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Brie Finegold summarizes one blog post below, but it's not because she's gone part-time. She and Evelyn Lamb are now editors of the new Blog on Math Blogs, on which the two former AMS-AAAS Media Fellows tour the mathematical blogosphere, much as Brie has been doing here on Math Digest. Their first two posts are about the Mathematics of Planet Earth and math puzzles.
"Fresh off the 3D Printer: Henry Segerman's Mathematical Sculptures," by Megan Gambino. Collage of Arts and Sciences, 15 March 2013.
Mathematician and artist Henry Segerman aims to literally hand over his love of mathematics to the public. “That is the big advantage of 3D printing. There is an awful lot of data in there, but the real world has excellent bandwidth,” says Segerman. “Give someone a thing, and they see it immediately, with all its complexity. There is no wait time.” By creating images using computer software such as 3-D modeller Rhinoceros and then sending the images to a 3D printing service (Shapeways.com), Segerman is able to turn virtual models into real ones. In the past, Segerman was known as "Seifert Surface" on Second Life, where he created many virtual designs, including the net of a hypercube, various Seifert Surfaces, and Escher-like designs. To see more about his endeavors there, see the 2009 blog Not Possible In Real Life. You can also read Evelyn Lamb's description of some of Segerman's puzzles (co-created with mathematician Saul Schleimer). In the Collage article, Segerman does a great job explaining some of the ideas embedded in his sculpture in an accessible way. For instance, he discusses the distortion that occurs in moving the Klein bottle from 4D to 3D as analogous to the Mercator projection used to render the surface of the earth in 2D. Playing with the recently fabricated "Triple Gear," a link consisting of three notched rings would give almost anyone an appreciation of mathematics on a tactile level. Be sure to watch the video on YouTube mentioned in the caption. To see (or buy) his beautiful objects, check out Segerman's site.
--- Brie Finegold
"Kenneth I. Appel, Mathematician Who Harnessed Computer Power, Dies at 80," by Dennis Overbye. The New York Times, 29 April 2013, page A19;
Kenneth Appel, who along with Wolfgang Haken proved the Four Color Theorem in the 1970s, died April 19. They announced their proof of a conjecture, which had resisted resolution for a long time, to their department colleagues at the University of Illinois at Urbana-Champaign (UIUC) in 1976 by writing these words on the department blackboard: Four colors suffice. Their proof was the first major proof to incorporate computers and because of the large number of cases checked by the computer, many wondered whether the proof was verifiable. Overbye quotes Edward Frenkel (University of California, Berkeley), "Like a landmark Supreme Court case, the proof's legacy is still hotly debated." Appel left UIUC in 1993 to become chair at the University of New Hampshire, retiring in 2003. He was also very involve in politics and math education. For more on the Four Color Theorem, see a Feature Column article written by Joe Malkevitch.
--- Mike Breen
"What's the Mathematically Optimum Jury Size? Is it 12, Six, or One?" by Dana Mackenzie. Slate, 25 April 2013.
Most of us picture a jury as a group of 12 people, whose decision must be unanimous. Dana Mackenzie gives examples of states for which fewer people sit on a jury and for which unanimity is not required for a verdict. The Supreme Court has allowed juries with as few as six people on them, but rejected five-person juries, and has not required unanimity for 12-person juries, but has required it for those with six people. In a talk at the 2013 Joint Mathematics Meetings, Jeff Suzuki (Brooklyn College) examined the Supreme Court decisions on juries from a mathematical point of view, extending work from the 1990s by Rutgers University law professor George Thomas and his student Barry Pollack. They found some mathematical justification for the Supreme Court decisions, depending on the model used (for example, the decisions were justified for small juries if no juror was biased, but if there was bias, small juries can arrive at "bad" decisions). Will the Court use this work in future decisions on jury size and procedures? Thomas thinks it's unlikely, "The Supreme Court is remarkably uninterested in statistical research."
--- Mike Breen
"Here's How Little Math Americans Actually Use at Work," by Jordan Weissmann. The Atlantic, 24 April 2013.
