Jeffrey Lagarias
{{short description|American mathematician}}
{{ Infobox scientist
| name = Jeffrey Clark Lagarias
| image =
| image_size =
| caption =
| birth_date = {{birth-date and age |November 16, 1949}}
| birth_place = Pittsburgh, Pennsylvania
| death_date =
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| nationality = American
| fields = Mathematics
| workplaces = University of Michigan (2004–)
| alma_mater = MIT (Ph.D., S.M., S.B.)
| thesis_title = The 4-part of the Class Group of a Quadratic Field
| thesis_url =
| thesis_year = 1974
| doctoral_advisor = Harold Stark
| doctoral_students =
| known_for =
| awards = Lester R. Ford Award (1986)
}}
Jeffrey Clark Lagarias (born November 16, 1949, in Pittsburgh, Pennsylvania, United States) is a mathematician and professor at the University of Michigan.
Education
While in high school in 1966, Lagarias studied astronomy at the Summer Science Program.
He completed an S.B. and S.M. in Mathematics at the Massachusetts Institute of Technology in 1972.{{cite web|title=Jeffrey C. Lagarias|url=http://www.math.lsa.umich.edu/~lagarias/PROFESSIONAL/VITA/vita2013a.pdf|work=CV}} The title of his thesis was "Evaluation of certain character sums". He was a Putnam Fellow at MIT in 1970.{{cite web |title=Putnam Competition Individual and Team Winners |url=http://www.maa.org/programs/maa-awards/putnam-competition-individual-and-team-winners |publisher=Mathematical Association of America |access-date=December 13, 2021 |archive-date=March 12, 2014 |archive-url=https://web.archive.org/web/20140312205244/http://www.maa.org/programs/maa-awards/putnam-competition-individual-and-team-winners |url-status=dead }} 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.{{cite web|title=Jeffrey Lagarias, Professor|url=http://www.math.lsa.umich.edu/people/facultyDetail.php?uniqname=lagarias|publisher=University of Michigan|access-date=2010-11-09|archive-date=2010-11-18|archive-url=https://web.archive.org/web/20101118201429/http://www.math.lsa.umich.edu/people/facultyDetail.php?uniqname=lagarias|url-status=dead}} His advisor for both his masters and Ph.D was Harold Stark.
Career
In 1974, he joined AT&T Bell Laboratories and eventually became a member of technical staff. From 1995 to 2004, he was a Technology Consultant at AT&T Research Laboratories. In 2004, he moved to the University of Michigan as a professor of mathematics.
Research
Lagarias originally worked in analytic algebraic number theory. His later work has been in theoretical computer science.{{citation needed|date=July 2021}}
Lagarias discovered an elementary problem that is equivalent to the Riemann hypothesis, namely whether
for all n > 0, we have
:
with equality only when n = 1. Here Hn is the nth harmonic number, the sum of the reciprocals of the first positive integers, and σ(n) is the divisor function, the sum of the positive divisors of n.{{Cite journal|arxiv = math/0008177|last1 = Lagarias|first1 = Jeffrey C.|title = An Elementary Problem Equivalent to the Riemann Hypothesis|journal = Amer. Math. Monthly|year = 2002|volume = 109|issue = 6|pages = 534–543|doi = 10.1080/00029890.2002.11919883|s2cid = 218549013}}
He disproved Keller's conjecture in dimensions at least 10. Lagarias has also done work on the Collatz conjecture and Li's criterion and has written several highly cited papers in symbolic computation with Dave Bayer.{{Citation needed|date=January 2016}}
Awards and honors
Lagarias received in 1986 a Lester R. Ford award from the Mathematical Association of America{{cite journal|title=The 3x + 1 Problem and Its Generalizations|journal=Amer. Math. Monthly|year=1985|volume=92|pages=3–23|doi=10.2307/2322189|jstor=2322189|url=http://www.maa.org/programs/maa-awards/writing-awards/the-3x-1-problem-and-its-generalizations|last1=Lagarias|first1=Jeffrey C.|issue=1}} and again in 2007.{{cite journal|title=Wild and Wooley Numbers|journal=Amer. Math. Monthly|volume=113|year=2006|pages=97–106|url=http://www.maa.org/programs/maa-awards/writing-awards/wild-and-wooley-numbers|doi=10.2307/27641862|jstor=27641862|last1=Lagarias|first1=Jeffrey C.|issue=2}}{{cite web|url=https://maa.org/programs-and-communities/member-communities/maa-awards/writing-awards/paul-halmos-lester-ford-awards|title=Lester R. Ford Awards|work=maa.org|publisher=Mathematical Association of America|access-date=2019-08-16}}
In 2012, he became a fellow of the American Mathematical Society.[https://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 2013-01-27.
In 2024 he was elected as a member of the National Academy of Sciences.{{cite web|url=https://www.nasonline.org/news-and-multimedia/news/2024-nas-election.html|date=April 30, 2024|title=National Academy of Sciences Elects Members and International Members}}
References
{{reflist}}
External links
{{Scholia}}
- {{MathGenealogy |id=36350}}
- [http://www.math.lsa.umich.edu/~lagarias/ Jeffrey Clark Lagarias homepage], University of Michigan
{{Authority control}}
{{DEFAULTSORT:Lagarias, Jeffrey}}
Category:Scientists from Pittsburgh
Category:Massachusetts Institute of Technology School of Science alumni
Category:Scientists at Bell Labs
Category:20th-century American mathematicians
Category:21st-century American mathematicians
Category:American number theorists
Category:American theoretical computer scientists
Category:University of Michigan faculty
Category:Summer Science Program
Category:Fellows of the American Mathematical Society
Category:Fellows of the Society for Industrial and Applied Mathematics
Category:Members of the United States National Academy of Sciences