__NOTOC__ Cornelius (Cornel) Lanczos (, ; born as Kornél Lőwy, until 1906: ''Löwy (Lőwy) Kornél''; February 2, 1893 – June 25, 1974) was a

Hungarian-Jewish The history of the Jews in Hungary dates back to at least the Kingdom of Hungary, with some records even predating the Hungarian conquest of the Carpathian Basin in 895 CE by over 600 years. Written sources prove that Jewish communities lived i ...

Hungarian-American Hungarian Americans (, ) are Americans of Hungarian descent. The U.S. Census Bureau has estimated that there are approximately 1.396 million Americans of Hungarian descent as of 2018. The total number of people with ethnic Hungarian backgroun ...

and later Hungarian-Irish

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

and

physicist A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate cau ...

. According to

György Marx György Marx (25 May 1927 – 2 December 2002) was a Hungarian physicist, astrophysicist, science historian and professor. He discovered the lepton numbers and established the Lepton number#Lepton flavor conservation, law of lepton flavor conse ...

he was one of The Martians.

Biography

He was born in Fehérvár (Alba Regia),

Fejér County Fejér (, ) is an administrative county in central Hungary. It lies on the west bank of the river Danube and nearly touches the eastern shore of Lake Balaton. It shares borders with the Hungarian counties Veszprém, Komárom-Esztergom County ...

Kingdom of Hungary The Kingdom of Hungary was a monarchy in Central Europe that existed for nearly a millennium, from 1000 to 1946 and was a key part of the Habsburg monarchy from 1526-1918. The Principality of Hungary emerged as a Christian kingdom upon the Coro ...

to Jewish parents, Károly Lőwy and Adél Hahn. Lanczos' Ph.D. thesis (1921) was on

relativity theory The theory of relativity usually encompasses two interrelated physics theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical phe ...

. He sent his thesis copy to

Albert Einstein Albert Einstein (14 March 187918 April 1955) was a German-born theoretical physicist who is best known for developing the theory of relativity. Einstein also made important contributions to quantum mechanics. His mass–energy equivalence f ...

, and Einstein wrote back, saying: "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."Barbara Gellai (2010) ''The Intrinsic Nature of Things: the life and science of Cornelius Lanczos'',

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

In 1924 he discovered an exact solution of the

Einstein field equation In the general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter within it. The equations were published by Albert Einstein in 1915 in the ...

representing a cylindrically symmetric rigidly rotating configuration of

dust Dust is made of particle size, fine particles of solid matter. On Earth, it generally consists of particles in the atmosphere that come from various sources such as soil lifted by wind (an aeolian processes, aeolian process), Types of volcan ...

particles. This was later rediscovered by

Willem Jacob van Stockum Willem Jacob van Stockum (20 November 1910 – 10 June 1944) was a Dutch mathematician who made an important contribution to the early development of general relativity. Biography Van Stockum was born in Hattem in the Netherlands. His father w ...

and is known today as the

van Stockum dust In general relativity, the van Stockum dust is an exact solution of the Einstein field equations where the gravitational field is generated by dust rotating about an axis of cylindrical symmetry. Since the density of the dust is ''increasing'' wi ...

. It is one of the simplest known exact solutions in general relativity and is regarded as an important example, in part because it exhibits

closed timelike curve In mathematical physics, a closed timelike curve (CTC) is a world line in a Lorentzian manifold, of a material particle in spacetime, that is "closed", returning to its starting point. This possibility was first discovered by Willem Jacob van St ...

s. Lanczos served as assistant to

during the period of 1928–29. In 1927 Lanczos married Maria Rupp. He was offered a one-year visiting professorship from

Purdue University Purdue University is a Public university#United States, public Land-grant university, land-grant research university in West Lafayette, Indiana, United States, and the flagship campus of the Purdue University system. The university was founded ...

. For a dozen years (1927–39) 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 Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. It was the first conceptually autonomous and logically consistent formulation of quantum mechanics. Its account of quantum ...

and

tensor analysis In mathematics and physics, a tensor field is a function (mathematics), function assigning a tensor to each point of a region (mathematics), region of a mathematical space (typically a Euclidean space or manifold) or of the physical space. Tens ...

. In 1933 his son Elmar was born; Elmar came to

Lafayette, Indiana Lafayette ( ) is a city in and is the county seat of Tippecanoe County, Indiana, United States, located northwest of Indianapolis and southeast of Chicago. According to the 2020 United States census, 2020 census, the population of Lafayette ...

with his father in August 1939, just before

WW II World War II or the Second World War (1 September 1939 – 2 September 1945) was a global conflict between two coalitions: the Allies and the Axis powers. Nearly all of the world's countries participated, with many nations mobilising ...

broke out. Maria was too ill to travel and died several weeks later from

tuberculosis Tuberculosis (TB), also known colloquially as the "white death", or historically as consumption, is a contagious disease usually caused by ''Mycobacterium tuberculosis'' (MTB) bacteria. Tuberculosis generally affects the lungs, but it can al ...