Based on data by Michael Handel from his paper, "What Do People Do at Work? A Profile of U.S. Jobs from the Survey of Workplace Skills, Technology and Management Practices (STAMP)," Weissmann reports that "less than a quarter of employees do any calculations more complicated than basic fractions, and blue-collar workers generally do more advanced math than their white-collar friends." Jobs are broken down into upper and lower level white and blue collar categories, and one chart shows the percentage of people in those job categories who use "Any advanced math," "Algebra (basic)," "Geometry/trig," "Statistics," "Algebra (complex)," and "Calculus." Weissmann states "These numbers alone aren't an open and shut case against teaching complex math to most high school students. But they do suggest that what we teach today has little relationship to the broad demands of the job market," and concludes that this "hints at an argument for more high level vocational programs: It might help if students actually knew that those boring equations really one day would earn them a paycheck."
The article and the comments it has generated (see the blog Solvable by Radicals for a reply to this article) recall the controversial "Is Algebra Necessary?" Opinion in The New York Times last July. See a summary of that on Math Digest, and pieces with commentary by Tony Phillips in September 2012 and again in March 2013. At this writing Weissmann's piece has generated over 200 comments on the value of mathematics, how it is taught, and why math literacy is important. .
--- Annette Emerson
"Obama vs. Bieber: French Geeks Compute Who's Bigger on Twitter," by Marie Mawad. Bloomberg, 18 April 2013.
We are all tired of reading about startups, but how about a startup whose tagline is "Maintaining a day to day interaction between mathematical research and real world applications"? How about a startup in Paris' 9th arrondissement housing a "Mathematics Think Tank," and co-founded by two mathematicians to pioneer the applications of their theories to business, economics and beyond? Well, that startup would be MFG Labs, founded by Jean-Michel Lasry and Fields medalist Pierre-Louis Lions, in collaboration with entrepreneur Henri Verdier. While it is tough to piece together just what MFG Labs does, between Marie Mawad's short article and MFG Labs' own website, its various missions seem to include: developing Lasry and Lions' mean field game theory--a theory of strategic decision-making in large populations of interacting individuals--and its applications; providing data science consulting; and developing apps and other products, including an open-source, vector-based symbolic font or "icon set."
Part of the startup's strategy seems to be moving rapidly from concept to finished product--one way of keeping research-application interactivity high--and this has resulted in a variety of apps during the group's three years of operation: one for visualizing Facebook social networks, another that uses pictures on Flickr to map out the most likely tourist destinations in France, and what seems to be the company's star, Where Does My Tweet Go. WDMTG tracks individual tweets, through followers and retweets, to give a picture of their influence. By examining multiple tweets from the same twit (isn't that what they call Twitter users these days?), WDMTG can be used to gauge those users' level of impact. For example, while Justin Bieber is the twit with the most followers, those followers rarely find his tweets worth retweeting. Barack Obama, on the other hand, has fewer followers, but his tweets are more frequently retweeted, so Obama, surprisingly, works out to be the bigger twit--er, the twit with the bigger impact (as if that sounds any better). MFG employs about 20 people, including mathematicians, statisticians, web developers, and advertisers--and, as they say on their website, they're "always looking for talented and hard-working people to join us." They also say, "work at MFG Labs gets challenging, but you can always unwind at a local bistro," and "our offices in the heart of Paris are in one of the best areas for food and good living." So, you might want to keep an eye on them.
--- Ben Polletta
"Pascal’s shell game," by Burkard Polster and Marty Ross. The Age, 15 April 2013.
Columnists Polster and Ross examine the repeating triangle patterns on giant sea snail shells, in particular their similarity to Sierpinski's triangle, and a theory to explain how the shell patterns arise. Sierpinski's triangle--created by dividing an equilateral triangle into four equal sub-triangles, cutting out the middle sub-triangle, then repeating the process indefinitely with each of the remaining sub-triangles--is linked to Pascal's triangle, a pyramid-shaped number pattern in which the value of each number depends on the other numbers adjacent to it. Polster and Ross hypothesize that snails create a Sierpinski-like design by way of a biologically yet-undiscovered mechanism for choosing the color of a new cell on the growing lip of the shell based on existing, adjacent cells. The columnists emphasize that their explanation is just a theory--albeit a more likely one than a "Shell God" with a "magic eraser"--but they note the importance of the principle that complicated patterns are created by simple, localized mechanisms. [Note: In a later column, Polster and Ross look at Euler and the Google doodle that commemorated his 306th birthday.]
