by Jennifer L. Atkinson

© Oxford University Press 2004 All rights reserved

**Lanczos, Cornelius** *[formerly* Kornél Löwy] (1893-1974), mathematician and mathematical physicist, was born on 2 February 1893 in Székesfehérvár, Hungary, the first of four children born to lawyer Károly Löwy (1854-1939) and his wife, Adél Hahn. Lanczos attended a Jewish elementary school and graduated from the local Catholic school in 1910. From 1911 he studied at the University of Budapest under Fejér and Eötvös. After graduating in 1915 until 1920 he worked at the Technical University of Budapest as physics assistant to Tangl. In 1921 Lanczos received his doctorate at the University of Szeged under Ortvay (a student of Sommerfeld).

Owing to antisemitism in Hungary, Lanczos spent the next ten years in Germany, first as a lecturer at the University of Freiburg in Breisgau, then, from 1924 to 1931, at Frankfurt am Main.

In papers of 1922 and 1923 Lanczos was the first to show that the de Sitter solution could be written in a form which avoided singularity at the mass horizon. He wrote a significant paper in 1924 on the surface distributions of matter in Einstein's theory and, in a series of papers published in 1925, developed a new approach to the problem of radiation, using the general theory of integral equations. In the same year ground-breaking papers in quantum mechanics were published by Heisenberg, Born, and Jordan. Lánczos recognized that by reformulating the matrix theoretical method of Heisenberg-Born-Jordan into integral equations, he would have the method to construct physical problems within a fluid field theory. In December 1925 he showed how the techniques of matrix mechanics could be represented in terms of integral equations, but the form of the universal kernal function in the integral equations remained unsolved. Schrödinger solved this and published four weeks later (in January 1926), so preceding Lanczos's idea of the field-like representation of quantum theory.

In 1928-9 Lanczos, who in 1922 had published a paper on the Einsteinian equations of gravity, was granted leave to work with Einstein at the University of Berlin. It was during this time that Lanczos met such people as Schrödinger and von Neumann and he continued a lively correspondence with Einstein throughout the following years. He married in 1927, Maria Rupp *(d.* 1939); they had a son.

In 1931 Lanczos was invited to the United States as professor of mathematical physics at the University of Purdue, Indiana. He had published his first paper on the quadratic action principle in relativity that year, but his main research area at Purdue was numerical analysis. In 1938 Lanczos developed his well-known theory of economization of polynomials (the Lanczos-Tau method). He also published two papers in 1942 on practical techniques of Fourier analysis which anticipated the Fast-Fourier Transform. In 1943-4 he was seconded to the National Bureau of Standards to work on the mathematical tables project in New York.

In 1946 Lanczos left Purdue to become senior research engineer at the Boeing Company in Seattle. A year later he was appointed Walker-Ames lecturer at the University of Washington, Seattle. From 1949 to 1952 he worked at the Institute for Numerical Analysis at the University of California. In 1949 his first book, *Variational Principles of Mechanics,* was published and in 1951 he published the first exact method for obtaining all the eigenvectors and eigenvalues of an arbitrary matrix.

It was in 1952 that Lanczos was invited to join Dublin Institute for Advanced Studies in Ireland as a visiting lecturer. He returned to the United States in 1953-4 as a computer specialist with North American Aviation, then took up a permanent position at the Dublin Institute as senior professor in 1954. He married Ilse Hildebrand in 1955. During his time in Dublin Lanczos held visiting professorships at a number of institutions in the United States. He was professor emeritus at Dublin from 1968 until his death. This period spent in Ireland was remarkably fruitful and productive. Lanczos wrote seven books on the topics of applied analysis, linear differential operators, Fourier analysis, number, geometry, and on Albert Einstein, in addition to over 120 papers during his lifetime. Significantly, Lanczos wished to be remembered for introducing a new type of mathematical textbook; he wrote with great clarity, possessing a very personal style.

Lanczos's mathematical research centred on Fourier series, Fourier analysis and synthesis, Fourier transforms, matrix eigenvalues and eigenfunctions, Chebyshev polynomials, the gamma function and numerical analysis; in physics he worked on relativity theory, quantum mechanics, classical mechanics, and electromagnetism, and published about a hundred scientific papers. In 1960 he was awarded the Chauvenet prize by the Mathematical Association of America for his fundamental paper on the decomposition of an arbitrary matrix, first published in 1958.

Despite his extreme humility Lanczos received much recognition throughout his distinguished career, including membership of the Royal Irish Academy and honorary doctorates from Trinity College, Dublin (1962), National University of Ireland (1970), University of Frankfurt am Main (1972), and University of Lancaster (1972).

Lanczos was a member of many professional bodies, including the American Mathematical Society, the American Physical Society, the Society for Industrial and Applied Mathematics, and the Mathematical Association of America. He was a fellow of the American Association for the Advancement of Science, a member of Sigma Xi, and an honorary member of Sigma Pi Sigma.

A devoutly religious man Lanczos was proud of his Jewish heritage and ministered as a Levite at the synagogue. He was fluent in three languages and was an accomplished pianist, holding regular ensembles at his home in Dublin, in addition to taking a keen interest in the arts. Towards the end of his life Lanczos was still active in research and had been working in the field of Fourier analysis in the days before he died. It was at the Roland Eötvös University in Budapest while on a lecturing visit that Lanczos suffered a heart attack, on 25 June 1974. His funeral was held on 5 July in Budapest, where he was buried. He was survived by his second wife.

JENNIFER L. ATKINSON

**Sources **

J. D. Brown and others, eds., *Cornelius Lánczos International Centenary Conference* [Raleigh, NC 1993] (1994)

R. Butler and H. G. Hopkins, 'Cornelius Lánczos, mathematician and mathematical physicist', *Advance,* 15 (Oct 1974), 53--6

*The Times* (9 July 1974)

B. K. P. Saife, ed., *Studies in numerical analysis: papers presented to Cornelius Lánczos* (1974)

W. Yourgrau, 'Cornelius Lánczos, 1893-1974', *Foundations of Physics,* 5 (1975), 19-20

private information (2004)

**Likenesses **

J. Chirnside, charcoal, University of North Carolina

photograph, University of Manchester Institute of Science and Technology

photograph, University of Manchester Institute of Science and Technology, mathematics department

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