Peter Lawrence Montgomery (September 25, 1947 – February 18, 2020) was an American mathematician who worked at the System Development Corporation and Microsoft Research.

[1][2] Montgomery began his undergraduate career at the University of California, Riverside, in 1965 and transferred to Berkeley in 1967, earning a BA in mathematics in 1969 and an MA in mathematics in 1971,[2] He joined the System Development Corporation (SDC) in 1972, where he worked for many years as a programmer implementing algorithms for the CDC 7600 and PDP series of computers, including the implementation of algorithms for multi-precision arithmetic that led to the invention of what is now known as Montgomery multiplication.

[1][3] He then returned to academia in 1987, earning his PhD in mathematics from UCLA in 1992 under the supervision of David Cantor.

[4] He also invented the block Lanczos algorithm for finding nullspace of a matrix over a finite field, which is very widely used for the quadratic sieve and number field sieve methods of factorization; he has been involved in the computations which set a number of integer factorization records.

[6] In that year, he was one of only two contestants, along with child prodigy Don Zagier of MIT, to solve all twelve of the exam problems.