June 2013
See also: Blog on Math Blogs: Two mathematicians tour the mathematical blogosphere. Editors Brie Finegold and Evelyn Lamb, both PhD mathematicians, blog on blogs on topics related to mathematics research, applied mathematics, mathematicians, math in the news, mathematics education, math and the arts and more. "Heavy metal or blue jeans? No, just maths," by Peter Lynch. The Irish Times, 27 June 2013. In this brief article, University College Dublin meteorology professor Peter Lynch writes about the history of the examinations at Cambridge University known as the Mathematical Tripos, and a few of the exceptional students who have taken them. Students who earn firstclass honours degrees in these exams are called Wranglers: of these, the student with the highest score is Senior Wrangler. In 1854, that honor went to Edward Routh who "went on to become the most successful coach" of future Wranglers. (James Clark Maxwellof electromagnetism fametook second place that year.) In 1890, the highest scorer was Philippa Fawcett who, because of her gender, was not allowed to receive a degree from Cambridge: instead, she was declared to be "above Senior Wrangler." The nature of the Tripos has changed over the years, Lynch notes. For example, "substantial reforms, introduced in 1909, changed the Tripos" so that its focus began shifting to more pure mathematics. It has also shifted away from the dozens of hourslong, grueling "test of speed and wellpracticed problemsolving techniques" that were the "Old Tripos." Nevertheless, it remains the case that "great prestige attaches to the top few Wranglers, opening opportunities for their future professional careers." Image: G. H. Hardy, who placed fourth in 1898, a finish that he was disappointed in and remembered for life.  Claudia Clark "Mathematicians think like machines for perfect proofs," by Jacob Aron. New Scientist, 25 June 2013. In a world where verifying a groundbreaking new proof can be nearly impossible within reasonable time constraints, a group of researchers at Princeton is working on a method to build proofs that require no verification, because they were checked by a computer as they were constructed. The method relies on "automated proof assistants," computer code that checks the proof at each step to verify that it complies with a certain set of rules. Unlike traditional proofs, which are grounded in set theory, the new method uses type theory. A researcher who worked on the project explains that sets are like sand that, with some work, can be formed into a castle, whereas types are like different configurations of a collection of building blocks. Because logical statements about types are also considered types, the researchers assert that constructing a proof with type theory makes it selfproving. The transition to type theory proofs may not happen quickly, but the Princeton researchers believe the method is a small step toward improving the ability of computers to undertake complex mathematical proofs.  Lisa DeKeukeleare "Mathematics: 1,000 Years Old, and Still Hot," by Bryna Kra. The Chronicle of Higher Education, 24 June 2013. Even while President Obama's administration has called for more funding for research, development, and education in STEM fields, "mathematicians, and the profession as a whole, are under scrutiny and attack," according to Northwestern University professor of mathematics Bryna Kra. For example, the President's Council of Advisors on Science and Technology in 2012 called mathematics the "bottleneck that is currently keeping many students from STEM majors" and encourages the use of "faculty from mathematicsintensive disciplines other than mathematics" to teach collegelevel mathematics. And E.O. Wilson "recently claimed that 'many of the most successful scientists in the world today are mathematically no more than semiliterate.'" Kra calls such statements, and the discussions that follow, "a distraction from the main issue: We need to train more people to be scientifically literate, and mathematics is a core component of such training," beginning at an early age. First of all, she notes that "mathematics provides a tool box for the sciences," i.e., mathematical models. But more than that, "its logical reasoning underpins all scientific discoveries, and it has transformed the way we understand our world." Consider, for instance, the fact that "long before experimental evidence was available, Galileo used mathematics to predict that the earth revolves around the sun." Kra adds, "This is not to say that every scientist needs a degree in mathematics. But every scientist needs the rigorous language and logic afforded by mathematics."  