Winning the U.S.A. Mathematical Olympiad three consecutive times starting in 1976 marked the early academic trajectory of Randall Dougherty. This American mathematician, born in 1961, has since navigated diverse fields within the discipline, ranging from set theory and logic to real analysis, discrete mathematics, computational geometry, information theory, and coding theory during his active career.
Academic Background
Dougherty completed his doctoral studies at the University of California, Berkeley, where he earned his Ph.D. in 1985 under the supervision of Jack Silver. His foundational training preceded an academic tenure at Ohio State University, where he held professional appointments. His formative years were defined by elite competitive success, securing medalist status at the International Mathematical Olympiad three times and earning distinction as a three-time Putnam Fellow in 1978, 1979, and 1980.
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In 1994, Dougherty collaborated with Matthew Foreman to address a longstanding problem posed by Marczewski. Their research, published in the Journal of the American Mathematical Society, demonstrated that the Banach-Tarski decomposition could be achieved using pieces possessing the Baire property. This resolution settled a mathematical question that had remained open for more than sixty years.
Network Coding Research
Beyond pure mathematics, Dougherty has contributed to the technical understanding of information flow. Working alongside Ken Zeger, he examined the limitations of network coding. Their findings, published in 2005 in IEEE Transactions on Information Theory, demonstrated that linear codes are insufficient to realize the full advantages of network coding, providing a critical assessment of architectural constraints in data transmission systems.
Fast facts
- Born: 1961
- Citizenship: United States
- Education: University of California, Berkeley
- Ph.D. Advisor: Jack Silver
- U.S.A. Mathematical Olympiad wins: 1976, 1977, 1978
- Putnam Fellow years: 1978, 1979, 1980
- Academic affiliation: Ohio State University
Questions readers ask
What is the primary significance of Dougherty's work on the Banach-Tarski paradox?
He proved that Banach-Tarski decompositions are possible using sets with the Baire property, solving a problem that had persisted for over six decades.
What did Dougherty demonstrate regarding network coding?
He showed that linear codes do not provide the full potential advantages required for network information flow.
Achievements
- Held posts at Ohio State University
- Fields: mathematics
