Hermann Minkowski
Encyclopedia
Hermann Minkowski was a German
mathematician
of Ashkenazi Jewish
descent, who created and developed the geometry of numbers
and who used geometrical methods to solve difficult problems in number theory
, mathematical physics
, and the theory of relativity
.
, a suburb of Kaunas
, which was then part of the Russian Empire
, now Lithuania
, to a family of Ashkenazi Jew
ish descent. Hermann was educated in Germany at the Albertina University of Königsberg
, where he achieved his doctorate in 1885 under direction of Ferdinand von Lindemann
. While still a student at Königsberg, in 1883 he was awarded the Mathematics Prize of the French Academy of Sciences
for his manuscript on the theory of quadratic form
s. He also became a friend of another German mathematician, David Hilbert
. His brother, Oskar Minkowski
(1858–1931), was a well-known physician and researcher.
Minkowski taught at the universities of Bonn
, Göttingen
, Königsberg
and Zürich
. At the Eidgenössische Polytechnikum, today the ETH Zurich
, he was one of Einstein
's teachers.
Minkowski explored the arithmetic of quadratic forms
, especially concerning n variables, and his research into that topic led him to consider certain geometric properties in a space of n dimension
s. In 1896, he presented his geometry of numbers
, a geometrical method that solved problems in number theory
.
In 1902, he joined the Mathematics Department of Göttingen and became one of the close colleagues of David Hilbert
, whom he first met in Königsberg. Constantin Carathéodory
was one of his students there.
Minkowski died suddenly of appendicitis
in Göttingen
in 1909.
in 1905 and based on previous work of Lorentz
and Poincaré
, could be best understood in a four dimensional space, since known as "Minkowski spacetime", in which time
and space
are not separated entities but intermingled in a four dimensional space-time, and in which the Lorentz geometry
of special relativity can be nicely represented. The beginning part of his address delivered at the 80th Assembly of German Natural Scientists and Physicians (September 21, 1908) is now famous:
's obituary of Minkowski illustrates the deep friendship between the two mathematicians:
The asteroid
12493 Minkowski
and M-matrices
are named in his honour.
Mathematical papers (posthumous)}}. Reprinted in one volume New York, Chelsea 1967
Germans
The Germans are a Germanic ethnic group native to Central Europe. The English term Germans has referred to the German-speaking population of the Holy Roman Empire since the Late Middle Ages....
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
of Ashkenazi Jewish
Ashkenazi Jews
Ashkenazi Jews, also known as Ashkenazic Jews or Ashkenazim , are the Jews descended from the medieval Jewish communities along the Rhine in Germany from Alsace in the south to the Rhineland in the north. Ashkenaz is the medieval Hebrew name for this region and thus for Germany...
descent, who created and developed the geometry of numbers
Geometry of numbers
In number theory, the geometry of numbers studies convex bodies and integer vectors in n-dimensional space. The geometry of numbers was initiated by ....
and who used geometrical methods to solve difficult problems in number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
, mathematical physics
Mathematical physics
Mathematical physics refers to development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines this area as: "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and...
, and the theory of relativity
Theory of relativity
The theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word relativity is sometimes used in reference to Galilean invariance....
.
Life and work
Hermann Minkowski was born in AleksotasAleksotas
Aleksotas is an elderate in the southern section of the city of Kaunas, Lithuania, bordering the left bank of the Neman River . Its population in 2006 was 21,694....
, a suburb of Kaunas
Kaunas
Kaunas is the second-largest city in Lithuania and has historically been a leading centre of Lithuanian economic, academic, and cultural life. Kaunas was the biggest city and the center of a powiat in Trakai Voivodeship of the Grand Duchy of Lithuania since 1413. During Russian Empire occupation...
, which was then part of the Russian Empire
Russian Empire
The Russian Empire was a state that existed from 1721 until the Russian Revolution of 1917. It was the successor to the Tsardom of Russia and the predecessor of the Soviet Union...
