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Past MAA Distinguished Lectures

Glen Van Brummelen, Quest University Canada
Monday, March 10, 2014

cosponsored by HOM SIGMAA (History of Mathematics)

Abstract: Although all triangles (plane and spherical) could already be solved in the early 16th century, trigonometry advanced almost beyond recognition by the time logarithms were invented in 1614. From just the sine function, all six of our current functions were born. With the new functions and the numerical tables that came with them, the theory could be enhanced, simplified, and made more elegant. Most crucially, rather than existing simply as a handmaiden to the astronomy that had given it life, trigonometry became a powerful tool in geography, optics, navigation, surveying, even architecture. This was the period, and trigonometry was the subject, that placed mathematics at the center of a quantitative scientific approach to our world that still flourishes today.

Biography: Glen Van Brummelen of Quest University Canada is a historian of mathematics, especially trigonometry and astronomy in ancient Greece and medieval Islam. He is president of the Canadian Society for History and Philosophy of Mathematics (2012-14), and governor-at-large for Canadian members of the Mathematical Association of America (2013-16). In addition to authoring 30 scholarly and 15 encyclopedia articles, he is co-editor of Mathematics and the Historian's Craft (Springer) and author the first history of trigonometry in over a century (The Mathematics of the Heavens and the Earth: The Early History of Trigonometry, Princeton University Press). Van Brummelen recently published Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry (Princeton) and finished co-editing with Nathan Sidoli From Alexandria, Through Baghdad: Surveys and Studies in the Ancient Greek and Medieval Islamic Mathematical Sciences in honor of J. L. Berggren (Springer, 2014).

Read more about Van Brummelen's lecture.

Laura Taalman, James Madison University
Wednesday, February 19, 2014

Abstract: For a pure mathematician, mathematics is a set of abstract constructs completely separated from reality, and using technology to explore mathematics can seem like, well, cheating. But with the rise of undergraduate research in mathematics comes a need for elementary unsolved problems that students can pursue. Modern technology can help fill this need and support exploratory, investigative mathematics, even for those of us who are old-school mathematical purists at heart. Going a step further, the recently accessible technology of 3D printing can take abstract mathematical objects and literally make them real. A 3D printing demonstration will accompany this talk.

Biography: Laura Taalman is a Professor in the Department of Mathematics and Statistics at James Madison University, where she joined the faculty after graduate work at Duke University and undergraduate work at the University of Chicago. Her mathematical research interests include singular algebraic geometry, knot theory, and the mathematics of games and puzzles. Dr. Taalman is the director of the JMU MakerLab mathematical 3D-printing lab and the JMU 3-SPACE general education 3D-printing classroom. She is a co-author of the recent Taalman/Kohn Calculus textbook and seven books on Sudoku and mathematics. In 2013 she was a recipient of the Outstanding Faculty Award from the State Council of Higher Education for Virginia, and has received the Alder Award and the Trevor Evans Award from the Mathematical Association of America.

Read more about Taalman's lecture.

William Dunham, Muhlenberg College
Tuesday, January 28, 2014

Abstract: Almost fifty years ago, Cambridge University Press published the correspondence of Isaac Newton, a seven-volume, 3000-page collection of letters that provides insight into this great, if difficult, genius. In this talk, I share my favorite examples of Newton as correspondent. From his earliest known letter in 1661 (where he scolded a friend for being drunk), through exchanges with Leibniz, Locke, and others, to documents from his days at the Mint in London, these writings give glimpses of Newton at his best…and his worst. 

To add a bit of mathematics to the narrative, I stop to take a look at his first great mathematical discovery—the generalized binomial theorem as described in a 1676 letter to Leibniz—and show how “…the extraction of roots is much simplified by this theorem.” I’ll end with Newton’s most-quoted line about standing on the shoulders of giants and how my search for its place of origin led me, improbably, to a library in Philadelphia.

Biography: William Dunham has been the Truman Koehler Professor of Mathematics at Muhlenberg College since 1992. His books Journey Through Genius: The Great Theorems of Mathematics (Wiley, 1990) and The Mathematical Universe (Wiley, 1994) were alternate selections for Book-of-the-Month Club, and the latter received the Association of American Publishers Award as the Best Mathematics Book of 1994. His next two books, Euler: The Master of Us All (MAA, 1999) and The Calculus Gallery: Masterpieces from Newton to Lebesgue (Princeton, 2005), were designated among their year’s Outstanding Academic Titles by Choice magazine of the American Library Association, and the Euler book received the MAA’s Beckenbach Prize in 2008. He has also edited a volume, The Genius of Euler: Selections from His Life and Work (MAA, 2007) and is featured in the Teaching Company’s DVD, “Great Thinkers, Great Theorems.”

