A professor who has devoted his career to resolving the mysteries of higher mathematics has solved two separate, fundamental problems that have perplexed mathematicians for decades.
A Rutgers University-New Brunswick professor who has devoted his career to resolving the mysteries of higher mathematics has solved two separate, fundamental problems that have perplexed mathematicians for decades.
In a sense, Tiep and his colleagues have been following a blueprint of challenges Brauer laid out for them in a series of mathematical conjectures posed and published in the 1950-60s. Insights from the solution are likely to greatly enhance mathematicians' understanding of traces, Tiep said. The solution also provides insights that could lead to breakthroughs in other important problems in mathematics, including conjectures posed by the University of Florida mathematician John Thompson and the Israeli mathematician Alexander Lubotzky, he added.
The reverse operation must work, too, Tiep said: One needs to be able to reconstitute the shape from the sequence of numbers. But progress can come from internal reflection, Tiep said, and ideas burst forth when he is least expecting it. For the second breakthrough, Tiep worked with Robert Guralnick of the University of Southern California and Michael Larsen of Indiana University. On the first of two papers that tackle the mathematical problems on traces and solve them, Tiep worked with Guralnick and Larsen. Tiep and Larsen are co-authors of the second paper.
Math Puzzles Mathematical Modeling Statistics Computer Modeling Computer Science Educational Technology Communications
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