This book recounts the extraordinary personal journey and scientific story of Hungarian-born mathematician and physicist Cornelius Lanczos. His life and his mathematical accomplishments are inextricably linked, reflecting the social upheavals and historical events that shaped his odyssey in 20th-century Hungary, Germany, the United States, and Ireland.

In his life Lanczos demonstrated a remarkable ability to be at the right place, or work with the right person, at the right time. At the start of his scientific career in Germany he worked as Einstein's assistant for one year and stayed in touch with him for years thereafter. Reacting to anti-Semitism in Germany in the 1930s, he moved to the United States, where he would work on some of the earliest digital computers at the National Bureau of Standards. After facing suspicion of Communist sympathies during the McCarthy era in the 1950s, Lanczos would relocate once again, joining Schrödinger at the Dublin Institute for Advanced Studies. Gellai's biography analyzes a rich life and a body of work that reaches across many scientific disciplines.

Lanczos made important contributions to several areas of mathematics and mathematical physics. His first major contribution was an exact solution of the Einstein field equations for gravity (in general relativity). He worked out the Fast Fourier Transform, but since there were no machines on which to run it, this accomplishment would be forgotten for 25 years. Once he had access to computers, Lanczos independently rediscovered what is now known as the singular value decomposition, a fundamental tool in numerical methods. Other significant contributions included an important discovery about the Weyl tensor, which is now known as the Lanczos potential, and an important contribution on algorithms for finding eigenvalues of large matrices.