- Person
- Hermann Minkowski
- Lived
- 1864–1909
- Field
- Mathematics
- From
- German
The story
Hermann Minkowski and David Hilbert met as students at the University of Königsberg in the early 1880s and became lifelong friends, together with the young lecturer Adolf Hurwitz. Their careers stayed linked: in 1902 Hilbert arranged for a chair to be created especially for Minkowski at Göttingen, and when Minkowski died in 1909 Hilbert called him his best and most dependable friend.
Their friendship also shaped the history of mathematics. Hilbert was invited to give a major lecture at the International Congress of Mathematicians in Paris in 1900, and in a letter dated 5 January 1900 Minkowski advised him on a theme. The lecture with the greatest impact, he wrote, would be an attempt to preview the future: a sketch of the problems with which mathematicians of the coming years should occupy themselves. Such a talk, he suggested, might be discussed for decades.
Hilbert took the advice. Speaking at the Sorbonne on 8 August 1900, he presented ten problems. The complete list of 23, then all unsolved, was published afterwards, first in German and in 1902 in English, translated by Mary Frances Winston Newson for the Bulletin of the American Mathematical Society. Minkowski was present at the congress as one of its secretaries.
The list set much of the agenda for twentieth-century mathematics. The third problem, on cutting and reassembling polyhedra, was the first to be solved; around ten have resolutions accepted by mathematicians today; and others, such as the Riemann hypothesis, the eighth problem, remain open and are among the most famous challenges in the field. Some, like the problems on quadratic forms and on algebraic curves, grew into flourishing areas of research in their own right.
MacTutor notes that Minkowski's role as the source of the idea is far less well known than the problems themselves, and adds that time has certainly proved him right. His letter is a reminder that great advances can begin with a friend's good counsel.
Why it matters
A friend's suggestion produced a research agenda that guided generations of mathematicians and drove progress across the discipline.
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 rewrote electrodynamics in four dimensionsAt Göttingen Hermann Minkowski worked out a four-dimensional treatment of electrodynamics, recasting the laws of electricity and magnetism for moving bodies.
- 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'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
- Hilbert's problems Wikipedia
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