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Undecidability in Number Theory

Award: Chauvenet Prize

Year of Award: 2011

Publication Information: Notices Amer. Math. Soc, 55(2008), no. 3, 344-350.

Summary: Poonen strikes a balance between technicality (for the experts) and accessibility (for the rest of us). His story involves Turing machines, quantum computers, Diophantine sets, undecidability, prime-producing polynomials, and the Riemann hypothesis.

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About the Author: (From Prizes and Awards, Joint Mathematics Meetings 2011) Bjorn Poonen is the Claude Shannon Professor of Mathematics at MIT. He received an A.B. in mathematics and physics from Harvard in 1989, and a Ph.D. in mathematics at the University of California, Berkeley in 1994. After postdoctoral positions at MSRI and Princeton University, he served on the faculty at UC Berkeley until 2008, when he moved to MIT.

Poonen's research focuses on number theory and algebraic geometry, but occasionally he has worked also 39 in combinatorics, probability, and computer science. Poonen is the founding managing editor of Algebra & Number Theory. He has received the Packard, Rosenbaum, and Sloan fellowships as well as a Miller Professorship. Earlier, he was a four-time Putnam Competition winner, and the unique perfect scorer out of 385,000 participants in the 1985 American High School Mathematics Exam. At MIT, Poonen serves as Graduate Co-Chair. Finally, 12 mathematicians have completed a Ph.D. under his guidance.

MSC Codes: 
01Axx
Author(s): 
Bjorn Poonen (MIT)
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Publication Date: 
Friday, January 21, 2011
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Summary: 

Poonen strikes a balance between technicality (for the experts) and accessibility (for the rest of us). His story involves Turing machines, quantum computers, Diophantine sets, undecidability, prime-producing polynomials, and the Riemann hypothesis.

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