MacTutor
Derrick H. Lehmer died of natural causes on May 22, 1991, at the age of 86. He was born in 1905 in Berkeley; his father, D.N. Lehmer, was also a Professor of mathematics at UC. His father's interest in number theory and computation started Derrick on his long and distinguished career in that field. Lehmer did his graduate work at Brown University, receiving the Ph.D. degree in 1930. After several years of research appointments, as National Research Council Fellow at the California Institute of Technology and the Carnegie Institution of Washington, and as a Member of the Institute for Advanced Study, Princeton, N.J., he joined the faculty of Lehigh University and then came to UCB in fall 1940. He retired in 1972.
In 1928 Lehmer married Emma Trotskaya, who was also a mathematician and a number theorist. (E. Lehmer is well known for her excellent translation of Pontrjagin's seminal work, Topological Groups.) In their more than 60 years of married life together, the Lehmers collaborated on over 11 papers in number theory.
Lehmer served as Chairman of the Mathematics Department from 1954 to 1957. This was a time of great importance for the department, since there had been no new appointments during 1950-54. Under Lehmer's chairmanship a number of new faculty were appointed, the beginning of the buildup of the department to its present size and eminence. Lehmer was a most considerate person; many Saturday mornings he and Emma invited graduate students and young faculty to accompany them on a hike in the Berkeley hills.
Lehmer was regarded as the foremost authority in the country in the field of number theory and computation. He published over 175 research papers and received a number of awards, invitations and honors. Among these are: Guggenheim Fellowship (Cambridge University, 1938), Fulbright Lectureship (Australia, 1959), Research Professorship (Miller Institute for Basic Research in Science, Berkeley, 1962-63), invited address at the 1958 International Congress of Mathematicians, Gibbs Lecturer (American Mathematical Society, 1964), Vice President of the American Mathematical Society (1953-54) and of the American Association for the Advancement of Science (1955-56), Governor at Large of the Association for Computing Machinery (1953-54) and of the Mathematical Association of America (1953-54).
Lehmer made contributions to many parts of number theory, but he was especially interested in relevant numerical calculations. He was unsurpassed in this field. Of course, the possible computations changed drastically during his lifetime. For example, while Lehmer was still a student, he and Emma spent hundreds of hours of computation disproving Mersenne's conjecture that 2257-1 is prime. To insure accuracy, both carried out each step independently and then compared their results. The same computation can be done on a modern computer in a fraction of a second.
While still an undergraduate, Lehmer realized that it would be helpful to have a mechanical device for combining linear congruences, and at various times, he supervised the construction of several such machines. These special-purpose computers, known as sieves, were particularly useful in factoring large numbers. The first model, constructed in 1927, used 19 bicycle chains. The number of links in these chains were 64, 27, 25, 49, 22, 26, and the various primes from 17 to 67. For any particular problem, a preliminary computation determined the admissible residues for each modulus. Small pins were attached to the appropriate links of each chain. The chains hung in loops from sprockets with ten teeth attached to a shaft which was driven by a motor. When pins reached the top of all chains at the same time, the circuit was broken, and the machine stopped, furnishing a solution to the problem.
In 1932, an improved sieve was constructed and displayed at the 1933 World's Fair in Chicago. Here, instead of bicycle chains, disk gears with various numbers of teeth were used, with holes opposite each tooth. For a given problem, the unwanted holes were plugged, and a photoelectric cell was used to stop the machine when open holes were lined up. This machine was much faster than the original model. Many years later, in 1965, the first electronic sieve was constructed under Lehmer's direction. An improved version was constructed later. By this time, general-purpose computers had appeared, but sieves still had an advantage for some problems.
Lehmer was a pioneer in the development of modern computing machines and in their use in the solution of scientific problems, particularly those arising in number theory. In 1945-46 he was called to the Ballistic Research Laboratory of the Aberdeen Proving Ground to prepare that laboratory for the installation of the ENIAC, the first general-purpose electronic computer. he observed the completion of that computer in Philadelphia and took part in its testing in Aberdeen. In 1950, during the lengthy loyalty oath controversy, he left Berkeley and served for two years as Director of the National Bureau of Standards' Institute for Numerical Analysis in Los Angeles. There he was in charge of the first fully automatic computer on the West Coast, the "SWAC." During this period he wrote a number of papers, including mathematical methods for using such machines, the sieve problem for them, and their application to Fermat's last theorem.
