Hermann Minkowski (; ; 22 June 1864 – 12 January 1909) was a German
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
and professor at
Königsberg
Königsberg (, ) was the historic Prussian city that is now Kaliningrad, Russia. Königsberg was founded in 1255 on the site of the ancient Old Prussian settlement ''Twangste'' by the Teutonic Knights during the Northern Crusades, and was named ...
,
Zürich
Zürich () is the list of cities in Switzerland, largest city in Switzerland and the capital of the canton of Zürich. It is located in north-central Switzerland, at the northwestern tip of Lake Zürich. As of January 2020, the municipality has 43 ...
and
Göttingen
Göttingen (, , ; nds, Chöttingen) is a college town, university city in Lower Saxony, central Germany, the Capital (political), capital of Göttingen (district), the eponymous district. The River Leine runs through it. At the end of 2019, t ...
. He created and developed the
geometry of numbers Geometry of numbers is the part of number theory which uses geometry for the study of algebraic numbers. Typically, a ring of algebraic integers is viewed as a lattice in \mathbb R^n, and the study of these lattices provides fundamental information ...
and used
geometrical
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ca ...
methods to solve problems in
number theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777 ...
,
mathematical physics
Mathematical physics refers to the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and t ...
, and the
theory of relativity
The theory of relativity usually encompasses two interrelated theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical phenomena in ...
.
Minkowski is perhaps best known for his foundational work describing space and time as a
four-dimensional space
A four-dimensional space (4D) is a mathematical extension of the concept of three-dimensional or 3D space. Three-dimensional space is the simplest possible abstraction of the observation that one only needs three numbers, called ''dimensions'', ...
, now known as "
Minkowski spacetime
In mathematical physics, Minkowski space (or Minkowski spacetime) () is a combination of three-dimensional Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two events is independent of the inert ...
", which facilitated geometric interpretations of
Albert Einstein
Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...
's
special theory of relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between Spacetime, space and time. In Albert Einstein's original treatment, the theory is based on two Postulates of ...
(1905).
Personal life and family
Hermann Minkowski was born in the town of
Aleksota, the
Suwałki Governorate
Suwałki Governorate (russian: Сувалкская губерния, pl, gubernia suwalska, lt, Suvalkų gubernija) was a governorate (administrative area) of Congress Poland ("Russian Poland") which had its seat in the city of Suwałki. It co ...
, the
Kingdom of Poland
The Kingdom of Poland ( pl, Królestwo Polskie; Latin: ''Regnum Poloniae'') was a state in Central Europe. It may refer to:
Historical political entities
*Kingdom of Poland, a kingdom existing from 1025 to 1031
*Kingdom of Poland, a kingdom exist ...
, part of the
Russian Empire
The Russian Empire was an empire and the final period of the Russian monarchy from 1721 to 1917, ruling across large parts of Eurasia. It succeeded the Tsardom of Russia following the Treaty of Nystad, which ended the Great Northern War. ...
, to Lewin Boruch Minkowski, a merchant who subsidized the building of the
choral synagogue in Kovno, and Rachel Taubmann, both of
Jewish descent
''Zera Yisrael'' ( he, זרע ישראל, , meaning "Seed fIsrael") is a legal category in Halakha, Jewish law that denotes the blood descendants of Jews who, for one reason or another, are not legally of Jewish ethnicity according to religiou ...
. Hermann was a younger brother of the
medical research
Medical research (or biomedical research), also known as experimental medicine, encompasses a wide array of research, extending from "basic research" (also called ''bench science'' or ''bench research''), – involving fundamental scientif ...
er
Oskar Oskar may refer to:
* oskar (gene), the Drosophila gene
* Oskar (given name) Oscar or Oskar is a masculine given name of Irish origin.
Etymology
The name is derived from two elements in Irish: the first, ''os'', means "deer"; the second element, ' ...
(born 1858). In different sources Minkowski's nationality is variously given as German,
Polish
Polish may refer to:
* Anything from or related to Poland, a country in Europe
* Polish language
* Poles, people from Poland or of Polish descent
* Polish chicken
*Polish brothers (Mark Polish and Michael Polish, born 1970), American twin screenwr ...
