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, a group of Hungarian scientific luminaries who immigrated to the United States to escape national socialism. He was remembered by his colleagues as an innovative scholar and an excellent educator.
He was born in Székesfehérvár, Fejér County, Kingdom of Hungary, Austria-Hungary 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. In mathematics, his notable teacher was Lipót Fejér, then a young mathematician. 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.
In his doctoral dissertation titled The Relation of Maxwell's Aether Equations to Functional Theory, Lanczos re-wrote Maxwell's equations of electromagnetism in terms of quaternions and applied a relativistic variational principle. 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." Lanczos maintained his contact with Einstein for another 35 years, until the latter's death. In 1921, Lanczos completed his Ph.D. training at the University of Szeged under the supervision of Rudolf Ortvay, a former student of Arnold Sommerfeld. While Ortvay was not distinguished as a researcher, he was an inspirational teacher who brought modern physics to Hungary.
As a consequence of the restrictions from the new right-wing regime in Hungary, Lanczos moved to Germany in search of employment. From 1921 to 1924, Lanczos served as a lecturer at the University of Freiburg. 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. This was later rediscovered by Willem Jacob van Stockum in 1938. 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 curves.
Lanczos worked at the University of Frankfurt from 1924 to 1931, delivering lectures for Erwin Madelung as a Privatdozent. He also briefly served as assistant to Albert Einstein in Berlin during the academic year 1928–29,upon invitation by the latter. It was Leo Szilard who recommended him to Einstein. Einstein wrote to Madelung, requesting a leave of absence for Lanczos, which was granted. Before leaving for Berlin, Lanczos wrote to Einstein that Hans Bethe was being considered as his temporary replacement. By the time he went to work with Einstein, Lanczos had already written multiple papers on relativity. 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. Although Einstein and Lanczos published no papers together, Einstein referred to the works of Lanczos in one of his subsequent articles on distant parallelism. Another innovation of Lanczos in this context was harmonic coordinates, which he introduced independently of Théophile De Donder. These were later used by Yvonne Choquet-Bruhat in her proof of the local existence and uniqueness of solutions to the Einstein field equations in vacuum with initial values and in algorithms of numerical relativity that simulate the spiral and merger of binary systems of compact objects, which emit gravitational waves.
Following the seminal publication of Werner Heisenberg announcing the creation of his matrix formulation of quantum mechanics in 1925, Lanczos wrote a paper demonstrating how the new theory could be expressed in terms of linear integral equations. However, at the time, this paper had little impact, in part because physicists were more used dealing with differential equations. Erwin Schrödinger published a series of papers detailing his own undulatory version of quantum theory, which proved rather popular among physicists. But Lanczos' paper made it clear that the two seemingly different formulations of quantum mechanics were in fact equivalent, something Schrödinger himself later proved. Carl Eckart independently reached the same conclusion, based on the work of Lanczos. This paper also helped Paul Dirac create his own formulation of quantum mechanics as a theory of linear transformations. Lanczos's 1926 paper was the earliest continuum-theoretic formulation of quantum mechanics; it was close to the notion of a quantum field. Moreover, Lanczos was willing to accept the probabilistic interpretation of the wave function. 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.
In 1927 Lanczos married Maria Rupp. He moved to the United States in 1931. Mindful of the Great Depression, he turned his attention towards applied mathematics. He began conducting research in numerical analysis, and developed a number of concepts in service of early digital computers. He served as a professor of mathematics and aeronautical engineering at Purdue University from 1931 to 1946. 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. His lecture notes on quantum mechanics examined in detail its mathematical formulation, including topics in function space and group theory. At Purdue, he introduced an "experimental" curriculum for female students.
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. Maria died in 1938, the same year Lanczos became an American citizen. His father died the following year. After the War, he left Purdue and moved to Seattle, working for the Boeing Aircraft Company and the University of Washington. 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). There, he participated in the Mathematical Tables Project.
In 1942, Lanczos and Gordon Charles Danielson developed a practical technique in Fourier analysis, now known as the fast Fourier transform (FFT). But the significance of his discovery was not appreciated at the time, partly because there were no machines to execute this algorithm, and today the FFT is credited to J. W. Cooley and John Tukey, who published the Cooley–Tukey algorithm in 1965. (As a matter of fact, similar claims can be made for several other mathematicians, including Carl Friedrich Gauss.) The FFT was implemented on a digital computer for the first time in 1966.
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, such as the Lanczos algorithm for determining the eigenvalues of large Hermitian matrices.