, now Lithuania
Lithuania
Lithuania , officially the Republic of Lithuania is a country in Northern Europe, the biggest of the three Baltic states. It is situated along the southeastern shore of the Baltic Sea, whereby to the west lie Sweden and Denmark...
, to a family of Ashkenazi Jew
Ashkenazi Jews
Ashkenazi Jews, also known as Ashkenazic Jews or Ashkenazim , are the Jews descended from the medieval Jewish communities along the Rhine in Germany from Alsace in the south to the Rhineland in the north. Ashkenaz is the medieval Hebrew name for this region and thus for Germany...
ish descent. Hermann was educated in Germany at the Albertina University of Königsberg
University of Königsberg
The University of Königsberg was the university of Königsberg in East Prussia. It was founded in 1544 as second Protestant academy by Duke Albert of Prussia, and was commonly known as the Albertina....
, where he achieved his doctorate in 1885 under direction of Ferdinand von Lindemann
Ferdinand von Lindemann
Carl Louis Ferdinand von Lindemann was a German mathematician, noted for his proof, published in 1882, that π is a transcendental number, i.e., it is not a root of any polynomial with rational coefficients....
. While still a student at Königsberg, in 1883 he was awarded the Mathematics Prize of the French Academy of Sciences
French Academy of Sciences
The French Academy of Sciences is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research...
for his manuscript on the theory of quadratic form
Quadratic form
In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables. For example,4x^2 + 2xy - 3y^2\,\!is a quadratic form in the variables x and y....
s. He also became a friend of another German mathematician, David Hilbert
David Hilbert
David Hilbert was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of...
. His brother, Oskar Minkowski
Oskar Minkowski
Oskar Minkowski He held a professor at at the University of Breslau and is most famous for his research on diabetes...
(1858–1931), was a well-known physician and researcher.
Minkowski taught at the universities of Bonn
Bonn
Bonn is the 19th largest city in Germany. Located in the Cologne/Bonn Region, about 25 kilometres south of Cologne on the river Rhine in the State of North Rhine-Westphalia, it was the capital of West Germany from 1949 to 1990 and the official seat of government of united Germany from 1990 to 1999....
, Göttingen
Göttingen
Göttingen is a university town in Lower Saxony, Germany. It is the capital of the district of Göttingen. The Leine river runs through the town. In 2006 the population was 129,686.-General information:...
, Königsberg
Königsberg
Königsberg was the capital of East Prussia from the Late Middle Ages until 1945 as well as the northernmost and easternmost German city with 286,666 inhabitants . Due to the multicultural society in and around the city, there are several local names for it...
and Zürich
Zürich
Zurich is the largest city in Switzerland and the capital of the canton of Zurich. It is located in central Switzerland at the northwestern tip of Lake Zurich...
. At the Eidgenössische Polytechnikum, today the ETH Zurich
ETH Zurich
The Swiss Federal Institute of Technology Zurich or ETH Zürich is an engineering, science, technology, mathematics and management university in the City of Zurich, Switzerland....
, he was one of Einstein
Albert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...
's teachers.
Minkowski explored the arithmetic of quadratic forms
Quadratic form
In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables. For example,4x^2 + 2xy - 3y^2\,\!is a quadratic form in the variables x and y....
, especially concerning n variables, and his research into that topic led him to consider certain geometric properties in a space of n dimension
Dimension
In physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it...
s. In 1896, he presented his geometry of numbers
Geometry of numbers
In number theory, the geometry of numbers studies convex bodies and integer vectors in n-dimensional space. The geometry of numbers was initiated by ....
, a geometrical method that solved problems in number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
.
In 1902, he joined the Mathematics Department of Göttingen and became one of the close colleagues of David Hilbert
David Hilbert
David Hilbert was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of...
, whom he first met in Königsberg. Constantin Carathéodory
Constantin Carathéodory
Constantin Carathéodory was a Greek mathematician. He made significant contributions to the theory of functions of a real variable, the calculus of variations, and measure theory...
was one of his students there.
