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Cornelius Lanczos

Hungarian-American mathematician (1893–1974) From Wikipedia, the free encyclopedia

Cornelius Lanczos
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"Lanczos" redirects here. For resampling method, see Lanczos resampling.

Cornelius (Cornel) Lanczos (Hungarian: Lánczos Kornél, pronounced [ˈlaːnt͡soʃ ˈkorneːl]; born as Kornél Lőwy, until 1906: Löwy (Lőwy) Kornél; February 2, 1893 – June 25, 1974) was a Hungarian, American, and later Irish mathematician and physicist. According to György Marx he was one of the Martians,[2] a group of Hungarian scientific luminaries who found refuge from national socialism in the United States.

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Early life and education

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He was born in Fehérvár (Alba Regia), Fejér County, Kingdom of Hungary,[3] to Károly Lőwy and Adél Hahn. He grew up in relative comfort and attended a Catholic Gymnasium (high school). Between 1911 and 1916, he studied at the University of Budapest, where one of his professors in physics was Roland Eötvös, whose skills as an experimental physicist impressed him.[4] In mathematics, his notable teacher was Lipót Fejér, then a young mathematician.[4] Lanczos graduated with a teacher's diploma in mathematics and physics. He worked an assistant of Károly Tangl at the Department of Experimental Physics at the Polytechnical University of Budapest from 1916 to 1921.[4]

In his doctoral dissertation titled The Relation of Maxwell's Aether Equations to Functional Theory,[5] Lanczos re-wrote Maxwell's equations of electromagnetism in terms of quaternions and applied a relativistic variational principle.[2] He sent a copy of his thesis to Albert Einstein, who replied, "I studied your paper as far as my present overload allowed. I believe I may say this much: this does involve competent and original brainwork, on the basis of which a doctorate should be obtainable... I gladly accept the honorable dedication."[6]: 20  Lanczos maintained his contact with Einstein for another 35 years, until the latter's death.[2] In 1921, Lanczos completed his Ph.D. training at the University of Szeged under the supervision of Rudolf Ortvay.[2] While Ortway, who had studied under Arnold Sommerfeld, was not distinguished as a researcher, he was an inspirational teacher, who brought modern physics to Hungary.[2][4]

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Career

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As a consequence of the restrictions from the new right-wing regime in Hungary, Lanczos moved to Germany in search of employment.[2] From 1921 to 1924, Lanczos served as a lecturer at the University of Freiburg.[3] In 1924 he discovered an exact solution to the Einstein field equations of general relativity representing a cylindrically symmetric rigidly rotating configuration of dust particles.[7] This was later rediscovered by Willem Jacob van Stockum in 1938.[8] It is one of the simplest known exact solutions in general relativity[9] and is regarded as an important example, in part because it exhibits closed timelike curves.[10]

Lanczos worked at the University of Frankfurt from 1924 to 1931,[3] delivering lectures for Erwin Madelung.[4] He also briefly served as assistant to Albert Einstein in Berlin during the academic year 1928–29,[6]: 27 upon invitation by the latter.[3] Leo Szilard recommended him to Einstein.[2] In Berlin, Lanczos examined the motion of singularities—meaning, particles—in curved spacetime as described by general relativity. Einstein had a high opinion of Lanczos for his mathematical skills. In this capacity, Lanczos replaced Marcel Grossmann as Einstein's collaborator, helping him with the difficult mathematics of general relativity.[2]

Following the seminal publication of Werner Heisenberg announcing the creation of his matrix formulation of quantum mechanics in 1925,[11] Lanczos wrote a paper demonstrating how the new theory could be expressed in terms of linear integral equations.[12][2] However, at the time, this paper had little impact. Erwin Schrödinger published a series of papers detailing his own undulatory version of quantum theory, which proved rather popular among physicists.[2] But Lanczos' paper made it clear that the two seemingly different formulations of quantum mechanics were in fact equivalent,[2] something Schrödinger himself later proved.[13] Carl Eckart independently reached the same conclusion, based on the work of Lanczos.[14][15] This paper also helped Paul Dirac create his own formulation of quantum mechanics as a theory of linear transformations.[16]: 300–1  Lanczos's 1926 paper was the earliest continuum-theoretic formulation of quantum mechanics.[4] In 1972, at an event organized by the European Physical Society in Trieste, Italy, Bartel Leendert van der Waerden publicly recognized the significance of that paper, which correctly formulated the eigenvalue problem in terms of integration and even came close to introducing the Dirac -distribution. But van der Waerden was unaware that Lanczos was in the audience until Léon Rosenfeld urged the latter to come to the stage.[4]

In 1927 Lanczos married Maria Rupp.[6]: 41, 53  He moved to the United States in 1931.[4] Due to the Great Depression hit, he turned his attention towards applied mathematics,[2] and began conducting research in numerical analysis.[4] He served as a professor of mathematics and aeronautical engineering at Purdue University from 1931 to 1946.[3] Between 1927 and 1939, Lanczos split his life between two continents. His wife Maria Rupp, who had contracted tuberculosis, stayed with Lanczos' parents in Székesfehérvár year-around while Lanczos went to Purdue for half the year, teaching graduate students matrix mechanics and tensor analysis.[6]: 41, 53  His lecture notes on quantum mechanics examined in detail its mathematical formulation, including topics in function space and group theory.[2]

In 1933 his son Elmar was born; Elmar came to Lafayette, Indiana with his father in August 1939, just before the Second World War broke out.[6]: 41, 53  Maria died in 1938, the same year Lanczos became an American citizen. Lanczos' father died the following year.[2] After the War, he left Purdue[4] and moved to Seattle, working for the Boeing Aircraft Company and the University of Washington.[3] Between 1949 and 1952, Lanczos worked for the National Bureau of Standards (now the National Institute of Standards and Technology) Institute for Numerical Analysis at the University of California at Los Angeles (UCLA).[3] There, he participated in the Mathematical Tables Project.[4]

In 1942, Lanczos and Gordon Charles Danielson worked on a practical technique in Fourier analysis, now known as the fast Fourier transform (FFT).[17][4] But the significance of his discovery was not appreciated at the time, and today the FFT is credited to J. W. Cooley and John Tukey, who published the Cooley–Tukey algorithm in 1965.[18] (As a matter of fact, similar claims can be made for several other mathematicians, including Carl Friedrich Gauss.[18]) The FFT was implemented on a digital computer for the first time in 1966.[4] Lanczos introduced Chebyshev polynomials to numerical computing.

