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X marks the unknown in algebra ' but X's origins are a math mystery
Posted by Mark Field from The Conversation in Algebra
Even though x is one of the least-used letters in the English alphabet, it appears throughout American culture ' from Stan Lee's X-Men superheroes to 'The X-Files' TV series. The letter x often symbolizes something unknown, with an air of mystery that can be appealing ' just look at Elon Musk with SpaceX, Tesla's Model X, and now X as a new name for Twitter. You might be most familiar with x from math class. Many algebra problems use x as a variable, to stand in for an unknown quantity. But why is x the letter chosen for this role' When and where did this convention begin' There are a few different explanations that math enthusiasts have put forward ' some citing translation, others pointing to a more typographic origin. Each theory has some merit, but historians of mathematics, like me, know that it's difficult to say for sure how x got its role in modern algebra. Algebra today is a branch of math in which abstract symbols are manipulated, using arithmetic, to solve different kinds of equations. But many ancient societies had well-developed mathematical systems and knowledge with no symbolic notation....
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He made linear algebra fun
Posted by Mark Field from MIT in Algebra
Strang received a BA and MA in 1957 as a Rhodes Scholar at Balliol College in Oxford, England, and a PhD in 1959 from the University of California at Los Angeles, where he was advised by Peter Henrici. His dissertation was "Difference Methods for Mixed Boundary Value Problems.' A CLE Moore instructor from 1959 to 1961, he joined the MIT faculty in 1962. A full professor in 1970, Strang focuses his research on mathematical analysis, linear algebra, and partial differential equations. 'He has had a tremendous impact on the teaching of mathematics to tens of thousands of students at MIT through his lectures, to countless students at other academic institutions through his textbooks, and to millions of people all over the globe through his online lectures and digital media,' says Professor Michel Goemans, head of the Department of Mathematics. His parents William and Mary Catherine Strang emigrated to the United States from Scotland. Strang and his sister Vivian grew up in Washington and Cincinnati, Ohio, and attended the Principia School in St. Louis, Missouri. He and his wife Jillian have three sons, David, John, and Robert, and 10 grandchildren....
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Faster big-data analysis
We live in the age of big data, but most of that data is “sparse.” Imagine, for instance, a massive table that mapped all of Amazon’s customers against all of its products, with a “1” for each product a given customer bought and a “0” otherwise. The table would be mostly zeroes. With sparse data, analytic algorithms end up doing a lot of addition and multiplication by zero, which is wasted computation. Programmers get around this by writing custom code to avoid zero entries, but that code is complex, and it generally applies only to a narrow range of problems. At the Association for Computing Machinery’s Conference on Systems, Programming, Languages and Applications: Software for Humanity (SPLASH), researchers from MIT, the French Alternative Energies and Atomic Energy Commission, and Adobe Research recently presented a new system that automatically produces code optimized for sparse data. That code offers a 100-fold speedup over existing, non-optimized software packages. And its performance is comparable to that of meticulously hand-optimized code for specific sparse-data operations, while requiring far less work on the programmer’s part....
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Victor Kac elected to the Accademia Nationale dei Lincei
Posted by Mark Field from MIT in Algebra
In 1977, math professor Victor Kac was a refugee from the Soviet Union living in Rome. As he was awaiting a U.S. visa so he could begin teaching at MIT, he met Claudio Procesi, an algebra professor at the Sapienza University of Rome, and other Italian mathematicians who set him up with a room in a family member’s home and helped him with paid talks in Pisa and with traveling throughout Italy. He said that those professors became his lifelong friends. More than 40 years later, he will return to Rome in November to be inducted as a foreign member of the Accademia Nationale dei Lincei, the Italian National Academy of Sciences, which is the oldest science academy in the world. “I was quite surprised and profoundly honored,” says Kac, who joins only 20 other Accademia foreign members in math, such as Fields medalists Pierre Deligne, Pierre-Louis Lions, David Mumford, and Shing-Tung Yau. Kac works in several areas of algebra and mathematical physics related to symmetries. “Victor’s development of Kac-Moody algebras has continued implications for mathematics, as well as theoretical physics research,” says Michael Sipser, dean of the MIT School of Science and the Donner Professor of Mathematics. “His work developing an algebraic theory of integrable systems, as well as his theory of Lie superalgebras, make him more than deserving of this extraordinary honor.”...
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