Minkowski died suddenly of appendicitis
Appendicitis
Appendicitis is a condition characterized by inflammation of the appendix. It is classified as a medical emergency and many cases require removal of the inflamed appendix, either by laparotomy or laparoscopy. Untreated, mortality is high, mainly because of the risk of rupture leading to...
in Göttingen
Göttingen
Göttingen is a university town in Lower Saxony, Germany. It is the capital of the district of Göttingen. The Leine river runs through the town. In 2006 the population was 129,686.-General information:...
in 1909.
Relativity
By 1907 Minkowski realized that the special theory of relativity, introduced by Albert EinsteinAlbert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...
in 1905 and based on previous work of Lorentz
Hendrik Lorentz
Hendrik Antoon Lorentz was a Dutch physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman for the discovery and theoretical explanation of the Zeeman effect...
and Poincaré
Henri Poincaré
Jules Henri Poincaré was a French mathematician, theoretical physicist, engineer, and a philosopher of science...
, could be best understood in a four dimensional space, since known as "Minkowski spacetime", in which time
Time
Time is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....
and space
Space
Space is the boundless, three-dimensional extent in which objects and events occur and have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum...
are not separated entities but intermingled in a four dimensional space-time, and in which the Lorentz geometry
Lorentz transformation
In physics, the Lorentz transformation or Lorentz-Fitzgerald transformation describes how, according to the theory of special relativity, two observers' varying measurements of space and time can be converted into each other's frames of reference. It is named after the Dutch physicist Hendrik...
of special relativity can be nicely represented. The beginning part of his address delivered at the 80th Assembly of German Natural Scientists and Physicians (September 21, 1908) is now famous:
"The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. 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."
Citations
David HilbertDavid Hilbert
David Hilbert was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of...
's obituary of Minkowski illustrates the deep friendship between the two mathematicians:
- Seit meiner Studienzeit war mir Minkowski der beste und zuverlässigste Freund, der an mir hing mit der ganzen ihm eigenen Tiefe und Treue. Unsere Wissenschaft, die uns das liebste war, hatte uns zusammengeführt; sie erschien uns wie ein blühender Garten. Gern suchten wir dort auch verborgene Pfade auf und entdeckten manche neue, uns schön dünkende Aussicht, und wenn der eine dem andern sie zeigte und wir sie gemeinsam bewunderten, war unsere Freude vollkommen. Er war mir ein Geschenk des Himmels, wie es nur selten jemand zuteil wird, und ich muss dankbar sein, dass ich es so lange besaß. Jäh hat ihn der Tod von unserer Seite gerissen. Was uns aber der Tod nicht nehmen kann, das ist sein edles Bild in unserem Herzen und das Bewusstsein, dass sein Geist in uns fortwirkt.
- Translated:
- Since my student years Minkowski was my best, most dependable friend who supported me with all the depth and loyalty that was so characteristic of him. Our science, which we loved above all else, brought us together; it seemed to us a garden full of flowers. In it, we enjoyed looking for hidden pathways and discovered many a new perspective that appealed to our sense of beauty, and when one of us showed it to the other and we marvelled over it together, our joy was complete. He was for me a rare gift from heaven and I must be grateful to have possessed that gift for so long. Now death has suddenly torn him from our midst. However, what death cannot take away is his noble image in our hearts and the knowledge that his spirit in us continue to be active.
The asteroid
Asteroid
Asteroids are a class of small Solar System bodies in orbit around the Sun. They have also been called planetoids, especially the larger ones...
12493 Minkowski
12493 Minkowski
12493 Minkowski is a main-belt asteroid discovered on August 4, 1997 by P. G. Comba at Prescott.- External links :*...
and M-matrices
M-matrix
In mathematics, especially linear algebra, an M-matrix is a Z-matrix with eigenvalues whose real parts are positive. M-matrices are a subset of the class of P-matrices, and also of the class of inverse-positive matrices In mathematics, especially linear algebra, an M-matrix is a Z-matrix with...
are named in his honour.
