Derrick henry lehmer biography of william

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His parents were Clara Eunice Mitchell and Derrick Norman Lehmer(often called DNL reach distinguish him from his sprog DHL, or as we acclaimed Dick). DNL was a associate lecturer of mathematics at Berkeley who was interested in number idea and mechanical computation. Eunice put forward DNL had five children middling Dick grew up in neat large family.

He attended college in Berkeley but it was his father who had say publicly greatest influence on him, explode even at a very ant age he became involved injure his father's ideas in give out theory and particularly his sponsorship in constructing machines to help with number theory calculations.

To give an indication oppress his father's work during high-mindedness time that Dick was green up, let us mention lose one\'s train of thought DNL published Factor table sponsor the first ten millions during the time that Dick was four years repress, and List of prime in large quantity from 1 to 10006721 considering that he was nine.

Dick was fascinated to listen to rulership father describe mathematical ideas take in hand him even at this detonation. After completing his school cultivation, Dick entered Berkeley to peruse physics. He was now enthusiastically involved with his father's burden so on the one uplift he studied physics courses, extent on the other hand loosen up helped his father both add the number theory computations inaccuracy was undertaking and with position mechanical ideas that he was developing to help him mark these calculations.

One business that DNL worked on at near the time that Dick was an undergraduate was his exert yourself on Factor Stencils which was published in 1929. This gave a method of factorising spiffy tidy up number using cards with holes punched in them and well-to-do was later described by Tec Lehmer as follows:-

Since ever and anon quadratic residue R of well-organized number N is also neat quadratic residue of every tenable factor of N, it chases that the problem of factorization a number N is herewith reduced to the discovery distinctive an adequate number of polynomial residues R of N put up with the superposition of the like stencils to reveal those fainting fit primes having these residues R.

They worked with residues R<240 alight covered 5000 primes which includes all primes up to 48611. This enabled integers up bare 486112=2363029321 to be factored. Spell DHL and his father were working on the stencils substitute undergraduate at Berkeley, Emma Trotskaia who was a mathematics proselyte studying DNL's courses, assisted them.

Emma would soon become Dick's wife and Dick and Hole Lehmer would become one contribution the most famous husband take up wife mathematics teams.

Imprison 1927 Lehmer graduated from Metropolis with a B.A. degree unembellished Physics and he went attain the University of Chicago explicate undertake research for his degree in mathematics with L Attach Dickson as his supervisor.

Entail the following year Emma Trotskaia graduated with a B.A. moment with honours in Mathematics cope with, just prior to her deputation her final examinations, Dick abstruse Emma Lehmer were married. In the past Emma's exams were over, they set out on a profile which began in the cypress forest, went on to Polish, and finally a visit which let Dick meet his recent wife's family before they reciprocal to Berkeley.

Dick was very different from happy working under Dickson consign Chicago so he had force an offer of an instructorship at Brown University in Bonus, Rhode Island. The recently husbandly couple drove across the Allied States to Brown University place both enrolled for a Master's degree.

Lehmer was awarded his Master's Degree in 1929 and his doctorate, also unfamiliar Brown University, in 1930.

Crown dissertation, which was supervised unwelcoming Tamarkin, was An Extended Shyly of Lucas's Functions. Lehmer's believable over the next few seniority involved moving from place anticipation place hoping for a hard and fast university post in the remarkably difficult times of the Really nice Depression. After receiving his degree, Lehmer was awarded a Nationwide Research Fellowship and with that he spent 1930-31 at class California Institute of Technology significant then 1931-32 at Stanford.

Sustenance a spell at the Guild for Advanced Study at University, where he held a specially Fellowship, Lehmer moved to adroit more permanent post at Lehigh University in Pennsylvania.

Lehmer and his wife remained nearby Lehigh until 1940 except affection the year 1938-39 which they spent in England visiting both the University of Cambridge opinion the University of Manchester.

Charge England they met, among remains, Hardy, Littlewood, Davenport, Mahler, Mordell, and Erdős.

Back transparent the United States not fritter after the outbreak of Universe War II, Lehmer spent preference year at Lehigh before appreciative a post in Berkeley give it some thought 1940. It was the occupation he always wanted and representation was a great joy admit Lehmer and his family attain return home.

The Lehmers spent 1945-46 at the City Proving Ground where Lehmer's pull was to help set race and operate the ENIAC (Electronic Numerical Integrator and Calculator) personal computer.

Although the computer worked accumulate of the time computing trajectories for ballistics problems, on sufficient weekends the Lehmers used bang to solve certain number cautiously problems using it as clean up electronic sieve [1]:-

When they could arrange child care, they often stayed at the stick all night long while interpretation ENIAC processed one of their problems.

They would return domicile at the break of entrance. They were pleased to locate that the sieve worked bind successfully solving problems.

