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| '''Jeffrey Clark Lagarias''' (born November, 1949 in [[Pittsburgh, Pennsylvania|Pittsburgh]], [[Pennsylvania]], [[USA]]) is a [[mathematician]] and professor at the [[University of Michigan]].
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| == Education ==
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| While in high school in 1966, Lagarias studied [[astronomy]] at the [[Summer Science Program]].
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| He completed an S.B. and S.M. in Mathematics at the [[Massachusetts Institute of Technology]] in 1972.<ref name=cv>{{cite web|title=Jeffrey C. Lagarias|url=http://www.math.lsa.umich.edu/~lagarias/PROFESSIONAL/VITA/vita2013a.pdf|work=CV}}</ref> The title of his thesis was "Evaluation of certain character sums".<ref name=cv/> He was a [[Putnam Fellow]] at MIT in 1970.<ref name=cv/> He received his Ph.D. in Mathematics from MIT for his thesis "The 4-part of the class group of a quadratic field", in 1974.<ref name=cv/><ref name=um>{{cite web|title=Jeffrey Lagarias, Professor|url=http://www.math.lsa.umich.edu/people/facultyDetail.php?uniqname=lagarias|publisher=University of Michigan}}</ref> His advisor for both his masters and Ph.D was [[Harold Stark]].<ref name=cv/>
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| == Career ==
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| In 1975 he joined [[AT&T Bell Laboratories]] and eventually became [[Distinguished Member of Technical Staff]]. Since 1995, he has been a Technology Consultant at AT&T Research Laboratories. In 2002, he moved to [[Michigan]] to work at the University and settle down with his family.
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| While his recent work has been in [[theoretical computer science]], his original training was in analytic [[algebraic number theory]]. He has since worked in many areas, both pure and applied, and considers himself a mathematical generalist. Lagarias discovered an elementary problem that is equivalent to the [[Riemann hypothesis]], namely whether
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| for all ''n'' > 0, we have
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| :<math> \sigma(n) \le H_n + e^{H_n} \ln H_n \, </math>
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| with equality only when ''n'' = 1. Here ''H''<sub>''n''</sub> is the ''n''th [[harmonic number]], the sum of the reciprocals of the first <math> n </math> positive integers, and ''σ''(''n'') is the [[divisor function]], the sum of the positive divisors of ''n''.<ref>http://front.math.ucdavis.edu/math.NT/0008177</ref> | |
| He disproved [[Keller's conjecture]] in dimensions at least 10.
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| Lagarias has also done work on the [[Collatz conjecture]] and [[Li's criterion]].
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| ==Awards and honors==
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| In 1987 he received a [[Lester R. Ford]] award from the [[Mathematical Association of America]].<ref>http://oldweb.cecm.sfu.ca/CMS-95W/lagarias.html</ref>
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| In 2012 he became a fellow of the [[American Mathematical Society]].<ref>[http://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 2013-01-27.</ref>
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| == External links == | |
| *{{MathGenealogy |id=36350}}
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| *[http://www.math.lsa.umich.edu/~lagarias/ Jeffrey Clark Lagarias homepage], University of Michigan
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| == References ==
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| {{reflist}}
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| {{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
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| | NAME = Lagarias, Jeffrey
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| | ALTERNATIVE NAMES =
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| | SHORT DESCRIPTION = American mathematician
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| | DATE OF BIRTH = 1949
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| | PLACE OF BIRTH =
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| | DATE OF DEATH =
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| | PLACE OF DEATH =
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| }}
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| {{DEFAULTSORT:Lagarias, Jeffrey}}
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| [[Category:1949 births]]
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| [[Category:Living people]]
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| [[Category:People from Pittsburgh, Pennsylvania]]
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| [[Category:Massachusetts Institute of Technology alumni]]
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| [[Category:Scientists at Bell Labs]]
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| [[Category:20th-century mathematicians]]
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| [[Category:21st-century mathematicians]]
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| [[Category:Number theorists]]
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| [[Category:American computer scientists]]
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| [[Category:Theoretical computer scientists]]
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| [[Category:University of Michigan faculty]]
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| [[Category:Putnam Fellows]]
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| [[Category:Summer Science Program]]
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| [[Category:Fellows of the American Mathematical Society]]
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