--- Lisa DeKeukeleare
"Want to Fight Disease? Do Your Math Homework," by Mitch Teich. WUWM, 12 April 2013.
This article summarizes an interview with mathematical biologist Carlos Castillo-Chavez (left), who recently gave the annual Marden Lecture in Mathematics at the University of Wisconsin–Milwaukee. Dr. Castillo-Chavez, a professor at Arizona State University, initially spoke about the value of using mathematics to model, and ultimately decrease, the spread of disease, as well as the importance of having an interdisciplinary background: "Today, most of the problems you want to solve … require multiple expertise." He talked about his background, starting with his work in a cheese factory, which led to his determination to go to college. Castillo-Chavez also described two of the challenges he faced: being one of two Hispanic students at University of Wisconsin–Stevens Point, as well as a particular financial challenge that the chancellor of the university helped him overcome. Castillo-Chavez also spoke about the institutional and economic hurdles that students who have been underrepresented in the STEM fields still face. Finally, he described what he sees as the role of state universities: they need to provide the type of intellectual opportunities and challenges that Ivy League universities provide. In addition, these universities need to provide students with the opportunity to participate in state of the art research that will have a positive impact on society. "When you receive taxpayers' money, you have to be accountable for what you do: serving first the people of your state and then your country is fundamental." Photo by Tom Story.
--- Claudia Clark
"Students honored for research," by Meghan Rosen. Science News, 6 April 2013, page 28.
Results of the 2013 Intel Science Talent Search (ISTS) have been announced. Three math projects were among the top 10 finishers:
Sara Volz of Colorado Springs won the first-place prize of $100,000 for her project on algae-based biofuels. The ISTS, which is administered by the Society for Science and the Public (SSP), began in 1942. Intel has been the sponsor since 1998. Photos: Chris Ayers Photography/SSP.
--- Mike Breen
"Great Scientist ≠ Good at Math," by E.O. Wilson. The Wall Street Journal, 5 April 2013.
In this editorial, which is thought-provoking, insightful and mostly sensible, renowned evolutionary biologist E.O. Wilson makes the case that success as a scientist does not require a high level of mathematical proficiency. Wilson's goal here is to stem "a hemorrhage of brain power"--namely, the loss (to science) of students who see their perceived mathematical illiteracy as an insurmountable obstacle to pursuing a scientific career. To this end, he offers reassurances that will ring bells for many mathematicians: the notion that "superior mathematical ability is similar to fluency in foreign languages" and improves with immersion and practice; the importance of intuition and imagination in scientific discovery; and the truism that scientific discovery often bears little resemblance to the careful organization of fact and theory presented in textbooks--"Real progress," he writes, "comes in the field writing notes, at the office amid a litter of doodled paper, in the hallway struggling to explain something to a friend, or eating lunch alone." Offering his experience picking up calculus as a tenured professor at age 32, Wilson suggests that excellence can be achieved by researchers at any level of mathematical competence, and that it is easy to find mathematicians and statisticians to collaborate with when investigations lead into quantitative territory.
Unfortunately, while making these points, Wilson overgeneralizes his experiences as a biologist somewhat, making statements that account for the 243 sometimes contentious comments following the article (as of this writing). He asserts that "exceptional mathematical fluency is required in only a few disciplines" but then later suggests that "most of physics and chemistry" "require a close alternation of experiment and quantitative analysis". He makes the perhaps debatable claims that "pioneers in science only rarely make discoveries by extracting ideas from pure mathematics" and that of mathematical models in biology "no more than 10% have any lasting value." More interesting than this insensitivity to the feelings of physical and quantitative scientists is Wilson's characterization of the ingredients necessary for conceptual advances in science: careful organization and close, focused study of the known facts surrounding a phenomenon, followed by the forging of creative links between these facts. Essential to this second step is "the ability to form concepts, during which the researcher conjures images and processes by intuition." While Wilson sees this step as divorced from mathematics, many mathematicians would disagree, and the connection between mathematics--which provides a vast library of complex concepts and structures--and this imaginative process of discovery is unclear. Does mathematical expertise expand or shackle the conceptual imagination? My own experience as a mathematician working in the biological sciences suggests that it does both. Mathematical fluency can allow the rapid deployment of time-tested structures in appropriate contexts, but new observations often require the invention of fundamentally new structures--and new mathematics in turn--which can be hindered by an overly dogmatic mathematical perspective. Of course, the struggle to make the existing methods of solution fit the problem at hand--or, failing that, to come up with new ones--occurs in both biology and mathematics proper. It just goes to show that, no matter their level of mathematical literacy, all scientists experience the same intellectual frustrations.