Claudia Clark "Solve This Math Problem, Win a Million Bucks," by Matt Peckham. Time, 11 June 2013. Those Texas billionaireswho knows what they'll spend their money on! It could be a baseball team, a presiden(tial candida)cy, or even a math problem. D. Andrew Beal, a Texas billionaire who successfully dropped out of Baylor to become the 43rd billionaire on Forbes' list (of billionaires), is offering one million dollars to anyone who can prove the Beal Conjecture. The conjecture, which is named for "Andy," states that for positive integers a through c, and positive integers x through z larger than two, if a^{x}+ b^{y}=c^{z}, then a, b, and c have a common factor. Beal formulated his conjecture in 1993, while studying generalizations of Fermat's Last Theorem. After constructing several solution algorithms for the equation a^{x}+ b^{y}= c^{z} (x, y and z > 2), Beal found that every algorithm assumed a, b, and c had a common factor (see this page for background). With a colleague's help, he then programmed 15 computers to check all variable values up to 99, and in none of the resulting solutions were a, b, and c relatively prime. Beal advertised his discovery widely in the mathematical community, writing letters to a number of mathematicians and mathematical periodicals. Number theorists Harold Edwards, Edward Taft, and Jarrell Tunnell confirmed that the conjecture was new, and while Robert Tijdeman and Don Zagier independently formulated the conjecture in 1994, it bears Beal's name. Presumably after struggling to find a proof himself (we've all been there), Andy went to the University of North Texas' R. Daniel Mauldin, who suggested that he offer a prize for the proof (we've all wished we could be there). So in 1997, a prize of $5,000 was offered for a solution published in a refereed mathematics journal. Beal increased the prize to $100,000 in 2000, and then, this year, to $1 million. The prize is administered by the American Mathematical Society, which will award the prize money to the authors of a solutiona solution that must, I remind you, be published in a refereed mathematics journal, not in an email, a handwritten letter, or a series of bar napkins mailed to the AMS. We at the AMS, however, would like to warn you that some of the staff writers here at Math in the Media have a pretty good lead on a solution (relying on a vast generalization of Shinichi Mochizuki's interuniversal Teichmuller theory), so you should probably just give up. [Editor's note: He's kidding.] Read more about the prize.  Ben Polletta "The Grueling Application Process To Land A Job At The NSAThe Largest Employer Of Mathematicians In The USA," by Walter Hickey. Business Insider, 10 June 2013. It seems getting into the National Security Agency (NSA) is almost as hard as getting out is (for major whistleblowers, at least). Now the largest employer of mathematicians in the U.S. and possibly the world (although the exact number of mathematicians they employ is classified), the NSA was created in 1952 by Harry Truman, as a consolidation of the cryptanalysis units of the Army and Navy. While mathematical cryptography continues to play an important role in the NSA's operations (it's rumored), the organization's broadly defined role as the central authority for signals intelligence (as opposed to human intelligence, which is handled by the CIA) means that work there involves many branches of mathematics, including dynamical systems, topology, statistics, and graph theory. Besides mathematicians with PhDs, as well as bachelor's and master's degrees, the NSA employs a wide variety of other professionalsincluding engineers, computer scientists, and linguists. But while you don't need a PhD to work at the NSA, you do need to undergo an intensive application process, beginning with a comprehensive phone screening of your friends and acquaintances (a list of roommates from the past ten years was supposedly requested from one applicant) and the frighteningly named "long form background." Then there are interviews with the NSA's Mathematics Hiring Authority, drug and polygraph tests, a mathematical proficiency test, more interviews, and a talkmandatory for PhDs. All thisplus security clearancegets you a phenomenal salary, restricted hours (although the actual hours you will work are classified), and what seems to be a very pleasant work environmentas long as you're comfortable with "the fact that you don’t know what problem you’re actually solving." But I suppose you wouldn't apply for a job at the NSA if you didn't have a high level of trust in the U.S. governmentyou just have to hope that access to the agency's classified database of mathematical research doesn't do anything to undermine that trust.  