Cornelius Lanczos | |
|---|---|
 Lanczos in 1947 | |
| Born | (1893-02-02)February 2, 1893 |
| Died | June 25, 1974(1974-06-25) (aged 81) |
| Alma mater | University of Budapest University of Szeged |
| Known for | |
| Spouses |
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| Awards | Chauvenet Prize (1960)[1] |
| Scientific career | |
| Fields | Mathematics Theoretical physics |
| Institutions | |
| Thesis | Relation of Maxwell's Aether Equations to Functional Theory (1921) |
| Doctoral advisor | Rudolf Ortvay |
| Other academic advisors | Loránd Eötvös Lipót Fejér Erwin Madelung |
Cornelius (Cornel) Lanczos (Hungarian:Lánczos Kornél,pronounced[ˈlaːnt͡soʃˈkorneːl]; born asKornél Lőwy, until 1906:Löwy (Lőwy) Kornél; February 2, 1893 – June 25, 1974) was a Hungarian, American, and later Irishmathematician andphysicist. According toGyörgy Marx he was one ofthe Martians,[2] a group of Hungarian scientific luminaries who immigrated to the United States to escapenational socialism. He was remembered by his colleagues as an innovative scholar and an excellent educator.[3][4]
He was born inFehérvár (Alba Regia),Fejér County,Kingdom of Hungary,[5] 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 theUniversity of Budapest, where one of his professors in physics wasRoland Eötvös, whose skills as an experimental physicist impressed him.[3] In mathematics, his notable teacher wasLipót Fejér, then a young mathematician.[3] 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.[3]
In his doctoral dissertation titledThe Relation of Maxwell's Aether Equations to Functional Theory,[6] Lanczos re-wroteMaxwell's equations of electromagnetism in terms ofquaternions and applied a relativisticvariational principle.[2] He sent a copy of his thesis toAlbert 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."[7]: 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 theUniversity of Szeged under the supervision of Rudolf Ortvay, a former student ofArnold Sommerfeld.[2] While Ortway was not distinguished as a researcher, he was an inspirational teacher who broughtmodern physics to Hungary.[2][3]
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 theUniversity of Freiburg.[5] In 1924 he discovered anexact solution to theEinstein field equations of general relativity representing a cylindrically symmetric rigidly rotating configuration ofdust particles.[8] This was later rediscovered byWillem Jacob van Stockum in 1938.[9] It is one of the simplest known exact solutions in general relativity[10] and is regarded as an important example, in part because it exhibitsclosed timelike curves.[11]
Lanczos worked at theUniversity of Frankfurt from 1924 to 1931,[5] delivering lectures forErwin Madelung as aPrivatdozent.[3]: 491 He also briefly served as assistant toAlbert Einstein in Berlin during the academic year 1928–29,[7]: 27 upon invitation by the latter.[5] It wasLeo Szilard who recommended him to Einstein.[2] Einstein wrote to Madelung, requesting a leave of absence for Lanczos, which was granted. Before leaving for Berlin, Lanczos wrote to Einstein thatHans Bethe was being considered as his temporary replacement.[12]: 491 By the time he went to work with Einstein, Lanczos had already written multiple papers on relativity.[12]: 491 In Berlin, Lanczos examined themotion of singularities—meaning, particles—in curved spacetime as described bygeneral relativity. Einstein had a high opinion of Lanczos for his mathematical skills. In this capacity, Lanczos replacedMarcel Grossmann as Einstein's collaborator, helping him with the difficultmathematics of general relativity.[2] Although Einstein and Lanczos published no papers together, Einstein referred to the works of Lanczos in one of his subsequent articles ondistant parallelism.[12]: 491
Following the seminal publication ofWerner Heisenberg announcing the creation of hismatrix formulation of quantum mechanics in 1925,[13] Lanczos wrote a paper demonstrating how the new theory could be expressed in terms of linearintegral equations.[14][2] However, at the time, this paper had little impact, in part because physicists were more used dealing withdifferential equations.[15]: 276 Erwin Schrödinger published a series of papers detailing his ownundulatory 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.[16]Carl Eckart independently reached the same conclusion, based on the work of Lanczos.[17][18] This paper also helpedPaul Dirac create his own formulation of quantum mechanics as a theory oflinear transformations.[15]: 300–1 Lanczos's 1926 paper was the earliest continuum-theoretic formulation of quantum mechanics;[3] it was close to the notion of aquantum field.[15]: 276 Moreover, Lanczos was willing to accept theprobabilistic interpretation of the wave function.[4] In 1972, at an event organized by theEuropean Physical Society inTrieste, Italy,Bartel Leendert van der Waerden publicly recognized the significance of that paper, which correctly formulated theeigenvalue problem in terms of integration and even came close to introducing theDirac-distribution. But van der Waerden was unaware that Lanczos was in the audience untilLéon Rosenfeld urged the latter to come to the stage.[3]
In 1927 Lanczos married Maria Rupp.[7]: 41, 53 He moved to the United States in 1931.[3] Mindful of theGreat Depression, he turned his attention towardsapplied mathematics.[2] He began conducting research innumerical analysis,[3] and developed a number of concepts in service of early digital computers.[4] He served as a professor of mathematics andaeronautical engineering atPurdue University from 1931 to 1946.[5] 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 andtensor analysis.[7]: 41, 53 His lecture notes on quantum mechanics examined in detail itsmathematical formulation, including topics infunction space andgroup theory.[2] At Purdue, he introduced an "experimental" curriculum for female students.[4]
