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Tropical Mathematics

by David Speyer (Massachusetts Institute of Technology) and Bernd Sturmfels (University of California at Berkeley)

Award: Carl B. Allendoerfer

Year of Award: 2009

Publication Information: Mathematics Magazine, vol. 82, no. 3, June 2009, pp. 163-173.

Summary: The adjective tropical was chosen by French mathematicians to honor Imre Simon, the Brazilian originator of min-plus algebra, which grew into this field. The basic object of study is the tropical semiring consisting of the real numbers R with a point at infinity under the operations of equals minimum and equals plus.

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About the Authors (From the Prizes and Awards Booklet, MathFest 2010) 

David Speyer has just begun serving as an associate professor of mathematics at the University of Michigan. Before that, he was a research fellow funded by the Clay Mathematics Institute. He has an A.B. and a Ph.D. in Mathematics, from Harvard University and the University of California Berkeley respectively. Speyer's research focuses on problems which combine questions of algebraic geometry and combinatorics; both the many such questions which arise in tropical geometry and those which occur in the study of classical algebraic varieties and representation theory. He blogs at

Bernd Sturmfels received doctoral degrees in Mathematics in 1987 from the University of Washington, Seattle, and the Technical University Darmstadt, Germany. After two postdoctoral years in Minneapolis and Linz, Austria, he taught at Cornell University before joining the University of California Berkeley in 1995, where he is Professor of Mathematics, Statistics and Computer Science. His honors include a National Young Investigator Fellowship, a Sloan Fellowship, a David and Lucile Packard Fellowship, a Clay Senior Scholarship, and an Alexander von Humboldt Senior Research Prize. Presently, he serves as Vice President of the American Mathematical Society. A leading experimentalist among mathematicians, Sturmfels has authored or edited fifteen books and 180 research articles, in the areas of combinatorics, algebraic geometry, polyhedral geometry, symbolic computation, and their applications. His current research focuses on algebraic methods in optimization, statistics, and computational biology.

Subject classification(s): Algebra and Number Theory | Abstract Algebra | Fields | Algebra | Applied Mathematics | Mathematical Biology | Discrete Mathematics | Combinatorics | Geometry and Topology | Algebraic Geometry
Publication Date: 
Wednesday, August 11, 2010