. When the Nazis purged Hungary of Jews in 1944, of Lanczos' family, only his sister and a nephew survived. Elmar married, moved to

Seattle Seattle ( ) is the most populous city in the U.S. state of Washington and in the Pacific Northwest region of North America. With a population of 780,995 in 2024, it is the 18th-most populous city in the United States. The city is the cou ...

and raised two sons. When Elmar looked at his own firstborn son, he said: "For me, it proves that Hitler did not win." During the McCarthy era, Lanczos came under suspicion for possible

communist Communism () is a sociopolitical, philosophical, and economic ideology within the socialist movement, whose goal is the creation of a communist society, a socioeconomic order centered on common ownership of the means of production, di ...

links. In 1952, he left the U.S. and moved to the School of Theoretical Physics at the

Dublin Institute for Advanced Studies The Dublin Institute for Advanced Studies (DIAS) () is a statutory independent research institute in Dublin, Ireland. It was established, under the Institute For Advanced Studies Act 1940, by the government of the then Taoiseach, Éamon de Vale ...

in Ireland, where he succeeded

Erwin Schrödinger Erwin Rudolf Josef Alexander Schrödinger ( ; ; 12 August 1887 – 4 January 1961), sometimes written as or , was an Austrian-Irish theoretical physicist who developed fundamental results in quantum field theory, quantum theory. In particul ...

and stayed until his death in 1974. 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 Analysis is the branch of mathematics dealing with continuous functions, limits, and related theories, such as differentiation, integration, measure, infinite sequences, series, and analytic functions. These theories are usually studied in ...

and

numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of ...

: it is roughly the theory of approximation by finite (or truncated infinite)

algorithm In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algo ...

s."

Research

Lanczos did pioneering work along with

G. C. Danielson Gordon Charles Danielson (October 28, 1912 - September 30, 1983) was a Distinguished Professor in Sciences and Humanities in 1964 at Iowa State University at Ames, Iowa. His name was added to the Distinguished Professor Award Wall in Beardsher ...

on what is now called the

fast Fourier transform A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT). A Fourier transform converts a signal from its original domain (often time or space) to a representation in ...

(FFT, 1940), but the significance of his discovery was not appreciated at the time, and today the FFT is credited to Cooley and Tukey (1965). (As a matter of fact, similar claims can be made for several other mathematicians, including

Carl Friedrich Gauss Johann Carl Friedrich Gauss (; ; ; 30 April 177723 February 1855) was a German mathematician, astronomer, geodesist, and physicist, who contributed to many fields in mathematics and science. He was director of the Göttingen Observatory and ...

.). Lanczos was the one who introduced

Chebyshev polynomials The Chebyshev polynomials are two sequences of orthogonal polynomials related to the cosine and sine functions, notated as T_n(x) and U_n(x). They can be defined in several equivalent ways, one of which starts with trigonometric functions: ...

to numerical computing. Working in Washington DC at the U.S.

National Bureau of Standards The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical sc ...

after 1949, Lanczos developed a number of techniques for mathematical calculations using digital computers, including: * the

Lanczos algorithm The Lanczos algorithm is an iterative method devised by Cornelius Lanczos that is an adaptation of power iteration, power methods to find the m "most useful" (tending towards extreme highest/lowest) eigenvalues and eigenvectors of an n \times n ...

for finding

eigenvalues In linear algebra, an eigenvector ( ) or characteristic vector is a vector that has its direction unchanged (or reversed) by a given linear transformation. More precisely, an eigenvector \mathbf v of a linear transformation T is scaled by a ...

of large symmetric matrices, * the

Lanczos approximation In mathematics, the Lanczos approximation is a method for computing the gamma function numerically, published by Cornelius Lanczos in 1964. It is a practical alternative to the more popular Stirling's approximation for calculating the gamma functio ...

for the gamma function, * the

conjugate gradient method In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is positive-semidefinite. The conjugate gradient method is often implemented as an it ...

for solving

systems of linear equations In mathematics, a system of linear equations (or linear system) is a collection of two or more linear equations involving the same variables. For example, : \begin 3x+2y-z=1\\ 2x-2y+4z=-2\\ -x+\fracy-z=0 \end is a system of three equations in ...

. In 1962, Lanczos showed that the

Weyl tensor In differential geometry, the Weyl curvature tensor, named after Hermann Weyl, is a measure of the curvature of spacetime or, more generally, a pseudo-Riemannian manifold. Like the Riemann curvature tensor, the Weyl tensor expresses the tidal for ...

