Jeffrey Lagarias
Encyclopedia
Jeffrey Clark Lagarias is a mathematics professor at the University of Michigan
.
at the Summer Science Program
.
He was an undergraduate at the Massachusetts Institute of Technology
, where he was a Putnam Fellow in 1970. He received his Ph.D. in Mathematics from MIT in 1974.
to work at the University and settle down with his family.
In 1987 he received a Lester R. Ford award from the Mathematical Association of America
.
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
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.
He disproved Keller's conjecture
in dimensions at least 10.
Lagarias has also done work on the Collatz conjecture
and Li's criterion
.
University of Michigan
The University of Michigan is a public research university located in Ann Arbor, Michigan in the United States. It is the state's oldest university and the flagship campus of the University of Michigan...
.
Education
While in high school in 1966, Lagarias studied astronomyAstronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...
at the Summer Science Program
Summer Science Program
The Summer Science Program is an intense six-week summer program for intellectually talented high school students. The program is based on a collaborative research project in celestial mechanics. Students study astronomy, physics, spherical trigonometry, and calculus while working to take...
.
He was an undergraduate at the Massachusetts Institute of Technology
Massachusetts Institute of Technology
The Massachusetts Institute of Technology is a private research university located in Cambridge, Massachusetts. MIT has five schools and one college, containing a total of 32 academic departments, with a strong emphasis on scientific and technological education and research.Founded in 1861 in...
, where he was a Putnam Fellow in 1970. He received his Ph.D. in Mathematics from MIT in 1974.
Career
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 MichiganMichigan
Michigan is a U.S. state located in the Great Lakes Region of the United States of America. The name Michigan is the French form of the Ojibwa word mishigamaa, meaning "large water" or "large lake"....
to work at the University and settle down with his family.
In 1987 he received a Lester R. Ford award from the Mathematical Association of America
Mathematical Association of America
The Mathematical Association of America is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university, college, and high school teachers; graduate and undergraduate students; pure and applied mathematicians; computer scientists;...
.
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
Riemann hypothesis
In mathematics, the Riemann hypothesis, proposed by , is a conjecture about the location of the zeros of the Riemann zeta function which states that all non-trivial zeros have real part 1/2...
, 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 functionDivisor function
In mathematics, and specifically in number theory, a divisor function is an arithmetical function related to the divisors of an integer. When referred to as the divisor function, it counts the number of divisors of an integer. It appears in a number of remarkable identities, including relationships...
, the sum of the positive divisors of n.
He disproved Keller's conjecture
Keller's conjecture
In geometry, Keller's conjecture is the conjecture introduced by that in any tiling of Euclidean space by identical hypercubes there are two cubes that meet face to face. For instance, as shown in the illustration, in any tiling of the plane by identical squares, some two squares must meet edge to...
in dimensions at least 10.
Lagarias has also done work on the Collatz conjecture
Collatz conjecture
The Collatz conjecture is a conjecture in mathematics named after Lothar Collatz, who first proposed it in 1937. The conjecture is also known as the 3n + 1 conjecture, the Ulam conjecture , Kakutani's problem , the Thwaites conjecture , Hasse's algorithm The Collatz conjecture is a...
and Li's criterion
Li's criterion
In number theory, Li's criterion is a particular statement about the positivity of a certain sequence that is completely equivalent to the Riemann hypothesis. The criterion is named after Xian-Jin Li, who presented it in 1997. Recently, Enrico Bombieri and Jeffrey C...
.
External links
- Jeffrey Clark Lagarias homepage, University of Michigan