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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]

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He was born in Fehérvár (Alba Regia), Fejér County, Kingdom of Hungary,[3] to Károly Lőwy and Adél Hahn. Lanczos obtained his Ph.D. from the University of Szeged in 1921 for a dissertation on relativity theory.[4] 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."[5]: 20 

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.[6] This was later rediscovered by Willem Jacob van Stockum in 1938.[7] It is one of the simplest known exact solutions in general relativity[8] and is regarded as an important example, in part because it exhibits closed timelike curves.

Lanczos lectured at the University of Frankfurt from 1924 to 1931,[3] and briefly served as assistant to Albert Einstein in Berlin during the academic year 1928–29,[5]: 27 upon invitation by the latter.[3]

In 1927 Lanczos married Maria Rupp.[5]: 41, 53  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 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. 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.[5]: 41, 53 During the War, he participated in the Manhattan Project. Afterwards, he moved to Seattle, working for Boeing and the University of Washington.[3] He also worked for the National Bureau of Standards (now the National Institute of Standards and Technology) and the Institute for Numerical Analysis at the University of California at Los Angeles (UCLA).[3]

Lanczos did pioneering work along with Gordon Charles Danielson on what is now called the fast Fourier transform (FFT) in 1942,[9] 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.[10] (As a matter of fact, similar claims can be made for several other mathematicians, including Carl Friedrich Gauss.[10]) 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 that is now called the Lanczos potential.[11]

During the McCarthy era, Lanczos came under suspicion for possible communist links.[5]: 89  In 1952, he left the U.S. and moved to the School of Theoretical Physics at the Dublin Institute for Advanced Studies in Ireland, where he succeeded Erwin Schrödinger[12] and stayed until his death in 1974.[13]

In 1956 Lanczos published Applied Analysis. The topics covered include "algebraic equations, matrices and eigenvalue problems, large scale linear systems, harmonic analysis, data analysis, quadrature and power expansions...illustrated by numerical examples worked out in detail." The contents of the book are stylized "parexic analysis lies between classical analysis and numerical analysis: it is roughly the theory of approximation by finite (or truncated infinite) algorithms."[14]

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.[15]

His book The Variational Principles of Mechanics (1949) is a graduate text on mechanics.[16] 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.[17]

During his career, he was invited to lecture of various topics of mathematical physics at many different institutions.[3] 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.[18]

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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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