Patrick Ximenes Gallagher (January 2, 1935 – March 30, 2019) was an American mathematician who pioneered large sieve theory and invented the

larger sieve In number theory, the larger sieve is a sieve invented by Patrick X. Gallagher. The name denotes a heightening of the large sieve. Combinatorial sieves like the Selberg sieve are strongest, when only a few residue classes are removed, while the te ...

Biography

Early life

Patrick Ximenes Gallagher was born on January 2, 1935, in

Elizabeth Elizabeth or Elisabeth may refer to: People * Elizabeth (given name), a female given name (including people with that name) * Elizabeth (biblical figure), mother of John the Baptist Ships * HMS ''Elizabeth'', several ships * ''Elisabeth'' (sch ...

New Jersey New Jersey is a state in the Mid-Atlantic and Northeastern regions of the United States. It is bordered on the north and east by the state of New York; on the east, southeast, and south by the Atlantic Ocean; on the west by the Delaware ...

to school superintendent Ralph P. Gallagher and elementary school teacher Natalie Forcheimer Gallagher. Gallagher graduated from Bound Brook High School and received a scholarship from the Harvard Club of New Jersey to attend

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...

Education

In 1956, Gallagher received a B.A. degree ''magna cum laude'' from Harvard University. At Harvard, he was a member of the Harvard Mathematics Club and

Eliot House Eliot House is one of twelve undergraduate residential Houses at Harvard University. It is one of the seven original houses at the college. Opened in 1931, the house was named after Charles William Eliot, who served as president of the universi ...

Mathematics-Physics Club and completed an undergraduate honors thesis entitled ''On a property of some entire functions''. In 1959, Gallagher received a PhD from

Princeton University Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...

with a doctoral dissertation entitled ''Metric Diophantine Approximation in One and Several Dimensions'' completed under the supervision of

Donald C. Spencer Donald Clayton Spencer (April 25, 1912 – December 23, 2001) was an American mathematician, known for work on deformation theory of structures arising in differential geometry, and on several complex variables from the point of view of pa ...

Career

After receiving his doctoral degree, Gallagher served as an instructor 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 ...

from 1959 to 1961. He spent one year living in the

Latin Quarter The Latin Quarter of Paris (french: Quartier latin, ) is an area in the 5th and the 6th arrondissements of Paris. It is situated on the left bank of the Seine, around the Sorbonne. Known for its student life, lively atmosphere, and bistros ...

of Paris before becoming an assistant professor at

Columbia University Columbia University (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manhatt ...

in 1962. He moved from Columbia to become a member of the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...

for the 1964-1965 academic year. From 1965 to 1972, he was an associate professor and then full professor at

Barnard College Barnard College of Columbia University is a private women's liberal arts college in the borough of Manhattan in New York City. It was founded in 1889 by a group of women led by young student activist Annie Nathan Meyer, who petitioned Columbia ...

. In 1972, Gallagher moved back to Columbia University as a professor of mathematics. Gallagher received the Columbia University Presidential Teaching Award in 2005 and became Director of Undergraduate Studies in the Department of Mathematics in 2013. He retired from Columbia in 2017 and was Professor Emeritus until his death in 2019.

Research

In the 1960s and 1970s, Gallagher proved several results in large sieve methods in

analytic number theory In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Peter Gustav Lejeune Dirichlet's 1837 introduction of Diric ...

and simplified key ingredients used in the proof of the

Bombieri–Vinogradov theorem In mathematics, the Bombieri–Vinogradov theorem (sometimes simply called Bombieri's theorem) is a major result of analytic number theory, obtained in the mid-1960s, concerning the distribution of primes in arithmetic progressions, averaged over a ...

. He also applied the large sieve to study the asymptotics of

Galois group In mathematics, in the area of abstract algebra known as Galois theory, the Galois group of a certain type of field extension is a specific group associated with the field extension. The study of field extensions and their relationship to the pol ...

s of monic integral polynomials of bounded

height Height is measure of vertical distance, either vertical extent (how "tall" something or someone is) or vertical position (how "high" a point is). For example, "The height of that building is 50 m" or "The height of an airplane in-flight is abou ...

, improving on results by

van der Waerden Bartel Leendert van der Waerden (; 2 February 1903 – 12 January 1996) was a Dutch mathematician and historian of mathematics. Biography Education and early career Van der Waerden learned advanced mathematics at the University of Amsterd ...

. In 1971, he invented the

Family

Gallagher met his wife, Minh Chau Gallagher, while he was an instructor at MIT in 1960. Minh Chau was born in

Hanoi Hanoi or Ha Noi ( or ; vi, Hà Nội ) is the capital and second-largest city of Vietnam. It covers an area of . It consists of 12 urban districts, one district-leveled town and 17 rural districts. Located within the Red River Delta, Hanoi is ...

to Roman Catholic parents. They had two sons together.

References

{{DEFAULTSORT:Gallagher, Patrick X. 20th-century American mathematicians 21st-century American mathematicians Bound Brook High School alumni Number theorists Columbia University faculty Institute for Advanced Study visiting scholars Princeton University alumni Harvard College alumni 1935 births People from Bound Brook, New Jersey 2019 deaths People from Elizabeth, New Jersey Mathematicians from New Jersey Massachusetts Institute of Technology faculty