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The Intrinsic Nature of Things: The Life and Science of Cornelius Lanczos

Barbara Gellai
American Mathematical Society
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The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries.

[Reviewed by
Tom Schulte
, on

At 127 pages, not counting addenda to the main text, this is a brief overview of a life of genius and import. Three main dimensions of this life interleave the chronological telling and make for an enlightening read. The subject is a mathematical innovator, exceptional educator, and key figure in the transition from relativity to quantum mechanics. Lanczos lived at a pivotal time and, as the book jacket states, “demonstrated a remarkable ability to be at the right place, or work with the right person, at the right time.” This makes the story of his life the story of a revolution in scientific thought and process during the generally pivotal era of the ‘30s through the ‘50s.

This physicist-mathematician early on provided fundamental support to general relativity with an exact solution of the Einstein field equations for gravity. He worked out the Fast Fourier Transform a quarter century before there existed machines on which to run it. When Lanczos did have his hands on such early computers, he independently rediscovered singular value decomposition. This is fundamental to many numerical methods. While providing practical advances to the mathematics of aeronautical engineering at Boeing and doing pioneering work for the National Bureau of Standards, he conceived an important contribution to finding eigenvalues of large matrices.

Said Einstein to Lanczos: “the clarity of your thinking and your ability for teaching are of an extraordinary level.” Apparently, it was the practical intuition of the physicist side of his intelligence that made him a success with students beginning with an “experimental” curriculum for women students at Purdue in the 1930s. He lectured on the history of mathematics with evangelical zeal, as we learn he felt it was imperative that the subject should not be dissociated from its history. Lanczos’ approach (from his notes) “pursues mathematics … as a noble and fascinating adventure on the vast sea of intellectual endeavors… the philosophical meaning of ideas and processes is considered as something so indispensable and important for true understanding of the spirit of mathematics that it has to come before anything else.” Thrilling! Lanczos continued developing and defending his approach to pedagogy for a decade and it is this reviewer’s hope that his unpublished lecture notes on the history of mathematics, reposing at Purdue, will see publication in some form.

At the start of his scientific career in Germany, Lanczos spent a year working as Einstein's assistant. The two were correspondents for years thereafter. Lanczos lectured on theoretical physics at University Frankfurt in the 1920s. During the time as a Heisenberg proponent he helped solidify the groundwork of the field-like representation of quantum mechanics. While Lanczos’ work was quickly outmoded by the wave mechanics of Schrödinger, Lanczos had the agility of mind to grasp the accuracy of this insight while Einstein remained bearish on such probabilistic theories.

Facing anti-Semitism in Germany in the 1930s, Lanczos moved to the United States to meet the rising tide of the earliest digital computers. There a brush with the more prejudice from McCarthyism in the 1950s saw Lanczos relocate once again, joining Schrödinger at the Dublin Institute for Advanced Studies in Ireland. Gellai’s biography tells the story of this fascinating life in a breathless, if captivating, fashion. This is a life story as much as scientific biography. The reader that finds a sentence like “he chose the fundamental action principle (the Lagrangian) to be a quadratic function of the space curvature components” to be a speed bump will still enjoy the thrills and curves of the fast road from subatomic insight to guiding the production of mathematical tables for the war effort to vistas of the Riemann space as globetrotting lecturer in his final years.

Tom Schulte works in history of mathematics topics lecturing to students at Oakland Community College.