Donald G. Saari
Donald G. Saari | |
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Born | March 1940 (age 84) |
Nationality | American |
Alma mater | |
Awards |
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Scientific career | |
Fields | |
Institutions | |
Thesis | Singularities of the n-Body Problem of Celestial Mechanics (1967) |
Doctoral advisor | Harry Pollard |
Doctoral students |
Donald Gene Saari (born March 1940) is an American mathematician, a Distinguished Professor of Mathematics and Economics and former director of the Institute for Mathematical Behavioral Sciences at the University of California, Irvine. His research interests include the n-body problem, the Borda count voting system, and application of mathematics to the social sciences.
Contributions
Saari has been widely quoted as an expert in
In economics, Saari has shown that natural price mechanisms that set the rate of change of the price of a commodity proportional to its excess demand can lead to chaotic behavior rather than converging to an economic equilibrium, and has exhibited alternative price mechanisms that can be guaranteed to converge. However, as he also showed, such mechanisms require that the change in price be determined as a function of the whole system of prices and demands, rather than being reducible to a computation over pairs of commodities.[SS][S85][S95b]
In
Overviewing his work in these diverse areas, Saari has argued that his contributions to them are strongly related. In his view, Arrow's impossibility theorem in voting theory, the failure of simple pricing mechanisms, and the failure of previous analysis to explain the speeds of galactic rotation stem from the same cause: a reductionist approach that divides a complex problem (a multi-candidate election, a market, or a rotating galaxy) into multiple simpler subproblems (two-candidate elections for the Condorcet criterion, two-commodity markets, or the interactions between individual stars and the aggregate mass of the rest of the galaxy) but, in the process, loses information about the initial problem making it impossible to combine the subproblem solutions into an accurate solution to the whole problem.[S15] Saari credits some of his research success to a strategy of mulling over research problems on long road trips, without access to pencil or paper.[10]
Saari is also known for having some discussion with
Education and career
Saari grew up in a Finnish American copper mining community in the Upper Peninsula of Michigan, the son of two labor organizers there. Frequently in trouble for talking in his classes, he spent his detention time in private mathematics lessons with a local algebra teacher, Bill Brotherton. He was accepted to an Ivy League university, but his family could only afford to send him to the local state university, Michigan Technological University, which gave him a full scholarship. He majored in mathematics there, his third choice after previously trying chemistry and electrical engineering.[12] While attending Michigan Tech, Saari joined the Beta Chapter of Theta Tau Professional Engineering Fraternity.
He received his Bachelor of Science in Mathematics in 1962 from Michigan Tech, and his Master of Science and PhD in Mathematics from Purdue University in 1964 and 1967, respectively.[13] At Purdue, he began working with his doctoral advisor, Harry Pollard, because of a shared interest in pedagogy, but soon picked up Pollard's interests in celestial mechanics and wrote his doctoral dissertation on the n-body problem.[12]
After taking a temporary position at Yale University, he was hired at Northwestern University by Ralph P. Boas Jr., who had also been doing similar work in celestial mechanics.[12] From 1968 to 2000, he served as assistant, associate, and full professor of mathematics at Northwestern, and eventually became Pancoe Professor of Mathematics there.[14] He was led to mathematical economics by discovering the high caliber of the economics students enrolling in his courses in functional analysis,[12] and added a second position as Professor of Economics.[14] He then moved to the
He was editor in chief of the Bulletin of the American Mathematical Society from 1998 to 2005,[17] and published a book on the early history of the journal.[S03]
Awards and honors
- In 1985, with John B. Urenko, Saari received a root of a polynomial can exhibit chaotic behavior when its initial conditions are poorly chosen.[SU]
- He has honorary doctorates from Purdue University (1989), the University of Caen Normandy (1998), Michigan Technological University (1999), and the University of Turku (2009).[14]
- He received in 1995 the Chauvenet Prize for another of his papers, relating the history of the n-body problem and showing how to use spinors to eliminate some of the singularities arising in this problem.[S90]
- In 1999, he and Fabrice Valognes won the Allendoerfer Award for their work on the geometry of voting schemes.[SV]
- In 1999, a conference on celestial mechanics was held at Northwestern in honor of his 60th birthday.[7]
- In 2001 he was elected to the United States National Academy of Sciences,[18] and in 2004 he was named a Fellow of the American Academy of Arts and Sciences.[19]
- He gave the Pacific Institute for the Mathematical Sciences Distinguished Chair Lecture at the University of Victoria in 2002, speaking on the title "Mathematical Social Sciences, an oxymoron?".[20]
- He was elected as an external member of the Finnish Academy of Science and Letters in 2009,[21] and in the same year he became a fellow of the Society for Industrial and Applied Mathematics "for contributions to dynamics, voting, and economics".[22]
- In 2012 he became one of the inaugural fellows of the American Mathematical Society.[23]
- In 2018 he was elected as a foreign member of the Russian Academy of Sciences.[24]
- Asteroid M.P.C. 121135).[25]
Selected publications
Books
S94. |
S95a. | Basic Geometry of Voting, Springer-Verlag, 1995.
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S01a. | Chaotic Elections! A Mathematician Looks at Voting, American Mathematical Society, 2001.
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S01b. | Decisions and Elections; Explaining the Unexpected, Cambridge University Press, 2001.
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S05. | Collisions, Rings, and Other Newtonian N-Body Problems, American Mathematical Society, 2005.
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S08. | Disposing Dictators, Demystifying Voting Paradoxes: Social Choice Analysis, Cambridge University Press, 2008.
