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 In number theory, the Selberg sieve is a technique for estimating the s ...

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) * Empress Elisabeth (disambiguation), lists various empresses named ''Elisabeth'' or ''Elizabeth'' * Princess Elizabeth ...

New Jersey New Jersey is a U.S. state, state located in both the Mid-Atlantic States, Mid-Atlantic and Northeastern United States, Northeastern regions of the United States. Located at the geographic hub of the urban area, heavily urbanized Northeas ...

to school superintendent Ralph P. Gallagher and elementary school teacher Natalie Forcheimer Gallagher. Gallagher graduated from

Bound Brook High School Bound Brook High School is a comprehensive community public high school that serves students in ninth through twelfth grades from Bound Brook, in Somerset County, in the U.S. state of New Jersey, operating as the lone secondary school of the ...

and received a scholarship from the Harvard Club of New Jersey to attend

Harvard University Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyma ...

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 Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...

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

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 university, private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of moder ...

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

Latin Quarter The Latin Quarter of Paris (, ) is an urban university campus 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, t ...

of Paris before becoming an assistant professor at

Columbia University Columbia University in the City of New York, commonly referred to as Columbia University, is a Private university, private Ivy League research university in New York City. Established in 1754 as King's College on the grounds of Trinity Churc ...

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

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

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

Barnard College Barnard College is a Private college, private Women's colleges in the United States, women's Liberal arts colleges in the United States, liberal arts college affiliated with Columbia University in New York City. It was founded in 1889 by a grou ...

. 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 Dir ...

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 ...

. 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 an example of vertical extent, "This basketball player is 7 foot 1 inches in height." For an e ...

, 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 Amster ...

. 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 ( ; ; ) is the Capital city, capital and List of cities in Vietnam, second-most populous city of Vietnam. The name "Hanoi" translates to "inside the river" (Hanoi is bordered by the Red River (Asia), Red and Black River (Asia), Black Riv ...

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 American 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