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|Derrick Henry Lehmer|
|Born||)February 23, 1905
|Died||May 22, 1991) (aged 86)
|Alma mater||Brown University|
|Doctoral advisor||Jacob Tamarkin|
|Doctoral students||Tom Apostol
Peter J. Weinberger
|Known for||Lehmer's polynomial
Lehmer's GCD algorithm
Lucas–Lehmer test for Mersenne numbers
Lehmer random number generator
Derrick Henry "Dick" Lehmer (February 23, 1905 – May 22, 1991) was an American mathematician who refined Édouard Lucas' work in the 1930s and devised the Lucas–Lehmer test for Mersenne primes. Lehmer's peripatetic career as a number theorist, with he and his wife taking numerous types of work in the United States and abroad to support themselves during the Great Depression, fortuitously brought him into the center of research into early electronic computing.
He and his father worked together on Lehmer sieves.
During his studies at Berkeley, Lehmer met Emma Markovna Trotskaia, a Russian student of his father's, who had begun with work toward an engineering degree but had subsequently switched focus to mathematics, earning her B.A. in 1928. Later that same year, Lehmer married Emma and, following a tour of Northern California and a trip to Japan to meet Emma's family, they moved by car to Providence, Rhode Island, after Brown University offered him an instructorship.
Lehmer received a Master's degree and a Ph.D., both from Brown University, in 1929 and 1930, respectively; his wife obtained a Master's degree in 1930 as well, coaching mathematics to supplement the family income, while also helping her husband type his Ph.D. thesis, An Extended Theory of Lucas' Functions, which he wrote under Jacob Tamarkin.
Movements during the Depression
Lehmer became a National Research Fellow, allowing him to take positions at the California Institute of Technology from 1930 to 1931 and at Stanford University from 1931 to 1932. In the latter year, the couple's first child Laura was born.
The year 1938-1939 was spent in England on a Guggenheim Fellowship visiting both the University of Cambridge and the University of Manchester, meeting G. H. Hardy, John Edensor Littlewood, Harold Davenport, Kurt Mahler, Louis Mordell, and Paul Erdős. The Lehmers returned to America by ship with second child Donald just before the beginning of the Battle of the Atlantic.
Lehmer continued at Lehigh University for the 1939-1940 academic year.
In 1940, Lehmer accepted a position back at the mathematics department of UC Berkeley. At some point in his career there, he developed the Linear congruential generator (pseudorandom number generator), which is frequently referred to as a Lehmer random number generator. The Lehmers also assisted Harry Vandiver with his work on Fermat's Last Theorem, computing many Bernoulli numbers required.
From 1945-1946, Lehmer served on the Computations Committee at Aberdeen Proving Grounds in Maryland, a group established as part of the Ballistics Research Laboratory to prepare the ENIAC for utilization following its completion at the University of Pennsylvania's Moore School of Electrical Engineering; the other Computations Committee members were Haskell Curry, Leland Cunningham, and Franz Alt. It was during this short tenure that the Lehmers ran some of the first test programs on the ENIAC—according to their academic interests, these tests involved number theory, especially sieve methods, but also pseudorandom number generation. When they could arrange child care, the Lehmers spent weekends staying up all night running such problems, the first over the Thanksgiving weekend of 1945. (Such tests were run without cost, since the ENIAC would have been left powered on anyway in the interest of minimizing vacuum tube failures.) The problem run during the 3-day Independence Day weekend of July 4, 1946, with John Mauchly serving as computer operator, ran around the clock without interruption or failure. The following Tuesday, July 9, 1946, Lehmer delivered the talk "Computing Machines for Pure Mathematics" as part of the Moore School Lectures, in which he introduced computing as an experimental science, and demonstrated the wit and humor typical of his teaching lectures.
Lehmer would remain active in computing developments for the remainder of his career. Upon his return to Berkeley, he made plans for building the California Digital Computer (CALDIC) with Paul Morton and Leland Cunningham.
In 1950, Lehmer was one of 31 University of California faculty fired after refusing to sign a loyalty oath, a policy initiated by the Board of Regents of the State of California in 1950 during the Communist scare personified by Senator Joseph McCarthy. Lehmer took a post as Director of the National Bureau of Standards' Institute for Numerical Analysis (INA), working with the Standards Western Automatic Computer (SWAC). On October 17, 1952, the State Supreme Court proclaimed the oath unconstitutional, and Lehmer returned to Berkeley shortly thereafter.
Lehmer continued to be active for many years and would certainly qualify as a dotagy, Paul Erdos's term for someone active in their dotage. When John Selfridge was at Northern Illinois University he twice invited Lehmer and Emma to spend a semester there. One year Selfridge arranged that Erdos and Lehmer taught a course together on Research Problems in the Theory of Numbers. Lehmer taught the first eight weeks and then Erdos taught the remainder. Erdos didn't often teach a course, and he said "You know it wasn't that difficult. The only problem was being there."
Lehmer had quite a wit. On the occasion of the first Asilomar number theory conference, which became an annual event (now called West Coast Number Theory), Lehmer, as the organizer, was inspecting the facilities of the Asilomar Conference Grounds—basically a wooden building on the beach. Someone said they couldn't find a blackboard and Lehmer spotted some curtains in the middle of the wall. Moving the curtains aside revealed a very small blackboard, whereupon Lehmer said "Well, I guess we won't be doing any analytic number theory!"
In addition to his significant contributions to number theory algorithms for multiprecision integers, such as factoring, Euclid's algorithm, long division, and proof of primality, he also formulated Lehmer's conjecture and participated in the Cunningham project.
His father Derrick Norman Lehmer, known mainly as a pioneer in number theory computing, also made major contributions to combinatorial computing, having devised algorithms for efficiently generating all the permutations on n elements He also developed two algorithms, rank(p) and unrank(k). Given a permutation p, if k = rank(p), then p is the kth permutation. Given an integer k, unrank(k) is the kth permutation. D N Lehmer's method uses his so-called factorial representation of the integer k. See section 5.1 in Permutation.
D. H. Lehmer continued his father's interest in combinatorial computing and in fact wrote the article "Machine tools of Computation," which is chapter one in the book "Applied Combinatorial Mathematics," by Edwin Beckenbach, 1964. It describes methods for producing permutations, combinations etc. This was a uniquely valuable resource and has only been rivaled recently by Volume 4 of Donald Knuth's series.
Lehmer died in Berkeley on May 22, 1991.
- Brillhart, J. (1992). "Derrick Henry Lehmer". Acta Arithmetica 62: 207–213.
- Photo of Derrick Henry Lehmer
- The Lehmers at Berkeley
- Timeline: Summary of events of the Loyalty Oath Controversy 1949-54
- O'Connor, John J.; Robertson, Edmund F., "Derrick Henry Lehmer", MacTutor History of Mathematics archive, University of St Andrews.
- Interview with the Lehmers and others about their experiences at Princeton
- Derrick Henry Lehmer at the Mathematics Genealogy Project
- Alt, Franz L. (1972-07). "Archaeology of Computers—Reminiscences, 1945-1947" (PDF). Communications of the ACM (ACM) 15 (7): 693–694. doi:10.1145/361454.361528. ISSN 0001-0782.