Patrick X. Gallagher

Patrick Ximenes Gallagher (1935 – 2019)[1] was an American mathematician who pioneered large sieve theory and invented the larger sieve.

Patrick X. Gallagher
Born(1935-01-02)January 2, 1935
DiedMarch 30, 2019(2019-03-30) (aged 84)
Alma materHarvard University
Princeton University
Known forlarge sieve
larger sieve
AwardsColumbia University Presidential Teaching Award (2005)
Scientific career
InstitutionsColumbia University
Barnard College
Institute for Advanced Study
Doctoral advisorDonald C. Spencer
Doctoral studentsDorian M. Goldfeld


Early lifeEdit

Patrick Ximenes Gallagher was born in 1935 to school superintendent Ralph P. Gallagher and elementary school teacher Natalie Forcheimer Gallagher.[2][3] Gallagher graduated from Bound Brook High School and received a scholarship from the Harvard Club of New Jersey to attend Harvard University.[3][4]


In 1956, Gallagher received a B.A. degree magna cum laude from Harvard University.[5][3] At Harvard, he was a member of the Harvard Mathematics Club and Eliot House Mathematics-Physics Club and completed an undergraduate honors thesis entitled On a property of some entire functions.[4] In 1959, Gallagher received a PhD from Princeton University with a doctoral dissertation entitled Metric Diophantine Approximation in One and Several Dimensions completed under the supervision of Donald C. Spencer.[6]


Gallagher held positions at the Institute for Advanced Study (1964–1965) and Barnard College (1965–1972).[5] In 1972, he became a Professor of Mathematics at Columbia University and he became Director of Undergraduate Studies in the Department of Mathematics in 2013.[7][8] He retired from Columbia in 2017 and was Professor Emeritus until his death in 2019.[1]


In the 1960s and 1970s, Gallagher proved several results in large sieve methods in analytic number theory and simplified key ingredients used in the proof of the Bombieri–Vinogradov theorem.[9][10] He also applied the large sieve to study the asymptotics of Galois groups of monic integral polynomials of bounded height, improving on results by van der Waerden.[11][12]

In 1971, he invented the larger sieve.[13]


His wife, Minh Chau Gallagher, was born in Hanoi to Roman Catholic parents.[14] Their son Andrew P. Gallagher was born in 1962.


  1. ^ a b "Memorial Conference for Patrick Ximenes Gallagher". Columbia University. August 21, 2019. Retrieved August 26, 2019.
  2. ^ "Natalie F. Gallagher, active in community". Courier News. February 4, 1995. p. B-2. Retrieved December 28, 2019.
  3. ^ a b c "Gets Princeton Assistant Post". Courier News. June 16, 1956. p. 12. Retrieved December 28, 2019.
  4. ^ a b "Bound Brook Man Awarded Assistantship At Princeton". The Central Jersey Home News. June 17, 1956. p. 8. Retrieved December 28, 2019.
  5. ^ a b "Patrick X. Gallagher". Institute for Advanced Study. Retrieved February 8, 2019.
  6. ^ Patrick X. Gallagher at the Mathematics Genealogy Project
  7. ^ "Patrick Gallagher". Columbia University. Retrieved February 8, 2019.
  8. ^ Tunnell, Amber (March 27, 2013). "Over Past 12 Years, Grade Inflation Increases". Columbia Daily Spectator. Retrieved February 8, 2019.
  9. ^ Tenenbaum, Gérald (2015). Introduction to Analytic and Probabilistic Number Theory. Graduate Studies in Mathematics. 163. American Mathematical Society. pp. 102–104. ISBN 9780821898543.
  10. ^ Iwaniec, Henryk; Kowalski, Emmanuel (2004). Analytic Number Theory. Colloquium Publications. 53. American Mathematical Society. p. 183. ISBN 978-0-8218-3633-0.
  11. ^ Gallagher, Patrick X. (1973). "The large sieve and probabilistic Galois theory". In Diamond, Harold G. (ed.). Analytic number theory. Proceedings of Symposia in Pure Mathematics. 24. American Mathematical Society. pp. 91–101.
  12. ^ Kowalski, Emmanuel (August 8, 2007). "The large sieve inequalities". Terry Tao Wordpress. Retrieved February 8, 2019.
  13. ^ Gallagher, Patrick (1971). "A larger sieve". Acta Arithmetica. 18: 77–81.
  14. ^ Sokolov, Raymond A. (July 22, 1971). "She Learned How to Cook as a Girl in Hanoi". NY Times. Born in Hanoi of Roman Catholic parents, she attended Boston College and has been in the United States ever since.