Ben Polletta "Keys: Locking stuff up is easyunlocking is the key," by Clive Thompson. The New York Times Magazine, 9 June 2013. This was the Innovations Issue of the magazine, with short articles in the same vein as the weekly feature "Who Made That?" The relevant part of this article is the mathematical aspects of keys, specifically publickey cryptography. Thompson gives a little history and background on the RSA algorithm, which was published by Ronald L. Rivest, Adi Shamir, and Leonard Adelman in 1978. Although the three didn't realize it at the time, the algorithm and others like it gives online merchants a way to encrypt and protect your credit card number when shopping online.  Mike Breen "ISU professors find missing page from Lincoln’s 'ciphering book'," by Lenore Sobota. The Pantagraph, 8 June 2013. Sobota writes about the discovery of a missing page from Abraham Lincoln's "cyphering book" (the term used then). It was Nerida Ellerton and her husband Ken Clements, both mathematics professors at Illinois State University, who came across the missing page as they did research in the archives of Houghton Library at Harvard University. It is believed that the newly discovered page was written in 1825 by a 16yearold Lincoln, which makes it among the oldest Lincoln manuscripts. Cyphering books were school books used for various calculations involving, for example, simple interest, compound interest and discounts. Daniel Stowell, director of the Papers of Abraham Lincoln Project, said connecting this document to the Lincoln cyphering bookand the context provided by Ellerton and Clementsprovides more "insight into Lincoln's early life." He said it showed Lincoln's commitment to get things right, which he carried all his life. Just to be sure, Ellerton and Clements doublechecked Lincoln's math, which turned out to be accurate. In case you want to try to solve a problem from Lincoln's cyphering book, here is one: If four men in five days eat 7 pounds of bread, how much will be sufficient for 16 men in 15 days? See a YouTube video of Ellerton and Clements announcing their find. Image: Reproduction of a leaf from Abraham Lincoln's mathematical exercise book, ca. 1825. MS Am 1326. Gift of Christian A. Zabriskie, 1954. Houghton Library, Harvard University.  Baldur Hedinsson "Bayes' Theorem in the 21st Century," by Bradley Efron. Science, 7 June 2013, pages 11771178. Statistician and former applied mathematics journal editor Bradley Efron explains that although many scientists uses Bayes' theorem in their work, they do so incorrectly, generating widespread controversy over its use. Efron argues that the main problem is improper assumptions about the prior distribution of a data set. For example, using Bayes' theorem to determine the probability that a sonogram of twin boys depicts identical twins requires the knowledge that onethird of all sets of twins are identical. If a scientist works without this accurate information about prior experience and instead assumes that half of all sets of twins are identical, Bayes' theorem will yield the wrong answer. Efron explains that in some situations where the data consists of many parallel cases, such as comparisons of different types of genes, the parallel cases can act as the prior distribution for any one case, which is known as empirical Bayes. The trick, however, is knowing when to apply which method, and evaluating Bayesbased proofs with a critical eye.  Lisa DeKeukeleare "Stanford student gaining cult status for rethinking NBA philosophy," by Daniel Brown. Contra Costa Times, 3 June 2013. Who would have thought that math skills could get you on Forbes magazine's "30 Under 30" list of influential sports industry figures, putting you in league with LeBron James, Usain Bolt and Sidney Crosby? The Contra Costa Times has a piece about Muthu Alagappan, a math savvy medical student who is at the forefront of rethinking NBA philosophy. Two years ago, Alagappan interned at Ayasdi, a Palo Altobased startup company that has developed sophisticated software that makes sense of complicated data sets by arranging them in shapes, using topology. Alagappan came up with the idea of using this mathematical tool to decode basketball statistics and after crunching the numbers his result was that basketball's traditional five positions of point guard, shooting guard, small forward, power forward and center should be replaced by at least 10 distinct positions. Alagappan's finding has received the attention of the national media and NBA executives, so much that two NBA teams have secured formal partnerships with the young math whiz. Image: Courtesy of Ayasdi, Inc.  Baldur Hedinsson

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