer, by Anna Haensch

What makes the sequence 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 1, 1,… so cool? In his blog for The Guardian, Alex Bellos explains that along with its crazy mathematical properties, it also has the distinction of being the second entry in the Online Encyclopedia of Integer Sequences (OEIS). From the beloved Fibonacci sequence, to the more obscure Kolakoski sequence, the OEIS is a database of hundreds of thousands of integer sequences. It's a tremendous technical tool for mathematics researchers, but also a cool resource for the casually number-curious. 

Neil Sloane

The OIES was created by Neil Sloane (above) when he was a graduate student at Cornell University in the 1960s. He was working with one particularly obscure sequence of integers, and it occurred to him that it would be handy to have a record of every integer sequence in the world. It started as a stack of 3 x 5 index cards on his desk, after a few decades became a book with 5,000 sequences, and eventually in 1996 a website with 10,000 sequences. Since then, the website has started crowdsourcing à la Wikipedia, and it now gathers about 15,000 new sequences each year. 

The OEIS was honored at a conference at the Center for Discrete Mathematics & Theoretical Computer Science (DIMACS) at Rutgers University recently, coinciding with the encyclopedia's 50th anniversary, and founder Neil Sloane's 75th birthday--a twofold celebration! Recently, the OEIS and the work of Sloane also got a nod in Wordplay, The New York Times's blog on crossword puzzles.

But wait, I still haven't told the mathematical properties that make that sequence so cool. You can see that 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 1, 1,… is kind of boring, just 1's and 2's, so the numbers themselves aren't all that remarkable. But notice that they always appear in runs of 1 or 2. So if we count the numbers of 1's and 2's and make a sequence out of that, we get 1,2,2,1,1,2,1,2,2,1,… --the original sequence! Pretty neat. There is only one other sequence that does this, and you get it by just removing the leading 1 from the sequence above. 

See "Neil Sloane: the man who loved only integer sequences," by Alex Bello. Alex's Adventures in Numberland--The Guardian, 7 October 2014.

--- Anna Haensch

Also now on Math Digest: Martin Gardner's 100th, Katia Koelle in PopSci's Brilliant 10, movements of sharks, Bayes hits the big time, how crustaceans swim, the mathematics of bike sharing,...

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Books, plays and films about mathematics

Citations for reviews of books, plays, movies and television shows that are related to mathematics (but are not aimed solely at the professional mathematician). The alphabetical list includes links to the sources of reviews posted online, and covers reviews published in magazines, science journals and newspapers since 1996.

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