Hermann Minkowski was a
GermanThe Germans are a Germanic ethnic group native to Central Europe. The English term Germans has referred to the Germanspeaking population of the Holy Roman Empire since the Late Middle Ages....
mathematicianA 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 JewishAshkenazi 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 numbersIn number theory, the geometry of numbers studies convex bodies and integer vectors in ndimensional space. The geometry of numbers was initiated by ....
and who used geometrical methods to solve difficult problems in
number theoryNumber theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
,
mathematical physicsMathematical 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 relativityThe 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 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
KaunasKaunas is the secondlargest 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 EmpireThe 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
LithuaniaLithuania , 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 JewAshkenazi 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 KönigsbergThe 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 LindemannCarl 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 SciencesThe French Academy of Sciences is a learned society, founded in 1666 by Louis XIV at the suggestion of JeanBaptiste Colbert, to encourage and protect the spirit of French scientific research...
for his manuscript on the theory of
quadratic formIn 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 HilbertDavid 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 MinkowskiOskar Minkowski He held a professor at at the University of Breslau and is most famous for his research on diabetes...
(1858–1931), was a wellknown physician and researcher.
Minkowski taught at the universities of
BonnBonn 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 RhineWestphalia, it was the capital of West Germany from 1949 to 1990 and the official seat of government of united Germany from 1990 to 1999....
,
GöttingenGöttingen 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:...
,
KönigsbergKönigsberg 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
ZürichZurich 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 ZurichThe 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
EinsteinAlbert Einstein was a Germanborn 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 formsIn 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 dimensionIn 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 numbersIn number theory, the geometry of numbers studies convex bodies and integer vectors in ndimensional space. The geometry of numbers was initiated by ....
, a geometrical method that solved problems in
number theoryNumber 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 HilbertDavid 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 CarathéodoryConstantin 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
appendicitisAppendicitis 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
GöttingenGöttingen 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 was a Germanborn 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
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...
and
PoincaréJules 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
timeTime 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
spaceSpace is the boundless, threedimensional 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 fourdimensional continuum...
are not separated entities but intermingled in a four dimensional spacetime, and in which the
Lorentz geometryIn physics, the Lorentz transformation or LorentzFitzgerald 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 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
asteroidAsteroids are a class of small Solar System bodies in orbit around the Sun. They have also been called planetoids, especially the larger ones...
12493 Minkowski12493 Minkowski is a mainbelt asteroid discovered on August 4, 1997 by P. G. Comba at Prescott. External links :*...
and
MmatricesIn mathematics, especially linear algebra, an Mmatrix is a Zmatrix with eigenvalues whose real parts are positive. Mmatrices are a subset of the class of Pmatrices, and also of the class of inversepositive matrices In mathematics, especially linear algebra, an Mmatrix is a Zmatrix 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, 169

 English translation: Space and Time. In: The Principle of Relativity (1920), Calcutta: University Press, 7088
 H. A. 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...
, Albert EinsteinAlbert Einstein was a Germanborn 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 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 theorem
The 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 addition
In 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 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 northnortheast of Lemaître, a formation of similar dimension...
 Minkowski diagram
The 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 functional
In 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 inequality
In 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 function
In 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 space
In 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 theorem
In 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 nonzero lattice point...
in geometry of numbersIn number theory, the geometry of numbers studies convex bodies and integer vectors in ndimensional space. The geometry of numbers was initiated by ....
 Separating axis theorem
For 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 formula
In 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...
External links