, or Lithuanian-German, or Russian.
To escape
persecution in the Russian Empire the family moved to Königsberg in 1872,
where the father became involved in rag export and later in manufacture of mechanical clockwork tin toys (he operated his firm Lewin Minkowski & Son with his eldest son Max).
Minkowski studied in
Königsberg
Königsberg (, ) was the historic Prussian city that is now Kaliningrad, Russia. Königsberg was founded in 1255 on the site of the ancient Old Prussian settlement ''Twangste'' by the Teutonic Knights during the Northern Crusades, and was named ...
and taught in
Bonn
The federal city of Bonn ( lat, Bonna) is a city on the banks of the Rhine in the German state of North Rhine-Westphalia, with a population of over 300,000. About south-southeast of Cologne, Bonn is in the southernmost part of the Rhine-Ruhr r ...
(1887–1894), Königsberg (1894–1896) and
Zurich (1896–1902), and finally in
Göttingen
Göttingen (, , ; nds, Chöttingen) is a college town, university city in Lower Saxony, central Germany, the Capital (political), capital of Göttingen (district), the eponymous district. The River Leine runs through it. At the end of 2019, t ...
from 1902 until his death in 1909. He married Auguste Adler in 1897 with whom he had two daughters; the
electrical engineer
Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the l ...
and inventor
Reinhold Rudenberg
Reinhold Rudenberg (or Rüdenberg; February 4, 1883 – December 25, 1961) was a German-American electrical engineer and inventor, credited with many innovations in the electric power and related fields. Aside from improvements in electric power eq ...
was his son-in-law.
Minkowski died suddenly of
appendicitis
Appendicitis is inflammation of the appendix. Symptoms commonly include right lower abdominal pain, nausea, vomiting, and decreased appetite. However, approximately 40% of people do not have these typical symptoms. Severe complications of a rup ...
in Göttingen on 12 January 1909.
David Hilbert
David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician, one of the most influential mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many a ...
's obituary of Minkowski illustrates the deep friendship between the two mathematicians (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 marveled 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 continues to be active in us.
Max Born
Max Born (; 11 December 1882 – 5 January 1970) was a German physicist and mathematician who was instrumental in the development of quantum mechanics. He also made contributions to solid-state physics and optics and supervised the work of a n ...
delivered the obituary on behalf of the mathematics students at Göttingen.
The main-belt
asteroid
An asteroid is a minor planet of the inner Solar System. Sizes and shapes of asteroids vary significantly, ranging from 1-meter rocks to a dwarf planet almost 1000 km in diameter; they are rocky, metallic or icy bodies with no atmosphere.
...
12493 Minkowski
1 (one, unit, unity) is a number representing a single or the only entity. 1 is also a numerical digit and represents a single unit of counting or measurement. For example, a line segment of ''unit length'' is a line segment of length 1 ...
and
M-matrices are named in Minkowski's honor.
Education and career
Minkowski was educated in
East Prussia
East Prussia ; german: Ostpreißen, label=Low Prussian; pl, Prusy Wschodnie; lt, Rytų Prūsija was a province of the Kingdom of Prussia from 1773 to 1829 and again from 1878 (with the Kingdom itself being part of the German Empire from 187 ...
at the ''Albertina'' University of Königsberg, where he earned his doctorate in 1885 under the direction of
Ferdinand von Lindemann
Carl Louis Ferdinand von Lindemann (12 April 1852 – 6 March 1939) was a German mathematician, noted for his proof, published in 1882, that (pi) is a transcendental number, meaning it is not a root of any polynomial with rational coefficien ...
. In 1883, while still a student at Königsberg, he was awarded the Mathematics Prize of the
French Academy of Sciences
The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV of France, Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific me ...
for his manuscript on the theory of
quadratic form
In mathematics, a quadratic form is a polynomial with terms all of degree two ("form" is another name for a homogeneous polynomial). For example,
:4x^2 + 2xy - 3y^2
is a quadratic form in the variables and . The coefficients usually belong to a ...
s. Due to the very young age of 18, which was unheard of in the mathematics community, and his obscurity as a mathematician at the time, his sharing the award with eminent English mathematician Henry Smith (who was certainly a great deal more famous than Hermann and to whom the prize was awarded posthumously) caused severe unrest among English mathematicians. The prize committee, despite the numerous complaints, never changed their decision. He also became a friend of another renowned mathematician, David Hilbert. His brother,
Oskar Minkowski
Oskar Minkowski (; 13 January 1858 – 18 July 1931) was a German physician and physiologist who held a professorship at the University of Breslau and is most famous for his research on diabetes. He was the brother of the mathematician Hermann Mi ...