In 1933 his son Elmar was born; Elmar came toLafayette, Indiana with his father in August 1939, just before the Second World War broke out.[7]: 41, 53 Maria died in 1938, the same year Lanczos became an American citizen. His father died the following year.[2] After the War, he left Purdue[3] and moved toSeattle, working for theBoeing Aircraft Company and theUniversity of Washington.[5] Between 1949 and 1952, Lanczos worked for the National Bureau of Standards (now theNational Institute of Standards and Technology) Institute for Numerical Analysis at theUniversity of California at Los Angeles (UCLA).[5] There, he participated in theMathematical Tables Project.[3]
In 1942, Lanczos andGordon Charles Danielson developed a practical technique inFourier analysis, now known as thefast Fourier transform (FFT).[19][3] But the significance of his discovery was not appreciated at the time, partly because there were no machines to execute this algorithm,[4] and today the FFT is credited toJ. W. Cooley andJohn Tukey, who published theCooley–Tukey algorithm in 1965.[20] (As a matter of fact, similar claims can be made for several other mathematicians, includingCarl Friedrich Gauss.[20]) The FFT was implemented on adigital computer for the first time in 1966.[3]
Working in at the U.S. National Bureau of Standards in theDistrict of Columbia after 1949, Lanczos developed a number of techniques for mathematical calculations using digital computers, such as theLanczos algorithm for determining theeigenvalues of largeHermitian matrices.[4]
In 1949, Lanczos showed that theWeyl tensor, which plays a fundamental role in general relativity, can be obtained from a tensor potential now called theLanczos potential.[21]
In 1952, Lanczos examined the utility of theChebyshev polynomials inapproximating the solution of linear systems.[22]
During theMcCarthy era, Lanczos came under suspicion for possiblecommunist links.[7]: 89 In 1955, he accepted an invitation fromÉamon de Valera, then the Prime Minister of Ireland, and moved to the School of Theoretical Physics at theDublin Institute for Advanced Studies,[3] where his colleagues included Schrödinger andJohn Lighton Synge.[3][23] Shortly after arriving he gave lectures on numerical methods, such asa new approximation for thegamma function he developed.[3] He remained there until his death in 1974.[24] He wrote many scientific papers and books during this period; he also became interested in some newly developed ideas in mathematical physics, notablySchwartz distributions andSobolev spaces.[3] Despite being a victim of Joseph McCarthy, Lanczos still referred to the United States as his "dream land" on conversations with those he knew.[3]
In 1956 Lanczos publishedApplied Analysis, an exposition of his investigations of ideas in the boundary betweenclassical and numerical analysis illustrated by worked examples. The topics covered include large scalelinear systems,harmonic analysis,data analysis,numerical quadrature andpower series expansions.[25] The chapter on numerical quadrature was inspired by a number of problems posed by Schrödinger.[3]
In 1960, he won theChauvenet Prize from theMathematical Association of America (MAA) for a paper explaining how to decompose an arbitrary rectangular matrix into three, the middle of which isdiagonal and the other twoorthogonal. This technique is now recognized assingular value decomposition, of use incomputer science andcomputational mathematics.[3]
Lanczos resampling is based on a windowedsinc function as a practical upsampling filter approximating the ideal sinc function, now widely used in video up-sampling for digital zoom applications andimage scaling. It was invented by Claude Duchon, who named it after Lanczos due to Duchon's use of thesigma approximation in constructing the filter, a technique created by Lanczos.[26]
His bookThe Variational Principles of Mechanics (1949) is a graduate text onmechanics.[27] He published it shortly after moving to Los Angeles.[3] 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 onrelativistic mechanics and the third (1966) has an appendix onNoether's theorem forcyclic coordinates. In the fourth edition (1970), Lanczos discusses at lengthcontinuum mechanics and makes further use of Noether's theorem.[28]
During his career, he was invited to lecture of various topics of mathematical physics at many different institutions.[5] he maintained contact with his doctoral supervisor Ortvay before the War,[3] and occasionally returned to Budapest to lecture on various topics, such as theStark effect (1930) andHamilton's principle andcanonical equations in classical mechanics (1933).[2] InSpace through the Ages (1970), based on a series of lectures given to mathematicians, physicists, chemists, engineers, and philosophers atNorth Carolina State University in 1968, Lanczos overviews thehistory of geometry from the time of the ancient Greeks up until the early twentieth century. He does not, however, discusstopology.[29] Throughout his life, Lanczos maintained his conviction that mathematics should not be separated from its history; he lectured on this topic with great enthusiasm.[4]
His last book wasThe 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 thescientific publications of Albert Einstein during that time.[3] In the same year, he published a paper on thevector potential in curved spacetime.[3]
He died in Budapest in 1974 of a suddenheart 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 ofrandom sequences, a topic he was scheduled to lecture on in Dublin in July that year.[3]
