By now we've all heard of Big Data. We're aware of the vast storehouses of data points being gathered on every imaginable thing, or non-things, under the sun. And we're probably aware of the challenges of analyzing such a humongous amount of data, in particular, in a sea of so much information, how does one separate the real trends from the background noise? The MIT News Office explains how one MIT mathematics professor is turning these mountains of raw data into meaningful answers.
Photo by Sandy Huffaker
Professor Alice Guionnet (above) uses a branch of mathematics called random matrix theory. By taking the data and putting it in in cleverly designed arrays, or matrices, Guionnet is able to tease out the important trends and separate them from the noise. In particular, Guionnet is interested in using these techniques to predict the likelihood of extremely unusual events occurring. She likens this process to sewing a patchwork quilt -- after analyzing the data she is left with many partial solutions, and the key is in deciding how these components fit together.
This field is particularly exciting, Guionnet says, because it lies at the intersection of so many branches of mathematics. "it crosses over into different fields," she says, "probability theory, operator algebra, and random matrices -- and I’m trying to advance these three theories at the same time." The techniques are also valuable across disciplines and have been used to analyze trends in statistics, telecommunications, and even neurobiology.
In 2012 Guionnet was a recipient of the Simons Foundation Investigators Grant.
See "Mathematical patchwork," by Helen Knight. MIT News, 27 June 2014.
--- Anna Haensch (Posted 7/29/14)
In this Ask A Physicist entry, Goldberg provides a short history of mathematician Emmy Noether, including a description of some of the professional barriers she faced as a female mathematician. He then explains how she provided "the mathematical foundation for much of the standard model of particle physics." Noether recognized that there is a mathematical relationship between symmetries of the natural universe and what are known as conservation laws. While there is a fair amount of mathematics behind it, the upshot of what's known as Noether's Theorem is essentially: Every symmetry corresponds to a conservation law. [Her theorem predicts] that the laws of physics don't change if you adjust the clock of the universe or move to a different place or point in a different direction. Photo: Portrait of Emmy Noether before 1910, Public domain-US-no notice per Wikimedia Commons.
For additional reading, check out Goldberg's new book, The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality, from which this article is adapted.
See: "The Most Important Mathematician You've Never Heard Of," by Dr. Dave Goldberg. io9, 25 June 2014.
--- Claudia Clark
Joshua Batson, the current AMS-AAAS Media Fellow, finds a collection of dusty plaster and string models of mathematical surfaces tucked away in a display case at MIT. As it turns out these models were manufactured over 100 years ago. One of the major builders of models of mathematical surfaces at the time, and an advocate for visual intuition, was mathematician Felix Klein. His laboratory in Göttingen manufactured plaster models of mathematical surfaces in an attempt "to keep algebra anchored to the physical world." It was not long after Klein's appearance at the World's Fair in Chicago in 1893 with models from his laboratory for sale that "major American universities had ordered hundreds of surface models from thick catalogs, and had them shipped thousands of miles over the Atlantic." However, "in the early 1900s, there was a growing realization that arguments made from geometric intuition, from drawing pictures and making models, might not be airtight logically," and the use of models eventually fell out of favor.
Read more of the story behind these types of models -- including how they were made and their influence on modern artists and designers -- and see some of the models in the collection at the University of Illinois at Urbana-Champaign. Photo: UIUC Altgeld collection.
See: "This Is What Math Equations Look Like in 3-D," by Joshua Batson. Wired, 25 June 2014.
--- Claudia Clark
In June, Russian investor Yuri Milner for the first time awarded his new "Breakthrough Prize" in mathematics to five mathematicians, who each received $3 million. Milner developed this mathematics prize, as well as prizes in physics and the life sciences, as part of an effort to celebrate and attract attention to science in a society that more frequently recognizes athletes and entertainers. In addition to Milner, other financial contributors to the awards include Facebook CEO Mark Zuckerberg and Google co-founder Sergey Brin. Three of the five mathematics Breakthrough Prize recipients previously received the prestigious Fields Medal, and most have indicated that they intend to use some of the money to support other mathematicians. Dr. Terence Tao, a Breakthrough Award recipient for his work with prime numbers and fluid flow, indicated he might use some of his award to finance open-access mathematics journals or large-scale online collaboration on important problems.
See: "The Multimillion-Dollar Minds of 5 Mathematical Masters," by Kenneth Chang. New York Times, 23 June 2014.
--- Lisa DeKeukelaere
Just when I thought I my excitement over the World Cup couldn't reach a more fevered pitch, a recent piece in The New York Times explains that along with the exhilaration of victory and the subsequent swelling of national pride, we are seeing economic principles at play. London School of Economics professor and die-hard soccer--or rather, football--fan, Ignacio Palacios-Huerta, breaks it down.
Palacios-Huerta analyzed over 9,000 penalty kicks and found that they exhibited precisely the strategic behavior predicted by the economist John Forbes Nash, Jr. His principle, called Nash Equilibrium, says that for a game that requires multiple zero-sum moves, the best strategy is to vary your moves randomly. Penalty kicks, where one player takes a shot directly on goal, are a great example of this sort of game. Obviously it would be silly for a player to always shoot to the left or right, because then the goalie would know what to expect. But then again, a player might prefer to shoot with a dominant leg, so we wouldn't expect to see a perfect 50-50 split. And indeed Palacious-Herta found that players varied their ball placement exactly as he predicted: 60% to the right, 40% to the left.
Soccer games, Palacios-Huerta claims, are also a great place to test the Efficient Market Hypothesis. In the stock market, this principle basically says that the market reacts so quickly that the price of a stock always reflects its true value based on all known information. So if this is true, no matter how fast you buy, you can never really get a stock for less than it's worth. It should also mean that the price of a stock should stay relatively still in the absence of new information. Of course this is just a hypothesis, and quite difficult to test in the real stock market.
To support this hypothesis, researchers Karen Croxson and J. James Reade found that in soccer, even if a goal was scored moments before the clock stopped, half-time betting remained relatively stable through the break. Although people continue to place bets over halftime, the prices for betting updated "swiftly and fully" within moments of the goal.
But then again, sometimes--er, think the infamous Brazil vs. Coratia penalty shot--there are subtleties that seem beyond the scope of the most sophisticated numerical methods. Palacios-Heurtas covers this, along with the economics of fear and corruption in his book "Beautiful Game Theory: How Soccer Can Help Economics."
Oh, and of course, GO USA!
See "The Beautiful Data Set," by Iganatio Palacios-Huerta. The New York Times, 13 June 2014.
--- Anna Haensch
Richard Tapia is an outstanding applied mathematician and a first-generation Mexican-American who has worked hard to recruit other members of minority groups into mathematics and science. This article is a profile of Tapia that offers a window into how the mathematical community regards the need to encourage members of underrepresented minorities to join the field. The article reports that Tapia has been going around the country giving a talk titled "Racism in Mathematics: A Direct Factor in Underrepresentation." No doubt the title rankles some, and Tapia acknowledges that he chose it partly to get attention. Nevertheless he does believe that students from underrepresented minorities face extra hurdles that students who are white or Asian do not. For more than 40 years, Tapia has worked energetically and on many fronts to remove those hurdles and get more minority students on track to positions in top mathematics departments. His efforts have been recognized by many awards, including the 2014 Vannevar Bush Award, the highest honor the National Science Foundation gives for lifetime achievement. Photo: Rice University.
See "Minority voice," by Jeffrey Mervis. Science, 6 June 2014, pages 1076-1079 (unfortunately, you need an account to read the article online). (Posted 6/18/14)
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