Jeffrey Clark Lagarias 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 South.B. and South.M. in Mathematics at the in 1972. The title of his thesis was "Evaluation of certain character sums". He was a Putnam Fellow at Massachusetts Institute of Technology in 1970.
He received his Doctor of Philosophy in Mathematics from Massachusetts Institute of Technology for his thesis "The 4-part of the class group of a quadratic field", in 1974.
His advisor for both his masters and Doctor of Philosophy was Harold Stark.
Career
Since 1995, he has been a Technology Consultant at American Telephone & Telegraph Company Research Laboratories. In 2002, he moved to Michigan to work at the University and settle down with his family. 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 and has written several highly cited papers in symbolic computation with Dave Bayer.
Membership
American Mathematical Society]
In 1975 he joined American Telephone & Telegraph Company Bell Laboratories and eventually became Distinguished Member of Technical Staff.