, which plays a fundamental role in general relativity, can be obtained from a tensor potential that is now called the Lanczos potential.

Lanczos resampling Lanczos filtering and Lanczos resampling are two applications of a certain mathematical formula. It can be used as a low-pass filter or used to smoothly interpolate the value of a digital signal between its samples. In the latter case, it maps ...

is based on a windowed

sinc function In mathematics, physics and engineering, the sinc function ( ), denoted by , has two forms, normalized and unnormalized.. In mathematics, the historical unnormalized sinc function is defined for by \operatorname(x) = \frac. Alternatively, ...

as a practical upsampling filter approximating the ideal sinc function. Lanczos resampling is widely used in video up-sampling for digital zoom applications and

image scaling In computer graphics and digital imaging, image scaling refers to the resizing of a digital image. In video technology, the magnification of digital material is known as upscaling or resolution enhancement. When scaling a vector graphic image ...

. His book ''The Variational Principles of Mechanics'' (1949) is a graduate text on

mechanics Mechanics () is the area of physics concerned with the relationships between force, matter, and motion among Physical object, physical objects. Forces applied to objects may result in Displacement (vector), displacements, which are changes of ...

. In the preface of the first edition it is described as a two-semester graduate course of three hours weekly.

Publications

Books

* 1949: ''The Variational Principles of Mechanics'' (dedicated to

University of Toronto Press The University of Toronto Press is a Canadian university press. Although it was founded in 1901, the press did not actually publish any books until 1911. The press originally printed only examination books and the university calendar. Its first s ...

, followed by 1962, 1966, 1970 editions. * 1956: ''Applied Analysis'',

Prentice Hall Prentice Hall was a major American publishing#Textbook_publishing, educational publisher. It published print and digital content for the 6–12 and higher-education market. It was an independent company throughout the bulk of the twentieth cen ...

* 1961: ''Linear Differential Operators'', Van Nostrand Company, * (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 Oliver and Boyd was a British publishing and printing firm that traded from 1807 or 1808 until 1990.

* 1968: ''Numbers without End'', Edinburgh: Oliver & Boyd * (1970: ''The Variational Principles of Mechanics'', 4th ed.) * 1970: ''Judaism and Science'', Leeds University Press (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 Academic Press (AP) is an academic book publisher founded in 1941. It launched a British division in the 1950s. Academic Press was acquired by Harcourt, Brace & World in 1969. Reed Elsevier said in 2000 it would buy Harcourt, a deal complete ...

Review
by

Max Jammer Max Jammer (; born Moshe Jammer, ; 13 April 1915 – 18 December 2010), was an Israeli physicist and philosophy of physics, philosopher of physics. He was born in Berlin, Germany. He was Rector and Acting President at Bar-Ilan University from 19 ...

Science Magazine ''Science'' is the peer-reviewed academic journal of the American Association for the Advancement of Science (AAAS) and one of the world's top academic journals. It was first published in 1880, is currently circulated weekly and has a subscrib ...

, December 11, 1970. * 1974: ''The Einstein Decade (1905 — 1915)'',

Granada Publishing Granada ( ; ) is the capital city of the province of Granada, in the autonomous community of Andalusia, Spain. Granada is located at the foot of the Sierra Nevada mountains, at the confluence of four rivers, the Darro, the Genil, the Monachil and ...

*1998: (William R. Davis, editor) ''Cornelius Lanczos: Collected Published Papers with Commentaries'',

North Carolina State University North Carolina State University (NC State, North Carolina State, NC State University, or NCSU) is a public university, public Land-grant university, land-grant research university in Raleigh, North Carolina, United States. Founded in 1887 and p ...

Articles

* Translated reprint * Research Paper 2133. September 1949. *

References

External links

* *
Cornelius Lanczos, Collected published papers with commentaries
published by North Carolina State University

by

Nicholas Higham Nicholas John Higham FRS (25 December 1961 – 20 January 2024) was a British numerical analyst. He was Royal Society Research Professor and Richardson Professor of Applied Mathematics in the Department of Mathematics at the University of ...

Series of historic video tapes
produced in 1972, digitalized on the occasion of the 120th anniversary of Cornelius Lanczos's birth {{DEFAULTSORT:Lanczos, Cornelius 1893 births 1974 deaths People from Székesfehérvár 20th-century Hungarian Jews Hungarian emigrants to the United States 20th-century Hungarian mathematicians American expatriates in the Republic of Ireland 20th-century Hungarian physicists 20th-century Irish mathematicians Numerical analysts Relativity theorists Jewish American physicists Mathematicians from Austria-Hungary Academics of the Dublin Institute for Advanced Studies Fellows of the American Physical Society Victims of McCarthyism