In the latter part of the 1950s and the early 1960s he, together with Professor Paul Morton of the Berkeley Electrical Engineering Department, worked on developing a computer using a rotating magnetic drum as a memory device. Lehmer served on numerous national and UC Berkeley Committees dealing with computer facilities, departmental existence, organization, and affairs. He was Vice Chairman of the newly formed (L&S) Computer Science Department during the period 1969-70.
Lehmer was extraordinarily successful in using computers in solving problems in number theory. His technique for dealing with conjectures that abound in number theory was described as follows by G.C. Evans: "For a given one Lehmer tries to limit the problem by planting poles here and there so that a machine calculation can be pushed between them, not to reach a verification of the conjecture but to prove it wrong."
He also took part in providing machine (electronic computer) proofs of theorems in number theory, but not in the sense of theorem-proving programs that begin with axioms and set their own goals. Lehmer and coworkers used any devices or previously known results that they considered useful. In particular, they aided and abetted the machine in its search for a theorem and its proof.
Lehmer was an exceedingly productive number theorist. In 1977, five years after his retirement his bibliography contained 150 items. At present it contains 179 and is still growing as Emma culls publishable material from his notebooks. Among the nineteen publications he produced that he himself considered most important, seven were concerned with computers and their use in dealing with number-theoretic problems. Four of the former list Emma Lehmer as a co-author. The 1977 bibliography lists eleven papers written jointly with others; her name appears in all of them.
Nineteen Ph.D. students, a number of whom went on to become distinguished mathematicians, wrote their theses under Lehmer's guidance. Their topics were in the main concerned with number-theory problems but a few dealt with topics in analysis. Lehmer's wide-ranging interests in mathematics and computers stood him and his students in good stead when dealing with topics such as "Arithmetical properties of Bessel functions" and "Applications of linear programming to the numerical solution of linear differential equations."
He was a popular lecturer at all levels. He had an informal method of lecturing which, together with his dry humor, served effectively to bring students to the heart of the subject matter. They appreciated his relaxed manner of teaching and the opportunity he provided for dialogue.
He is survived by his wife Emma, his son Donald and his daughter Laura Ornstein.
He is sorely missed by all who knew him.
John L. Kelley
Raphael M. Robinson
Abraham H. Taub
P. Emery Thomas
In 1928 Lehmer married Emma Trotskaya, who was also a mathematician and a number theorist. (E. Lehmer is well known for her excellent translation of Pontrjagin's seminal work, Topological Groups.) In their more than 60 years of married life together, the Lehmers collaborated on over 11 papers in number theory.
Lehmer served as Chairman of the Mathematics Department from 1954 to 1957. This was a time of great importance for the department, since there had been no new appointments during 1950-54. Under Lehmer's chairmanship a number of new faculty were appointed, the beginning of the buildup of the department to its present size and eminence. Lehmer was a most considerate person; many Saturday mornings he and Emma invited graduate students and young faculty to accompany them on a hike in the Berkeley hills.
Lehmer was regarded as the foremost authority in the country in the field of number theory and computation. He published over 175 research papers and received a number of awards, invitations and honors. Among these are: Guggenheim Fellowship (Cambridge University, 1938), Fulbright Lectureship (Australia, 1959), Research Professorship (Miller Institute for Basic Research in Science, Berkeley, 1962-63), invited address at the 1958 International Congress of Mathematicians, Gibbs Lecturer (American Mathematical Society, 1964), Vice President of the American Mathematical Society (1953-54) and of the American Association for the Advancement of Science (1955-56), Governor at Large of the Association for Computing Machinery (1953-54) and of the Mathematical Association of America (1953-54).
Lehmer made contributions to many parts of number theory, but he was especially interested in relevant numerical calculations. He was unsurpassed in this field. Of course, the possible computations changed drastically during his lifetime. For example, while Lehmer was still a student, he and Emma spent hundreds of hours of computation disproving Mersenne's conjecture that 2257-1 is prime. To insure accuracy, both carried out each step independently and then compared their results. The same computation can be done on a modern computer in a fraction of a second.