(1858–1931), was a well-known physician and researcher.
Minkowski taught at the universities of Bonn, Königsberg, Zürich, and Göttingen. At the
''Eidgenössische Polytechnikum'', today the
ETH Zurich
(colloquially)
, former_name = eidgenössische polytechnische Schule
, image = ETHZ.JPG
, image_size =
, established =
, type = Public
, budget = CHF 1.896 billion (2021)
, rector = Günther Dissertori
, president = Joël Mesot
, ac ...
, he was one of Einstein's teachers.
Minkowski explored the arithmetic of
quadratic form
In mathematics, a quadratic form is a polynomial with terms all of degree two ("form" is another name for a homogeneous polynomial). For example,
:4x^2 + 2xy - 3y^2
is a quadratic form in the variables and . The coefficients usually belong to a ...
s, especially concerning ''n'' variables, and his research into that topic led him to consider certain geometric properties in a space of ''n''
dimension
In physics and mathematics, the dimension of a Space (mathematics), mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any Point (geometry), point within it. Thus, a Line (geometry), lin ...
s. In 1896, he presented his ''
geometry of numbers Geometry of numbers is the part of number theory which uses geometry for the study of algebraic numbers. Typically, a ring of algebraic integers is viewed as a lattice in \mathbb R^n, and the study of these lattices provides fundamental information ...
'', a geometrical method that solved problems in
number theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777 ...
. He is also the creator of the
Minkowski Sausage and the
Minkowski cover of a curve.
In 1902, he joined the Mathematics Department of Göttingen and became a close colleague of David Hilbert, whom he first met at university in Königsberg.
Constantin Carathéodory
Constantin Carathéodory ( el, Κωνσταντίνος Καραθεοδωρή, Konstantinos Karatheodori; 13 September 1873 – 2 February 1950) was a Greek mathematician who spent most of his professional career in Germany. He made significant ...
was one of his students there.
Work on relativity
By 1908 Minkowski realized that the special theory of relativity, introduced by his former student Albert Einstein in 1905 and based on the previous work of
Lorentz
Lorentz is a name derived from the Roman surname, Laurentius, which means "from Laurentum". It is the German form of Laurence. Notable people with the name include:
Given name
* Lorentz Aspen (born 1978), Norwegian heavy metal pianist and keyboar ...
and
Poincaré, could best be understood in a four-dimensional space, since known as the "Minkowski spacetime", in which
time
Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, to ...
and
space
Space is the boundless three-dimensional extent in which objects and events have relative position and direction. In classical physics, physical space is often conceived in three linear dimensions, although modern physicists usually consider ...
are not separated entities but intermingled in a four-dimensional
space–time, and in which the
Lorentz geometry of special relativity can be effectively represented using the invariant interval
(see
History of special relativity
The history of special relativity consists of many theoretical results and empirical findings obtained by Albert A. Michelson, Hendrik Lorentz, Henri Poincaré and others. It culminated in the theory of special relativity proposed by Albert Eins ...
).
The mathematical basis of Minkowski space can also be found in the
hyperboloid model
In geometry, the hyperboloid model, also known as the Minkowski model after Hermann Minkowski, is a model of ''n''-dimensional hyperbolic geometry in which points are represented by points on the forward sheet ''S''+ of a two-sheeted hyperboloid ...
of
hyperbolic space
In mathematics, hyperbolic space of dimension n is the unique simply connected, n-dimensional Riemannian manifold of constant sectional curvature equal to -1. It is homogeneous, and satisfies the stronger property of being a symmetric space. Th ...
already known in the 19th century, because isometries (or motions) in hyperbolic space can be related to
Lorentz transformations
In physics, the Lorentz transformations are a six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that moves at a constant velocity relative to the former. The respective inverse transformation i ...
