- Person
- Hermann Minkowski
- Lived
- 1864–1909
- Field
- Mathematics
- From
- German
The story
In 1902 Hermann Minkowski moved to the University of Göttingen, where his close friend David Hilbert had arranged for a new chair to be created especially for him. Minkowski had built his reputation in pure mathematics, in quadratic forms and the geometry of numbers, but at Göttingen he grew increasingly interested in mathematical physics, drawing enthusiasm from Hilbert and his circle. In 1905 he took part in a seminar on the electron theory, learning the latest results in electrodynamics.
Physics was then in upheaval. The work of Hendrik Lorentz and of Minkowski's former Zurich student Albert Einstein had shown that measurements of space and time depend on the motion of the observer. By 1907 Minkowski had concluded that these results were best understood geometrically, in a four-dimensional world in which space and time, formerly thought to be independent, are joined together.
He applied this insight directly to electricity and magnetism. In 1908 he published "Die Grundgleichungen für die elektromagnetischen Vorgänge in bewegten Körpern" (The Fundamental Equations for Electromagnetic Processes in Moving Bodies) in the proceedings of the Göttingen Society of Sciences. In it he worked out a four-dimensional treatment of electrodynamics, reformulating the theory of moving bodies in the new geometry. His work on the subject was gathered in Zwei Abhandlungen über die Grundgleichungen der Elektrodynamik, which MacTutor dates to 1909, and an English translation of the 1908 paper later appeared in the collection The Principle of Relativity (1920).
Einstein did not think much of this mathematical approach at first. Minkowski presented the wider vision in his famous lecture on space and time in September 1908, but he died of appendicitis in Göttingen in January 1909, aged only 44, and did not see his ideas take hold.
They took hold all the same. MacTutor notes that his four-dimensional framework underlay all later mathematical work on relativity and was used by Einstein in developing general relativity, and that Minkowski and Hilbert helped change Einstein's view of mathematics from a mere tool into a source of creativity. Writing the laws of electricity and magnetism in four-dimensional form makes their symmetry under relativity plain to see, and it remains the standard way physicists write Maxwell's equations.
Why it matters
Minkowski's approach gave physicists the four-dimensional mathematical language in which electromagnetism and relativity are still written.
About Hermann Minkowski
Mathematician who taught the young Einstein and in 1908 fused space and time into a single four-dimensional “spacetime”, the geometry on which relativity still rests.
More about Hermann Minkowski
- Minkowski helped launch the world's maths congressHermann Minkowski helped organise the first International Congress of Mathematicians in Zurich in 1897, chairing its arithmetic and algebra section.
- Minkowski invented the geometry of numbersHermann Minkowski created the 'geometry of numbers', solving problems about whole numbers by picturing them as points in a grid, published from 1896.
- Hermann Minkowski joined space and time into spacetimeIn a 1908 lecture Hermann Minkowski, once Einstein's teacher, showed that relativity is best understood in a single four-dimensional 'spacetime', the language of modern physics.
- Minkowski suggested Hilbert's famous list of problemsIn a January 1900 letter, Hermann Minkowski urged David Hilbert to sketch the problems future mathematicians should tackle, inspiring Hilbert's celebrated 23 problems.
- Minkowski's maths guides robots and machine toolsThe Minkowski sum, a way of adding shapes named after Hermann Minkowski, is used in robot motion planning, collision detection and machining.
Sources
- Hermann Minkowski MacTutor History of Mathematics, University of St Andrews
- Hermann Minkowski Wikipedia
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