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Derrick Norman Lehmer | D.H. and Emma Lehmer

THE LEHMERS AT BERKELEY
Derrick H. Lehmer (1905-1991)
and Emma Trotskaia Lehmer (1906- )
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D. H. Lehmer, probably around the time of his graduation from Berkeley, ca. 1927.
2.8 x 3.8 inches 
Private collection

Derrick (“Dick”) H. Lehmer was born in Berkeley in 1905. At a very early age he absorbed his father’s interest in number theory and computation, which provided a solid foundation for his own long and distinguished career. He graduated from Berkeley with a B.A. degree in Physics in 1927 and received his Ph.D. degree in Mathematics from Brown University in 1930. 

He held appointments in various capacities at the California Institute of Technology, the Institute for Advanced Study at Princeton, and Lehigh University before joining the Department of Mathematics at Berkeley in 1940.  He later served as chair of the Department, as well as vice chair of the Computer Science Department, and retired in 1972. 

 

“An Extended Theory of Lucas’ Functions,” Ph.D. dissertation
Berkeley: University of California, 1930 
8.5 x 11.0 inches
 

Here is a page from Lehmer's famous dissertation on the functions named after the French mathematician Edouard Lucas (1842-1891). It subsequently appeared in Annals of Mathematics and as a monograph published in Hamburg by Lutcke & Wulff, both in 1930. 

In a separate paper, Lehmer continued the inquiry begun with his dissertation.  Lucas' functions describe sequences that are defined by a linear recurrence of order 2, such as the Fibonacci sequence  0, 1, 1, 2, 3, 5, 8, 13, ... in which each term is the sum of the previous two, and its companion sequence  2, 1, 3, 4, 7, 11, ... Lehmer's interest in these functions was largely motivated by their importance in primality testing. In his thesis, Lehmer completed and clarified the theory developed by Lucas in several essential respects. 

Emma Lehmer during her Berkeley days, ca. 1928.
5.9 x 4.0 inches
Private collection
 


I was born in a town with the lovely sounding name of Samara on the great Volga river..."


Emma Trotskaia Lehmer was born in Samara, Russia in 1906, and at the age of 4 moved with her family to Manchuria where her father worked for a Russian sugar company. She was tutored at home until she was 14 and, blocked from returning to Russia for higher education due to the turmoil of the Russian Revolution, conceived a plan for an American college education. 

"My Life and Times," corrected typescript, 
3 l., n.d.
8.5 x 11.0 inches
Private collection

In her memoir, "My Life and Times," Emma Lehmer vividly recalls her early days in Russia and Manchuria, before emigrating to the United States.

"A Numerical Function Applied to Cyclotomy." 
Reprint from Bulletin of the American Mathematical 
Society, Vol. 36:291-298, 1930.
6.0 x 9.5 inches
 

Emma Lehmer was admitted to UC Berkeley and received her B.A. degree with highest honors in Mathematics in 1928. 

While working for her favorite professor D. N. Lehmer, she met his son and they married the year she graduated. While her husband worked on his Ph.D. degree at Brown University, Emma Lehmer earned her Sc.M. degree; both were awarded in 1930. 

Her thesis, "A Numerical Function Applied to Cyclotomy," was published in the April 1930 issue of Bulletin of the American Mathematical Society

Although she taught briefly at Berkeley during World War II (under a wartime exception to the nepotism rule that prevented two members of the same family from holding faculty positions), the majority of Emma Lehmer's mathematical career was spent in independent research. 

The story is told that, while still undergraduates, they spent hundreds of hours on a computation, each working independently then comparing results to ensure their accuracy. They continued their professional partnership throughout their lives and co-authored 21 mathematical papers.

Autograph letter to D. N. Lehmer, 2 l.
4 February 1932
8.5 x 11.0 inches
 

This letter from Dick and Emma Lehmer to his father on Lucas' functions indicates the early, close professional collaboration among the three Lehmers. At the same time, the father and son were working together on the design and construction of the first electric factoring machine while the younger Lehmers were briefly at Caltech and Stanford.

“Stanford Laboratory Note Book,” autograph manuscript notebook, 120 pp., 1932
10.0 x 7.5 inches
 

On pages 12 and 13 Lehmer applies a primality test. 

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