, which included contributions of
Wilhelm Killing
Wilhelm Karl Joseph Killing (10 May 1847 – 11 February 1923) was a German mathematician who made important contributions to the theories of Lie algebras, Lie groups, and non-Euclidean geometry.
Life
Killing studied at the University of Mü ...
(1880, 1885),
Henri Poincaré
Jules Henri Poincaré ( S: stress final syllable ; 29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as "The ...
(1881),
Homersham Cox (1881),
Alexander Macfarlane
Alexander Macfarlane FRSE LLD (21 April 1851 – 28 August 1913) was a Scottish logician, physicist, and mathematician.
Life
Macfarlane was born in Blairgowrie, Scotland, to Daniel MacFarlane (Shoemaker, Blairgowire) and Ann Small. He s ...
(1894) and others (see
History of Lorentz transformations The history of Lorentz transformations comprises the development of linear transformations forming the Lorentz group or Poincaré group preserving the Lorentz interval -x_^+\cdots+x_^ and the Minkowski inner product -x_y_+\cdots+x_y_.
In mathemati ...
).
The beginning part of his address called "Space and Time" delivered at the 80th Assembly of German Natural Scientists and Physicians (21 September 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.
Publications
;Relativity
*
*
** English translation: "
The Fundamental Equations for Electromagnetic Processes in Moving Bodies". In: The Principle of Relativity (1920), Calcutta: University Press, 1–69.
*
** Various English translations on Wikisource: "
Space and Time Space and Time or Time and Space, or ''variation'', may refer to:
* ''Space and time'' or ''time and space'' or ''spacetime'', any mathematical model that combines space and time into a single interwoven continuum
* Philosophy of space and time
Sp ...
".
* Blumenthal O. (ed): ''Das Relativitätsprinzip'', Leipzig 1913, 1923 (Teubner), Engl tr (W. Perrett & G. B. Jeffrey) ''The Principle of Relativity'' London 1923 (Methuen); reprinted New York 1952 (Dover) entitled
H. A. Lorentz, Albert Einstein, Hermann Minkowski, and
Hermann Weyl
Hermann Klaus Hugo Weyl, (; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, he is assoc ...
, ''The Principle of Relativity: A Collection of Original Memoirs''.
* Space and Time – Minkowski's Papers on Relativity, Minkowski Institute Press, 2012 (free ebook).
;Diophantine approximations
*
;Mathematical (posthumous)
*
*
Reprinted in one volume New York, Chelsea 1967.
See also
*
List of things named after Hermann Minkowski
*
Abraham–Minkowski controversy
The Abraham–Minkowski controversy is a physics debate concerning electromagnetic momentum within dielectric media. Two equations were first suggested by Hermann Minkowski (1908)
:* Wikisource translationThe Fundamental Equations for Electromagne ...
*
Brunn–Minkowski theorem In mathematics, the Brunn–Minkowski theorem (or Brunn–Minkowski inequality) is an inequality relating the volumes (or more generally Lebesgue measures) of compact subsets of Euclidean space. The original version of the Brunn–Minkowski theor ...
*
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 o ...
*
Hermite–Minkowski theorem
*
Minkowski addition
In geometry, the Minkowski sum (also known as dilation) of two sets of position vectors ''A'' and ''B'' in Euclidean space is formed by adding each vector in ''A'' to each vector in ''B'', i.e., the set
: A + B = \.
Analogously, the Minkowski ...
*
Minkowski (crater)
Minkowski is a crater on the far side of the Moon, in the lower latitudes of the southern hemisphere. The lunar crater lies about one crater diameter to the north-northeast of crater Lemaître, a formation of similar dimension. To the northwest ...
*
Minkowski distance
The Minkowski distance or Minkowski metric is a metric in a normed vector space which can be considered as a generalization of both the Euclidean distance and the Manhattan distance. It is named after the German mathematician Hermann Minkowski.
...
*
Minkowski functional
In mathematics, in the field of functional analysis, a Minkowski functional (after Hermann Minkowski) or gauge function is a function that recovers a notion of distance on a linear space.