Working in at the U.S. National Bureau of Standards in the District of Columbia after 1949, Lanczos developed a number of techniques for mathematical calculations using digital computers, including:

In 1949, Lanczos showed that the Weyl tensor, which plays a fundamental role in general relativity, can be obtained from a tensor potential now called the Lanczos potential.[19]

During the McCarthy era, Lanczos came under suspicion for possible communist links.[6]: 89  In 1955, he accepted an invitation from Éamon de Valera, then the Prime Minister of Ireland, and moved to the School of Theoretical Physics at the Dublin Institute for Advanced Studies,[4] where he succeeded Schrödinger[20] and stayed until his death in 1974.[21] He wrote many scientific papers and books during this period.[4]

In 1956 Lanczos published Applied Analysis, an exposition of his investigations of ideas in the boundary between classical and numerical analysis illustrated by worked examples. The topics covered include large scale linear systems, harmonic analysis, data analysis, quadrature and power expansions.[22]

In 1960, he won the Chauvenet Prize from the Mathematical Association of America (MAA) for a paper explaining how to decompose an arbitrary rectangular matrix into three, the middle of which is diagonal and the other two orthogonal. This technique is now recognized as singular value decomposition, of use in computer science and computational mathematics.[4]

Lanczos resampling is based on a windowed sinc function as a practical upsampling filter approximating the ideal sinc function, now widely used in video up-sampling for digital zoom applications and image scaling. It was invented by Claude Duchon, who named it after Lanczos due to Duchon's use of the sigma approximation in constructing the filter, a technique created by Lanczos.[23]

His book The Variational Principles of Mechanics (1949) is a graduate text on mechanics.[24] In the preface of the first edition it is described as a two-semester graduate course of three hours weekly. The second edition (1962) contains a new chapter on relativistic mechanics and the third (1966) has an appendix on Noether's theorem for cyclic coordinates. In the fourth edition (1970), Lanczos discusses at length continuum mechanics and makes further use of Noether's theorem.[25]

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A commemorative plaque at the childhood home of Lanczos. The inscription reads: "Kornél Lánczos spent the years of his youth in this house from 1893 to 1911, an excellent practitioner of mathematics and physics, a world-renowned scientist of quantum mechanics and relativity."

During his career, he was invited to lecture of various topics of mathematical physics at many different institutions.[3] he maintained contact with his doctoral supervisor Ortvay before the War,[4] and occasionally returned to Budapest to lecture on various topics, such as the Stark effect (1930) and Hamilton's principle and canonical equations in classical mechanics (1933).[2] In Space through the Ages (1970), based on a series of lectures given to mathematicians, physicists, chemists, engineers, and philosophers at North Carolina State University in 1968, Lanczos overviews the history of geometry from the time of the ancient Greeks up until the early twentieth century. He does not, however, discuss topology.[26]

His last book was The Einstein Decade: 1905–1915 (1974). In it, Lanczos made use of his fluency in the German language as his grasp of to mathematics and physics discuss in detail the scientific publications of Albert Einstein during that time.[4] In the same year, he published a paper on the vector potential in curved spacetime.[4]

He died in Budapest in 1974 of a sudden heart attack during a summer visit. His collected works, six volumes in all, are held at North Carolina State University in collaboration with the Eötvös Physical Society in Budapest.[2] He was of sound mind mind up until the day he died, when he was working on the Fourier analysis of random sequences, a topic he was scheduled to lecture on in Dublin in July that year.[4]

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Publications

Books

  • 1949: The Variational Principles of Mechanics (dedicated to Albert Einstein), University of Toronto Press ISBN 0-8020-1743-6, followed by 1962, 1966, 1970 editions. ISBN 0-486-65067-7
  • 1956: Applied Analysis, Prentice Hall
  • 1961: Linear Differential Operators, Van Nostrand Company, ISBN 048665656X
  • (1962: The Variational Principles of Mechanics, 2nd ed.)
  • (1966: The Variational Principles of Mechanics, 3rd ed.)
  • 1966: Albert Einstein and the cosmic world order: six lectures delivered at the University of Michigan in the Spring of 1962, Interscience Publishers
  • 1966: Discourse on Fourier Series, Oliver & Boyd
  • 1968: Numbers without End, Edinburgh: Oliver & Boyd
  • (1970: The Variational Principles of Mechanics, 4th ed.)
  • 1970: Judaism and Science, Leeds University Press ISBN 085316021X (22 pages, S. Brodetsky Memorial Lecture)
  • 1970: Space through the Ages (the Evolution of the geometric Ideas from Pythagoras to Hilbert and Einstein), Academic Press ISBN 0124358500
  • 1974: The Einstein Decade (1905 — 1915), Granada Publishing ISBN 0236176323
  • 1998: (William R. Davis, editor) Cornelius Lanczos: Collected Published Papers with Commentaries, North Carolina State University ISBN 0-929493-01-X

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