While still an undergraduate, Lehmer realized that it would be helpful to have a mechanical device for combining linear congruences, and at various times, he supervised the construction of several such machines. These special-purpose computers, known as sieves, were particularly useful in factoring large numbers. The first model, constructed in 1927, used 19 bicycle chains. The number of links in these chains were 64, 27, 25, 49, 22, 26, and the various primes from 17 to 67. For any particular problem, a preliminary computation determined the admissible residues for each modulus. Small pins were attached to the appropriate links of each chain. The chains hung in loops from sprockets with ten teeth attached to a shaft which was driven by a motor. When pins reached the top of all chains at the same time, the circuit was broken, and the machine stopped, furnishing a solution to the problem.
In 1932, an improved sieve was constructed and displayed at the 1933 World's Fair in Chicago. Here, instead of bicycle chains, disk gears with various numbers of teeth were used, with holes opposite each tooth. For a given problem, the unwanted holes were plugged, and a photoelectric cell was used to stop the machine when open holes were lined up. This machine was much faster than the original model. Many years later, in 1965, the first electronic sieve was constructed under Lehmer's direction. An improved version was constructed later. By this time, general-purpose computers had appeared, but sieves still had an advantage for some problems.
Lehmer was a pioneer in the development of modern computing machines and in their use in the solution of scientific problems, particularly those arising in number theory. In 1945-46 he was called to the Ballistic Research Laboratory of the Aberdeen Proving Ground to prepare that laboratory for the installation of the ENIAC, the first general-purpose electronic computer. he observed the completion of that computer in Philadelphia and took part in its testing in Aberdeen. In 1950, during the lengthy loyalty oath controversy, he left Berkeley and served for two years as Director of the National Bureau of Standards' Institute for Numerical Analysis in Los Angeles. There he was in charge of the first fully automatic computer on the West Coast, the "SWAC." During this period he wrote a number of papers, including mathematical methods for using such machines, the sieve problem for them, and their application to Fermat's last theorem.
In the latter part of the 1950s and the early 1960s he, together with Professor Paul Morton of the Berkeley Electrical Engineering Department, worked on developing a computer using a rotating magnetic drum as a memory device. Lehmer served on numerous national and UC Berkeley Committees dealing with computer facilities, departmental existence, organization, and affairs. He was Vice Chairman of the newly formed (L&S) Computer Science Department during the period 1969-70.
Lehmer was extraordinarily successful in using computers in solving problems in number theory. His technique for dealing with conjectures that abound in number theory was described as follows by G.C. Evans: "For a given one Lehmer tries to limit the problem by planting poles here and there so that a machine calculation can be pushed between them, not to reach a verification of the conjecture but to prove it wrong."
He also took part in providing machine (electronic computer) proofs of theorems in number theory, but not in the sense of theorem-proving programs that begin with axioms and set their own goals. Lehmer and coworkers used any devices or previously known results that they considered useful. In particular, they aided and abetted the machine in its search for a theorem and its proof.
Lehmer was an exceedingly productive number theorist. In 1977, five years after his retirement his bibliography contained 150 items. At present it contains 179 and is still growing as Emma culls publishable material from his notebooks. Among the nineteen publications he produced that he himself considered most important, seven were concerned with computers and their use in dealing with number-theoretic problems. Four of the former list Emma Lehmer as a co-author. The 1977 bibliography lists eleven papers written jointly with others; her name appears in all of them.
Nineteen Ph.D. students, a number of whom went on to become distinguished mathematicians, wrote their theses under Lehmer's guidance. Their topics were in the main concerned with number-theory problems but a few dealt with topics in analysis. Lehmer's wide-ranging interests in mathematics and computers stood him and his students in good stead when dealing with topics such as "Arithmetical properties of Bessel functions" and "Applications of linear programming to the numerical solution of linear differential equations."
He was a popular lecturer at all levels. He had an informal method of lecturing which, together with his dry humor, served effectively to bring students to the heart of the subject matter. They appreciated his relaxed manner of teaching and the opportunity he provided for dialogue.
He is survived by his wife Emma, his son Donald and his daughter Laura Ornstein.
He is sorely missed by all who knew him.
John L. Kelley
Raphael M. Robinson
Abraham H. Taub
P. Emery Thomas
This University of California obituary is available at THIS LINK