Dunham’s interest in the history of mathematics has led to numerous talks at colleges and universities around the country and has carried him to speaking engagements at the Smithsonian Institution, on NPR’s “Talk of the Nation: Science Friday,” and at the Swiss Embassy in Washington, DC. In the fall of 2008 and again in the spring of 2013, he was a visiting professor at Harvard University, where he taught an undergraduate course on the mathematics of Leonhard Euler (course title: “Much Ado About Everything”). After stepping down from his Muhlenberg position in December of 2013, Dunham will be a visitor at Princeton University (spring, 2014) and then at the University of Pennsylvania (fall, 2014), and he hopes to continue as an itinerant math historian into the foreseeable future.

Read more about Dunham's lecture.

Steven J. Brams, New York University
Thursday, November 14, 2013

Abstract: While game theory finds frequent application in economics, political science, psychology, sociology, and evolutionary biology, mathematical calculations of strategic choice are seldom associated with the worlds of literature, history, philosophy, religion, or law.   

But game theory can illuminate wrenching choices, including those fueled by such emotions as anger, jealousy, or love. These will be illustrated by some of the following: Abraham's biblical decision to offer his son, Isaac, for sacrifice when God commanded him to do so; difficult and sometimes murderous choices of characters in Aristophanes’s Lysistrata, Shakespeare's Hamlet and Macbeth, and Joseph Heller’s Catch-22; and historical choices by the Supreme Court, presidents, and other leaders, especially in crises and wars. 

Biography: Steven J. Brams is Professor of Politics at New York University and the author, co-author, or co-editor of 18 books and more than 250 articles. His books include Theory of Moves (Cambridge, 1994) and, co-authored with Alan D. Taylor, Fair Division: From Cake-Cutting to Dispute Resolution (Cambridge, 1996) and The Win-Win Solution: Guaranteeing Fair Shares to Everybody (Norton, 1999). His newest books are Mathematics and Democracy: Designing Better Voting and Fair-Division Procedures (Princeton, 2008) and Game Theory and the Humanities: Bridging Two Worlds (MIT, 2011). He holds two patents for fair-division algorithms and is chairman of the advisory board of Fair Outcomes, Inc.

Brams has applied game theory and social-choice theory to voting and elections, bargaining and fairness, international relations, and the Bible, theology, and literature. He is a former president of the Peace Science Society (1990-91) and of the Public Choice Society (2004-2006). He is a Fellow of the American Association for the Advancement of Science (1986), a Guggenheim Fellow (1986-87), and was a Visiting Scholar at the Russell Sage Foundation (1998-99). 

Read more about Brams's lecture.

Arthur Benjamin, Harvey Mudd College
Wednesday, October 23, 2013

Abstract: Art Benjamin is a mathematician and a magician. In this performance, he will demonstrate and explain how to mentally multiply numbers faster than a calculator, how to memorize pi to 100 places, how to calculate the day of the week of any date in history, and other amazing feats of mind. He has presented his mixture of math and magic to audiences all over the world.

"The Magic of Math and Mental Calculation," co-sponsored by Math for America-DC, is a Martin Gardner Celebration of Mind event. 

Biography: Arthur Benjamin earned his B.S. in Applied Mathematics from Carnegie Mellon and his Ph.D. in Mathematical Sciences from Johns Hopkins. Since 1989, he has taught at Harvey Mudd College, where he is Professor of Mathematics and past chair. In 2000, he received the Haimo Award for Distinguished Teaching from the Mathematical Association of America, and served as the MAA's Pólya Lecturer from 2006 to 2008.

His research interests include combinatorics and number theory, with a special fondness for Fibonacci numbers. Many of these ideas appear in his book (co-authored with Jennifer Quinn), Proofs That Really Count: The Art of Combinatorial Proof, published by MAA. In 2006, that book received the MAA's Beckenbach Book Prize. Professors Benjamin and Quinn were the editors of Math Horizons magazine from 2004 through 2008. He is a Fellow of the American Mathematical Society. 

Dr. Benjamin has created four DVD courses for The Great Courses on The Joy of MathematicsDiscrete MathematicsThe Secrets of Mental Math, and The Mathematics of Games and Puzzles. He is a past winner of the American Backgammon Tour. 

He is also a magician who performs his mixture of math and magic to audiences all over the world, including the Magic Castle in Hollywood. He has demonstrated and explained his calculating talents in his book Secrets of Mental Math and on numerous television and radio programs, including The Today Show, CNN, and National Public Radio. He has been featured in Scientific AmericanOmniDiscoverPeopleEsquireNew York TimesLos Angeles Times, and Reader's Digest. In 2005, Reader's Digest called him "America's Best Math Whiz."

Read more about Benjamin's presentation.