Jeffrey Clark Lagarias (born November 16, 1949 in

Pittsburgh Pittsburgh ( ) is a city in the Commonwealth (U.S. state), Commonwealth of Pennsylvania, United States, and the county seat of Allegheny County, Pennsylvania, Allegheny County. It is the most populous city in both Allegheny County and Wester ...

Pennsylvania Pennsylvania (; ( Pennsylvania Dutch: )), officially the Commonwealth of Pennsylvania, is a state spanning the Mid-Atlantic, Northeastern, Appalachian, and Great Lakes regions of the United States. It borders Delaware to its southeast, ...

, United States) is a

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

and professor at the

University of Michigan , mottoeng = "Arts, Knowledge, Truth" , former_names = Catholepistemiad, or University of Michigania (1817–1821) , budget = $10.3 billion (2021) , endowment = $17 billion (2021)As o ...

Education

While in high school in 1966, Lagarias studied

astronomy Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...

at the

Summer Science Program The Summer Science Program (SSP) is an academic summer program where high school students experience college-level education and do research in celestial mechanics by studying the orbits of asteroids, biochemistry by studying the kinetic propertie ...

. He completed an S.B. and S.M. in Mathematics at the

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the ...

in 1972. The title of his thesis was "Evaluation of certain character sums". He was a

Putnam Fellow The William Lowell Putnam Mathematical Competition, often abbreviated to Putnam Competition, is an annual mathematics competition for undergraduate college students enrolled at institutions of higher learning in the United States and Canada (regar ...

at MIT in 1970. 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. His advisor for both his masters and Ph.D was

Harold Stark Harold Mead Stark (born August 6, 1939 in Los Angeles, California) is an American mathematician, specializing in number theory. He is best known for his solution of the Gauss class number 1 problem, in effect correcting and completing the earl ...

Career

In 1975, he joined

AT&T Bell Laboratories Nokia Bell Labs, originally named Bell Telephone Laboratories (1925–1984), then AT&T Bell Laboratories (1984–1996) and Bell Labs Innovations (1996–2007), is an American industrial research and scientific development company owned by mult ...

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 Michigan () is a state in the Great Lakes region of the upper Midwestern United States. With a population of nearly 10.12 million and an area of nearly , Michigan is the 10th-largest state by population, the 11th-largest by area, and the ...

to work at the University and settle down with his family. While his recent work has been in

theoretical computer science Theoretical computer science (TCS) is a subset of general computer science and mathematics that focuses on mathematical aspects of computer science such as the theory of computation, lambda calculus, and type theory. It is difficult to circumsc ...

, his original training was in analytic

algebraic number theory Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic ob ...

. 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 In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part . Many consider it to be the most important unsolved problem in ...

, namely whether for all ''n'' > 0, we have :

\sigma(n) \le H_n + e^ \ln H_n

with equality only when ''n'' = 1. Here ''H''_''n'' is the ''n''th

harmonic number In mathematics, the -th harmonic number is the sum of the reciprocals of the first natural numbers: H_n= 1+\frac+\frac+\cdots+\frac =\sum_^n \frac. Starting from , the sequence of harmonic numbers begins: 1, \frac, \frac, \frac, \frac, \dot ...

, the sum of the reciprocals of the first

n

positive integers, and ''σ''(''n'') is the

divisor function In mathematics, and specifically in number theory, a divisor function is an arithmetic function related to the divisors of an integer. When referred to as ''the'' divisor function, it counts the ''number of divisors of an integer'' (including ...

, the sum of the positive divisors of ''n''. He disproved

Keller's conjecture In geometry, Keller's conjecture is the conjecture that in any tiling of -dimensional Euclidean space by identical hypercubes, there are two hypercubes that share an entire -dimensional face with each other. For instance, in any tiling of the pl ...

in dimensions at least 10. Lagarias has also done work on the

Collatz conjecture The Collatz conjecture is one of the most famous unsolved problems in mathematics. The conjecture asks whether repeating two simple arithmetic operations will eventually transform every positive integer into 1. It concerns sequences of integ ...

and

Li's criterion In number theory, Li's criterion is a particular statement about the positivity of a certain sequence that is equivalent to the Riemann hypothesis. The criterion is named after Xian-Jin Li, who presented it in 1997. In 1999, Enrico Bombieri and J ...

and has written several highly cited papers in symbolic computation with

Dave Bayer David Allen Bayer (born November 29, 1955) is an American mathematician known for his contributions in algebra and symbolic computation and for his consulting work in the movie industry. He is a professor of mathematics at Barnard College, Columbi ...

Awards and honors

He received in 1986 a

Lester R. Ford :''This is about early- and mid-20th-century mathematician. For his mathematician son, active from the mid-20th century, see L. R. Ford Jr.'' Lester Randolph Ford Sr. (October 25, 1886 – November 11, 1967) was an American mathematician, e ...

award from the

Mathematical Association of America The Mathematical Association of America (MAA) 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 a ...

and again in 2007. In 2012, he became a fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

.List of Fellows of the American Mathematical Society
retrieved 2013-01-27.

References

External links

*
Jeffrey Clark Lagarias homepage
University of Michigan {{DEFAULTSORT:Lagarias, Jeffrey 1949 births Living people Scientists from Pittsburgh Massachusetts Institute of Technology School of Science alumni Scientists at Bell Labs 20th-century American mathematicians 21st-century American mathematicians Number theorists American computer scientists Theoretical computer scientists University of Michigan faculty Putnam Fellows Summer Science Program Fellows of the American Mathematical Society Fellows of the Society for Industrial and Applied Mathematics