McCarthy enjoyed a- highly successful few years hunk making these charges of subversion that, though mostly undocumented, extremely badly hurt government employees, teachers, squeeze university professors. Although McCarthy was the most prominent person alluring this line, it was clean road that the United States was already on and blue blood the gentry State of California had provision some time been discussing patriotism oaths.

In 1950 the Plank of Regents of the Situation of California decided to put into practice a policy that all lecturers sign a loyalty oath, with the University of California eye Berkeley was chosen as of a nature of the first test cases for it. Nineteen faculty branchs of the University of Calif. refused; Lehmer was one specified faculty member.

The speculation was that anyone who would not sign the oath oxidize be a communist sympathiser most important must be sacked, so Lehmer, as one of those who refused, lost his position. Innumerable considered that the oath fragmented their rights of academic footage which university researchers valued chief highly. Of course the witch-hunts against imaginary communists in nobility early 1950s was a ignominious affair which cost many their jobs and led to general suffering.

For Lehmer, however, rank problem was not so inquiring for he was able hopefulness take up the post be more or less Director of the National Company of Standards' Institute for Numeric Analysis for the time ditch he was unable to lure his faculty position in Philosopher. Others were not as flourishing as he was and accepted real hardships.

After the courts proclaimed the oath to put in writing unconstitutional, Lehmer was reinstated separate Berkeley.

Lehmer's Selected Papers published in 1981 gives far-out good indication of the allotment of topics on which powder worked. The chapter headings are: Lucas's functions; Tests for primality; Continued fractions; Bernoulli numbers topmost polynomials; Diophantine equations; Numerical functions; Matrices; Power residues; Analytic digit theory; Partitions; Modular forms; Cyclotomy; Combinatorics; Sieves; Equation solving; Technology techniques; and Miscellaneous.

His wellnigh famous monograph was Guide sure of yourself Tables in the Theory work for Numbers. R D Carmichael, post-mortem the book, wrote:-

A lively account is given of existent tables in the theory worry about numbers; this is set in the matter of in such a way gorilla to indicate clearly what harangue table contains.

A bibliography, laid alphabetically by authors, gives tax references to the material unimportant and supplies information concerning rank holdings, in libraries of loftiness United States and Canada, signal the books and pamphlets come to an end which reference is made. Errata in the tables are catalogued, the sources being given detect the cases of errata a while ago printed; Lehmer's contributions in honesty way of new indications pale errata are notable.

Depiction citation reads in part:-

Prolific in research, you have forceful far-reaching contributions to number conjecture. You were among the foremost to recognize the importance some high-speed computers as an 1 to mathematical research. With state energy and enthusiasm, you demonstrated how, in both theory added practice, computers can be authentic invaluable tool in testing conjectures.

His talk, Factorization commit fraud and now, covered one raise the topics to which soil had made major contributions. Bankruptcy was a pioneer in honourableness application of mechanical methods, counting digital computers, to the thought of problems in number presumption and he talked about tiresome of the methods used union factorise numbers including: factor tables, trial division, Legendre's method, item stencils, the continued fraction approach, Fermat's method, methods based keep on quadratic forms, and Shanks's representation.

Let us mention unornamented number of other topics will which Lehmer will be honoured. One must be the Lucas-Lehmer primality test which uses influence Fermat congruence, and in dole out his application to testing not a Mersenne number was pioneering. He also made major offerings to studying the density methodical primes with a given original root and to the recite of the partition function, drag particular verifying certain conjectures offspring Ramanujan.

He was the eminent person to attack the Mathematician Hypothesis by using a personal computer to check if the race lie on the critical pencilmark. Luck, however, often plays dialect trig large role in determining be that as it may famous a mathematician will grasp, and Lehmer's attack on ethics Riemann Hypothesis only provided remnant that the hypothesis was estimate whereas had the world archaic different it might have surrender a counterexample.

Brillhart, who received a Ph.D. in 1967 for a thesis supervised make wet Lehmer, comments in [1] submission Lehmer as a lecturer:-

As a lecturer [Lehmer] was unnecessary appreciated not only for her highness classical scholarship in mathematics abstruse number theory, but also untainted his dry sense of wit and wit.

As a thinker [Lehmer] was sagaciously independent, not being committed to dogmas, systems, or rituals.

1. J Brillhart, Derrick Henry Lehmer, Acta Arith.62(3)(1992), 207-213.
2. J Brillhart, Derrick h Lehmer (1905-1991), Notices Amer.

   Calculation. Soc.40(1)(1993), 31-32.

3. J Brillhart, Derrick Orator Lehmer, Bull. Inst. Combin. Appl.5(1992), 58-59.
4. H D Huskey, Derrick Orator Lehmer [1905-1991], IEEE Ann. Hist. Comput.17(2)(1995), 64-68.
5. Publications of D Revolve Lehmer, Acta Arith.62(3)(1992), 215-220.

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Written by J Specify O'Connor and E F Robertson
Last Update November 2002