Hermann Minkowski

Hermann Minkowski was born in Aleksotas, Russian Empire (now part of Kaunas, Lithuania), in 1864, the son of a German-Jewish merchant family who emigrated to Königsberg in East Prussia when he was eight. He studied mathematics at the universities of Königsberg and Berlin, took his doctorate in 1885 under Ferdinand von Lindemann with a dissertation on quadratic forms, and held early professorships at Bonn (1892) and Königsberg (1894) before being called to ETH Zürich in 1896. There, his lectures on calculus and analytic mechanics were attended by a young Albert Einstein, who later remarked that Minkowski had considered him a lazy student — the relationship was one of mutual irritation, and Minkowski never fully forgave Einstein for cutting most of his classes. In 1902 Minkowski accepted a chair at Göttingen, joining David Hilbert (his close friend from Königsberg days) at what was then the world's leading centre for mathematical physics.

The central work that bears his name came late and quickly. In 1907, two years after Einstein's special-relativity paper, Minkowski recognised that the symmetry group of Maxwell's equations and the Lorentz transformations was the symmetry group of a four-dimensional pseudo-Euclidean geometry — and that the spacetime interval ds² = c²dt² − dx² − dy² − dz² was the natural invariant of that geometry. His 1907 paper *Die Grundgleichungen für die elektromagnetischen Vorgänge in bewegten Körpern* and 1908 Cologne lecture *Raum und Zeit* announced the result: "Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality." The reformulation made the field tensor F^{μν} a natural rank-2 antisymmetric object, the four-current J^μ a natural Lorentz vector, and the entire structure of electromagnetism manifestly covariant under the Lorentz group. Einstein, who had initially dismissed the geometric reformulation as superfluous mathematical decoration, later acknowledged that without Minkowski's geometry he could not have developed general relativity.

Minkowski died in Göttingen on 12 January 1909 of acute appendicitis, four months after the Cologne lecture and four years after publishing the geometric framework that would define the rest of twentieth-century physics. He was 44. His mathematical legacy beyond relativity was substantial: the *geometry of numbers* (1896), a deep theory of lattice points and convex bodies that became foundational to algebraic number theory; significant work on quadratic forms and Diophantine approximation; and the *Minkowski inequality* in functional analysis. The lunar crater Minkowski bears his name, as do the Minkowski space and Minkowski metric of every special-relativity textbook ever written.