--- Ben Polletta
"Solid or Liquid? Physicists Redefine States of Matter," by Natalie Wolchover (Simons Science News). Wired, 5 April 2013.
Scientists have long explained the difference between liquids and solids based on the fact that liquids flow and solids do not, but this explanation fails to account properly for materials such as glass or so-called "quasicrystals," which are rigid but have a non-repeating crystalline structure. An article in the March issue of the Notices of the American Mathematical Society ("A Revolutionary Material," by Charles Radin, pp. 310-315) presents a new approach, based on research by French and American scientists, that focuses on a material's response to shear, or twisting forces. Liquids, for example, offer little resistance to shear, but solids do not easily change shape. The American researchers arrived at their novel approach using complicated calculations to model a material's response to shear without using equations that assume that the material is edgeless, unlike typical calculations by physicists. The French models also hinge on response to shear, but instead examined a material's viscosity--the response to changes in shear over time--as a measure of the rate of flow.
--- Lisa DeKeukeleare
"Applicants’ weak math skills sum up problem for those looking to hire," by Renee Schoof. The Seattle Times, 4 April 2013.
The writer of this article begins by describing a test that Tacoma, Washington manufacturer General Plastics gives to potential employees. Test-takers are asked to perform unit conversions, read a tape measure, and calculate density, among other tasks. However, for every 10 high-school educated persons taking the test, only 1 passes it. This concerns company executive Eric Hahn, who sits on an aerospace workforce-training committee; he notes that most other suppliers across the state in this industry are seeing the same thing. Jacey Wilkins, a spokeswoman for the Manufacturing Institute, also notes that math is needed "even" for production jobs because they are "incredibly complex and integrate multiple functions and systems." This spells trouble for job seekers without basic math knowledge, according to Linda Nguyen, CEO of Workforce Central, "Manufacturers are willing to train people about the specifics of their machines and technology. But they can't afford to hire someone who needs to relearn basic math."
However, educators are aware of and working to address this problem. Groups like the National Council of Teachers of Mathematics are trying to "help teachers teach mathematics so kids make sense of what they're doing and it really does stick beyond what they learn in class." Implementation of the Common Core State Standards will also have an impact on math learning. Sam Houston, president and CEO of the North Carolina Science, Math, and Technology Education Center, points out that these standards will correspond to what students need to know for college and career success. "In the hands of trained professionals, the Common Core should give everyone a better means to answer the question, 'Why do I need to know this?'"
--- Claudia Clark
"Mathematician who speaks at UNR Thursday gives advice for amateur gamblers, has surprising answer on why people should learn math." Reno Gazette Journal, 2 April 2013.
The Reno Gazette Journal talked math via Skype with mathematician and author Steven Strogatz (left) prior to his lecture "Doing Math in Public" at the University of Nevada, Reno. Fittingly for Reno, the first topic of conversation was gambling. Strogatz noted that there have been many mathematicians among skilled gamblers, but his main advice for gamesters was to keep the betting sessions brief. The shorter you play, the better odds you have of walking away with a profit. Asked about the need to know math in the smart-phone age, Strogatz surprisingly answered that it isn´t really necessary to know math. Just as humans don't need music or art they don´t need math, but like music and art, math makes life richer, more beautiful and more interesting. Strogatz noted an additional advantage of mathematical understanding, the many professional opportunities it opens up that otherwise would be out of reach. Pressed on the question as to which math skills are most important today, Strogatz answered that some understanding of risk, volatility and uncertainty, which are all a part of a good probability and statistics class, is essential today. Photo: Cornell University.
--- Baldur Hedinsson
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