Publications
Relativity papers-
- English translation: The Fundamental Equations for Electromagnetic Processes in Moving Bodies. In: The Principle of Relativity (1920), Calcutta: University Press, 1-69
-
- English translation: Space and Time. In: The Principle of Relativity (1920), Calcutta: University Press, 70-88
- H. A. LorentzHendrik LorentzHendrik Antoon Lorentz was a Dutch physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman for the discovery and theoretical explanation of the Zeeman effect...
, Albert EinsteinAlbert EinsteinAlbert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...
, Hermann Minkowski, and Hermann WeylHermann WeylHermann Klaus Hugo Weyl was a German mathematician and theoretical physicist. Although much of his working life was spent in Zürich, Switzerland and then Princeton, he is associated with the University of Göttingen tradition of mathematics, represented by David Hilbert and Hermann Minkowski.His...
, 1952. The Principle of Relativity: A Collection of Original Memoirs. Dover.
Mathematical papers (posthumous)}}. Reprinted in one volume New York, Chelsea 1967
See also
- Abraham–Minkowski controversy
- Brunn–Minkowski theorem
- Hasse–Minkowski theoremHasse–Minkowski theoremThe Hasse–Minkowski theorem is a fundamental result in number theory which states that two quadratic forms over a number field are equivalent if and only if they are equivalent locally at all places, i.e. equivalent over every completion of the field...
- Minkowski additionMinkowski additionIn geometry, the Minkowski sum of two sets A and B in Euclidean space is the result of adding every element of A to every element of B, i.e...
- Minkowski–Bouligand dimension
- Minkowski (crater)Minkowski (crater)Minkowski is a lunar crater on the far side of the Moon, in the lower latitudes of the southern hemisphere. It lies about one crater diameter to the north-northeast of Lemaître, a formation of similar dimension...
- Minkowski diagramMinkowski diagramThe Minkowski diagram was developed in 1908 by Hermann Minkowski and provides an illustration of the properties of space and time in the special theory of relativity. It allows a quantitative understanding of the corresponding phenomena like time dilation and length contraction without mathematical...
- Minkowski functionalMinkowski functionalIn functional analysis, given a linear space X, a Minkowski functional is a device that uses the linear structure to introduce a topology on X.-Example 1:...
- Minkowski inequalityMinkowski inequalityIn mathematical analysis, the Minkowski inequality establishes that the Lp spaces are normed vector spaces. Let S be a measure space, let 1 ≤ p ≤ ∞ and let f and g be elements of Lp...
- Minkowski's question mark functionMinkowski's question mark functionIn mathematics, the Minkowski question mark function, sometimes called the slippery devil's staircase and denoted by ?, is a function possessing various unusual fractal properties, defined by Hermann Minkowski in 1904...
- Minkowski spaceMinkowski spaceIn physics and mathematics, Minkowski space or Minkowski spacetime is the mathematical setting in which Einstein's theory of special relativity is most conveniently formulated...
- Minkowski–Steiner formula
- Minkowski's theoremMinkowski's theoremIn mathematics, Minkowski's theorem is the statement that any convex set in Rn which is symmetric with respect to the origin and with volume greater than 2n d contains a non-zero lattice point...
in geometry of numbersGeometry of numbersIn number theory, the geometry of numbers studies convex bodies and integer vectors in n-dimensional space. The geometry of numbers was initiated by .... - Separating axis theoremSeparating axis theoremFor objects lying in a plane , the separating axis theorem states that, given two convex shapes, there exists a line onto which their projections will be separate if and only if they are not intersecting. A line for which the objects have disjoint projections is called a separating axis...
- Smith–Minkowski–Siegel mass formulaSmith–Minkowski–Siegel mass formulaIn mathematics, the Smith–Minkowski–Siegel mass formula is a formula for the sum of the weights of the lattices in a genus, weighted by the reciprocals of the orders of their automorphism groups...