If K is a subset of a real or complex vector space X, then ...
*
Minkowski inequality
In mathematical analysis, the Minkowski inequality establishes that the L''p'' spaces are normed vector spaces. Let ''S'' be a measure space, let and let ''f'' and ''g'' be elements of L''p''(''S''). Then is in L''p''(''S''), and we have the tr ...
*
Minkowski model
In geometry, the hyperboloid model, also known as the Minkowski model after Hermann Minkowski, is a model of ''n''-dimensional hyperbolic geometry in which points are represented by points on the forward sheet ''S''+ of a two-sheeted hyperboloid ...
*
Minkowski plane
In mathematics, a Minkowski plane (named after Hermann Minkowski) is one of the Benz planes (the others being Möbius plane and Laguerre plane).
Classical real Minkowski plane
Applying the pseudo-euclidean distance d(P_1,P_2) = (x'_1-x'_2) ...
*
Minkowski problem
In differential geometry, the Minkowski problem, named after Hermann Minkowski, asks for the construction of a strictly convex compact surface ''S'' whose Gaussian curvature is specified. More precisely, the input to the problem is a strictly posit ...
*
Minkowski problem for polytopes
*
Minkowski's second theorem
*
Minkowski space
In mathematical physics, Minkowski space (or Minkowski spacetime) () is a combination of three-dimensional Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two events is independent of the inerti ...
*
Minkowski's bound
In algebraic number theory, Minkowski's bound gives an upper bound of the norm of ideals to be checked in order to determine the class number of a number field ''K''. It is named for the mathematician Hermann Minkowski.
Definition
Let ''D'' be t ...
*
Minkowski's theorem
In mathematics, Minkowski's theorem is the statement that every convex set in \mathbb^n which is symmetric with respect to the origin and which has volume greater than 2^n contains a non-zero integer point (meaning a point in \Z^n that is not t ...
in geometry of numbers
*
Minkowski–Hlawka theorem
In mathematics, the Minkowski–Hlawka theorem is a result on the lattice packing of hyperspheres in dimension ''n'' > 1. It states that there is a lattice in Euclidean space of dimension ''n'', such that the corresponding best packing of hypersp ...
*
Minkowski–Steiner formula In mathematics, the Minkowski–Steiner formula is a formula relating the area, surface area and volume of compact space, compact subsets of Euclidean space. More precisely, it defines the surface area as the "derivative" of enclosed volume in an ap ...
*
Smith–Minkowski–Siegel mass formula In mathematics, the Smith–Minkowski–Siegel mass formula (or Minkowski–Siegel mass formula) is a formula for the sum of the weights of the lattices (quadratic forms) in a genus, weighted by the reciprocals of the orders of their automorphism gr ...
*
Proper time
In relativity, proper time (from Latin, meaning ''own time'') along a timelike world line is defined as the time as measured by a clock following that line. It is thus independent of coordinates, and is a Lorentz scalar. The proper time interval b ...
*
Separating axis theorem
In geometry, the hyperplane separation theorem is a theorem about disjoint convex sets in ''n''-dimensional Euclidean space. There are several rather similar versions. In one version of the theorem, if both these sets are closed and at least on ...
*
Taxicab geometry
A taxicab geometry or a Manhattan geometry is a geometry whose usual distance function or metric of Euclidean geometry is replaced by a new metric in which the distance between two points is the sum of the absolute differences of their Cartesian co ...
*
World line
The world line (or worldline) of an object is the path that an object traces in 4-dimensional spacetime. It is an important concept in modern physics, and particularly theoretical physics.
The concept of a "world line" is distinguished from con ...
Notes and references
External links
*
{{DEFAULTSORT:Minkowski, Hermann
1864 births
1909 deaths
Scientists from Kaunas
People from Suwałki Governorate
Lithuanian Jews
Emigrants from the Russian Empire to Germany
German people of Lithuanian-Jewish descent
German people of Polish-Jewish descent
19th-century German mathematicians
20th-century German mathematicians
Geometers
Number theorists
German relativity theorists
University of Königsberg alumni
University of Königsberg faculty
ETH Zurich faculty
University of Bonn faculty
University of Göttingen faculty
Deaths from appendicitis