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Edited volumes
SX. | Hamiltonian Dynamics and Celestial Mechanics (with Z. Xia), Contemporary Mathematics 198, American Mathematical Society, 1996.
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S03. | The Way it Was: Mathematics From the Early Years of the Bulletin, American Mathematical Society, 2003.
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Papers
SS. | Saari, Donald G.; Simon, Carl P. (1978), "Effective price mechanisms" (PDF),
JSTOR 1911438 .
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SU. | Saari, Donald G.; Urenko, John B. (1984), "Newton's method, circle maps, and chaotic motion",
JSTOR 2322163
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S85. |
S90. | Saari, Donald G. (1990), "A Visit to the Newtonian N-body problem via elementary complex variables",
JSTOR 2323910
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S95b. | Saari, Donald (1995), "Mathematical complexity of simple economics", Notices of the American Mathematical Society, 42 (2): 222–230.
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SV. | Saari, Donald G.; Valognes, Fabrice (1998), "Geometry, voting, and paradoxes",
JSTOR 2690696
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S15. | Saari, Donald G. (2015), "From Arrow's Theorem to 'Dark Matter'",
S2CID 154799988
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References
- National Public Radio, October 14, 1995.
Craven, Jo (November 1, 1998), "In Some Elections, The 'Bullet' Rules: Tactic Has Voters Skipping 2nd Choice", The Washington Post, archived from the original on April 24, 2017, retrieved April 23, 2017.
"Has there been any progress in developing fairer ways for people to vote in elections?", Questions and Answers, Scientific American, October 1999, archived from the original on 2010-06-30, retrieved 2017-04-23.
Mackenzie, Dana (November 1, 2000), "May The Best Man Lose",Discover Magazine.
Guterman, Lila (November 3, 2000), "When Votes Don't Add Up", The Chronicle of Higher Education.
JSTOR 4014063.
Begley, Sharon (March 14, 2003), "How Beef-Hungry Voters Can Get Tofu for President", The Wall Street Journal.
Cooper, Michael (July 27, 2003), "How to Vote? Let Us Count the Ways", The New York Times.
Hoffman, Jascha (August 24, 2003), "Are All Elections Chaotic?",Boston Globe.
Begley, Sharon (January 26, 2008), "When Math Warps Elections", Newsweek
Schneider, Max (October 22, 2008), Voter Turnout Low, Apathy High Among Youngest Age Bracket, CBS News.
Uninformed 'vital for democracy', BBC News, December 16, 2011. - Orange County Register, June 23, 2001.
- ^ a b c See Vincent Merlin's review of Geometry of Voting.[S94]
- ^ a b Peterson, Ivars (October 1998), "How to Fix an Election", Mathtrek, Science News, archived from the original on April 23, 2004.
Peterson, Ivars (March 12, 2008), "Spoil-Proofing Elections", Mathtrek, Science News. - ^ Peterson, Ivars (October 2003), "Election Reversals", Mathtrek, Science News.
- ^ Gilbert, Curtis (September 24, 2009), IRV advocates fire back at math prof., Minnesota Public Radio.
- ^ MR 1885140. Proceedings of an International Conference on Celestial Mechanics December 15–19, 1999 Northwestern University, Evanston, Illinois. Preface, pp. ix–x.
- S2CID 16695757
- ^ Mackenzie, Dana (September 2013), "Rethinking "Star Soup"" (PDF), SIAM News, vol. 46, no. 7, archived from the original (PDF) on 2014-07-07, retrieved 2017-04-21
- Orange County Register.
- ^ Golab, Art (May 1, 1996), "NU Prof: Kaczynski Vowed to 'Get Even'", Chicago Sun-Times, archived from the original on April 24, 2017.
Walsh, Edward (May 2, 1996), "Teacher May Have Met Kaczynski in '78; Man Trying to Get Paper Published Was Rebuffed and Angry, He Says", The Washington Post. - ^ ISBN 978-0-691-14829-8.
- ^ Donald G. Saari at the Mathematics Genealogy Project
- ^ a b c Faculty profile, University of California, Irvine, retrieved 2017-04-22.
- ^ IMBS Faculty, Institute for Mathematical Behavioral Sciences, UC Irvine, retrieved 2018-12-26.
- ^ "Company Overview of Mathematical Sciences Research Institute, Donald Saari Ph.D., Trustee", bloomberg.com, 14 July 2023
- ^ Past Editorial Board Members, Bulletin of the American Mathematical Society, retrieved 2017-04-20.
- Orange County Register, May 2, 2001.
- Orange County Register, May 16, 2004.
American Academy Announces 2004 Fellows and Foreign Honorary Members, American Academy of Arts and Sciences, April 30, 2004, retrieved 2017-04-22. - ^ PIMS Distinguished Chair at the University of Victoria: Donald G. Saari, Pacific Institute for the Mathematical Sciences, archived from the original on January 2, 2007
- ^ Suomalaisen Tiedeakatemian ulkomaiset jäsenet [External members] (in Finnish), Finnish Academy of Science and Letters, retrieved 2017-04-22.
- ^ SIAM Fellows, Society for Industrial and Applied Mathematics, retrieved 2017-04-22.
- ^ List of Fellows, American Mathematical Society, retrieved 2013-07-11.
- ^ Saari elected to Russian Academy of Sciences, UC Irvine School of Social Sciences, December 3, 2018
- ^ "(9177) Donsaari", Minor Planet Center, retrieved 20 February 2020; "MPC/MPO/MPS Archive", Minor Planet Center, retrieved 20 February 2020