D. H. Lehmer | |
|---|---|
.jpg) Lehmer in 1984 | |
| Born | Derrick Henry Lehmer (1905-02-23)February 23, 1905 Berkeley, California, U.S. |
| Died | May 22, 1991(1991-05-22) (aged 86) Berkeley, California, U.S. |
| Nationality | American |
| Education | University of California, Berkeley Brown University |
| Known for | Lehmer's polynomial Lehmer matrix Lehmer sieve Lehmer–Schur algorithm Lehmer's GCD algorithm Lehmer code Lehmer's conjecture Lehmer number Lehmer five Lucas–Lehmer test Lehmer mean Meissel–Lehmer algorithm Lehmer pair Pocklington–Lehmer test Lehmer random number generator Lehmer sequence Lehmer's totient problem Continued fraction factorization |
| Scientific career | |
| Fields | Mathematics |
| Institutions | UC Berkeley |
| Doctoral advisor | Jacob Tamarkin |
| Doctoral students | Tom Apostol John Brillhart Ronald Graham David Singmaster Harold Stark Peter J. Weinberger |
Derrick Henry "Dick"Lehmer (February 23, 1905 – May 22, 1991), almost always cited asD.H. Lehmer,[1][2][3] was an American mathematician significant to the development ofcomputational number theory. Lehmer refinedÉdouard Lucas' work in the 1930s and devised theLucas–Lehmer test forMersenne primes. His peripatetic career as anumber theorist, with him and his wife taking numerous types of work in the United States and abroad to support themselves during theGreat Depression, fortuitously brought him into the center of research into early electronic computing.
Lehmer was born inBerkeley, California, toDerrick Norman Lehmer, a professor of mathematics at theUniversity of California, Berkeley, andClara Eunice Mitchell.
He studiedphysics and earned abachelor's degree from UC Berkeley, and continued with graduate studies at theUniversity of Chicago.
He and his father worked together onLehmer sieves.
During his studies at Berkeley, Lehmer metEmma Markovna Trotskaia, a Russian student of his father's, who had begun with work toward anengineering 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 toProvidence, Rhode Island, afterBrown University offered him aninstructorship.
Lehmer received amaster's degree and aPh.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 underJacob Tamarkin.
Lehmer became aNational Research Fellow, allowing him to take positions at theCalifornia Institute of Technology from 1930 to 1931 and atStanford University from 1931 to 1932. In the latter year, the couple's first child Laura was born.
After being awarded a second National Research Fellowship, the Lehmers moved on toPrinceton, New Jersey between 1932 and 1934, where Dick spent a short time at theInstitute for Advanced Study.
He worked atLehigh University inPennsylvania from 1934 until 1938. Their son Donald was born in 1934 while Dick and Emma were at Lehigh.
The year 1938–1939 was spent inEngland on aGuggenheim Fellowship visiting both theUniversity of Cambridge and theUniversity of Manchester, meetingG. H. Hardy,John Edensor Littlewood,Harold Davenport,Kurt Mahler,Louis Mordell, andPaul Erdős. The Lehmers returned to America by ship with second child Donald just before the beginning of theBattle 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. Lehmer was chairman of the Department of Mathematics atUniversity of California, Berkeley from 1954 until 1957. He continued working at UC Berkeley until 1972, the year he becameprofessor emeritus.
From 1945 to 1946, Lehmer served on the Computations Committee atAberdeen Proving Grounds inMaryland, a group established as part of theBallistics Research Laboratory to prepare theENIAC for utilization following its completion at theUniversity of Pennsylvania'sMoore School of Electrical Engineering; the other Computations Committee members wereHaskell Curry,Leland Cunningham, andFranz 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, especiallysieve 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 theThanksgiving 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-dayIndependence Day weekend of July 4, 1946, withJohn 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 theMoore 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 September 1949, he presented thepseudorandom number generator now known as theLehmer random number generator.[4]
D. H. Lehmer wrote the article "The Machine Tools of Combinatorics," which is the first chapter inEdwin Beckenbach'sApplied Combinatorial Mathematics (1964).[5] It describes methods for producing permutations, combinations, etc. This was a uniquely valuable resource and has only been rivaled recently by Volume 4 ofDonald Knuth's series.
The Lehmers also assistedHarry Vandiver with his work onFermat's Last Theorem, using theStandards Western Automatic Computer to do many calculations involvingBernoulli numbers.[6]
In 1950, Lehmer was one of 31 University of California faculty fired after refusing to sign aloyalty oath, a policy initiated by the Board of Regents of the State of California in 1950 during the Communist scare personified by SenatorJoseph McCarthy. Lehmer took a post as Director of theNational 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. WhenJohn Selfridge was at Northern Illinois University he twice invited Lehmer and Emma to spend a semester there. One year Selfridge arranged that Erdős and Lehmer taught a course together on Research Problems in the Theory of Numbers. Lehmer taught the first eight weeks and then Erdős taught the remainder. Erdős 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 calledWest Coast Number Theory), Lehmer, as the organizer, was inspecting the facilities of theAsilomar 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 anyanalytic 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 formulatedLehmer's conjecture and participated in theCunningham project.
Lehmer died in Berkeley on May 22, 1991.
