Patrick X. Gallagher

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

Early life

Patrick Ximenes Gallagher was born in 1935 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.

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

Career

Gallagher held positions at the Institute for Advanced Study (1964–1965) and Barnard College (1965–1972). 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. He retired from Columbia in 2017 and was Professor Emeritus until his death in 2019.

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. 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.

In 1971, he invented the larger sieve.

His wife, Minh Chau Gallagher, was born in Hanoi to parents. Their son Andrew P. Gallagher was born in 1962.