Walther Mayer

Background

Walther Mayer was born on March 11, 1887, in Graz, then part of Austria-Hungary. He was Jewish, and antisemitism later restricted his advancement within Austrian academic institutions despite his mathematical ability and research record.

Mayer served in the First World War from 1914 to 1919. After the war he returned to mathematical research, concentrating particularly on differential geometry and topology. His wartime service and subsequent academic work unfolded during a period in which Vienna remained an important center of Central European mathematics but was also affected by political and antisemitic pressures.

Education

Mayer studied mathematics at the Federal Institute of Technology in Zürich, the University of Vienna, the University of Göttingen, and the University of Paris, including the Sorbonne. The Zürich institution, now ETH Zürich, was established as Switzerland's federal center for advanced technical and scientific education; Göttingen was one of Europe's leading mathematical research centers; and the University of Paris was a major international institution for mathematical study.

He received his doctorate from the University of Vienna in 1912 for a dissertation on applications of the Fredholm functional equation to boundary-value problems involving logarithmic potentials. The University of Vienna, founded in 1365, had developed a distinguished mathematical tradition that included research in analysis, geometry, and topology. Mayer completed his habilitation in differential geometry there in 1926 and later held the formal status of associate professor.

Career

Mayer began his academic career through mathematical research and university teaching in Vienna. He completed his doctorate at the University of Vienna in 1912 and, after military service during the First World War, continued research in differential geometry. In 1926 he became a Privatdozent at the University of Vienna, and in 1931 he was appointed an associate professor. The university's mathematics institute was part of Vienna's influential interwar mathematical community, although political and antisemitic conditions limited the careers of many Jewish scholars.

In 1929, on the recommendation of Richard von Mises, Mayer became Albert Einstein's mathematical assistant. Their collaboration concerned distant parallelism, unified field theory, and relativity. Mayer and Einstein published joint work on static solutions of field equations and on semivectors and spinors; Mayer continued working with Einstein through the early 1930s and contributed mathematical expertise to Einstein's attempts to connect gravitation with electromagnetism.

After the Nazi seizure of power in Germany, Mayer followed Einstein to the United States in 1933. He became an associate in mathematics at the Institute for Advanced Study in Princeton, an institution founded in 1930 as an independent center for advanced research without a teaching program. The Institute's School of Mathematics brought together leading mathematicians and mathematical physicists, including Einstein, John von Neumann, and Hermann Weyl.

Mayer's independent mathematical work included topology, differential geometry, homology theory, calculus of variations, and the geometry of submanifolds. With Leopold Vietoris, he is commemorated in the Mayer–Vietoris sequence, a fundamental tool for relating the topology of a space to that of overlapping subspaces. He remained associated with the Institute for Advanced Study until his death in Princeton on September 10, 1948.

Achievements

• Mayer's work with Leopold Vietoris gave his name to the Mayer–Vietoris sequence, a central construction in algebraic topology used to analyze the homology of spaces assembled from overlapping subspaces.

• Mayer developed an axiomatic treatment of homology in work that preceded the later Eilenberg–Steenrod axioms and contributed to the formal development of algebraic topology.

• Mayer collaborated with Albert Einstein on distant parallelism, unified field theory, and relativity, providing mathematical analysis for Einstein's attempts to connect gravitation and electromagnetism.

• Mayer made sustained contributions to differential geometry through research on Riemannian geometry, submanifolds, Lie groups, parallel vector fields, and the calculus of variations.

Works

• research article

  • Die Differentialgeometrie der Untermannigfaltigkeiten des R_n konstanter Krümmung

    (This paper studied the differential geometry of submanifo...)

    1935

  • Semi-Vektoren und Spinoren

    (Co-authored with Albert Einstein, this paper treated semi...)

    1932

  • Über abstrakte Topologie

    (This paper developed Mayer's work in abstract topology an...)

    1929

  • Zwei strenge statische Lösungen der Feldgleichungen der einheitlichen Feldtheorie

    (Co-authored with Albert Einstein, this paper presented ex...)

    1930

  • On the foundations of calculus of variations

    (Written with Herbert Busemann, this paper contributed to ...)

    1941

  • A new homology theory

    (This work, published in two parts, advanced Mayer's axiom...)

    1942

  • Foundations of the theory of Lie groups

    (Written with T. Y. Thomas, this paper addressed foundatio...)

    1935

  • Fields of parallel vectors in non-analytic manifolds in the large

    (Written with T. Y. Thomas, this paper examined parallel v...)

    1938

• textbook

  • Lehrbuch der Differentialgeometrie, Band 2: Riemannsche Geometrie

    (Mayer's volume on Riemannian geometry formed the second p...)

    1930

Personality

Quotes from others about the person

• Einstein reportedly referred to Mayer as his "calculator," a description associated with Mayer's role in supplying mathematical expertise during their collaboration on unified field theory and relativity.

Connections

Mayer's most significant documented professional connection was with Albert Einstein. Beginning in 1929, he served as Einstein's mathematical assistant and collaborated with him on distant parallelism, unified field theory, and relativity. Their joint work continued after Mayer moved to the United States and formed an important part of his mathematical-physical career.

Collegue :

Albert Einstein

Einstein recommended Mayer for mathematical assistance in 1929 and collaborated with him on distant parallelism, unified field theory, and relativity until the early 1930s.

Collegue :

Leopold Vietoris

Mayer and Vietoris are jointly commemorated in the name of the Mayer–Vietoris sequence in topology.

References

• Walther Mayer | Institute for Advanced Study Institutional profile documenting Mayer's affiliation with the Institute for Advanced Study School of Mathematics from September 1933 until June 1948.
• Walther Mayer – More than “Einstein’s calculator” Biographical account of Mayer's education, work at the University of Vienna, collaboration with Einstein, and contributions beyond his popular association with Einstein.
  2023
• Walther Mayer Contemporary obituary notice identifying Mayer as an Austrian mathematician, Einstein collaborator, and associate at the Institute for Advanced Study.
  1948
• Albert Einstein's mathematical assistant Walther Mayer National Diet Library reference entry summarizing biographical sources and bibliographic information concerning Mayer's education, academic career, Einstein collaboration, and publications.
  2009
• History of Mathematics at the University of Vienna Institutional history placing Mayer among the mathematicians who conducted research and taught at the University of Vienna's Institute of Mathematics.