Hermann Minkowski

TheInfoList

OR:

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, mathematical structure, structure, space, Mathematica ...
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 (group), lattice in \mathbb R^n, and the study of these lattices provides fundame ...
and used
geometrical Geometry (; ) is, with arithmetic Arithmetic () is an elementary part of mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are co ...
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 integer An integer is the number zero (), a positive natural number (, , , etc.) or a negative intege ...
,
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 space, three-dimensional Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two Event (rel ...
", which facilitated geometric interpretations of
Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born Theoretical physics, theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for d ...
'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, 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 *History of Poland during the Piast dynasty#The reign of Bolesław I and establishment of a ...
, part of the
Russian Empire The Russian Empire was an empire and the final period of the List of Russian monarchs, 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 th ...
, to Lewin Boruch Minkowski, a merchant who subsidized the building of the choral synagogue in Kovno, and Rachel Taubmann, both of Jewish descent. 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 scienti ...
er Oskar (born 1858). In different sources Minkowski's nationality is variously given as German, Polish, 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 was his son-in-law. Minkowski died suddenly of
appendicitis Appendicitis is inflammation of the Appendix (anatomy), appendix. Symptoms commonly include right lower abdominal pain, nausea, vomiting, and anorexia (symptom), decreased appetite. However, approximately 40% of people do not have these typical ...
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 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 dialect, Low Prussian; pl, Prusy Wschodnie; lt, Rytų Prūsija was a Provinces of Prussia, province of the Kingdom of Prussia from 1773 to 1829 and again from 1878 (with the Kingdom itse ...
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 A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematici ...
. 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 of a polynomial, degree two ("form (mathematics), form" is another name for a homogeneous polynomial). For example, :4x^2 + 2xy - 3y^2 is a quadratic form in the variables ...
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 professor Professor (commonly abbreviated as Prof.) is an Academy, academic rank at university, universities and other post-secondary e ...
(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 , ...
, 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 of a polynomial, degree two ("form (mathematics), form" is another name for a homogeneous polynomial). For example, :4x^2 + 2xy - 3y^2 is a quadratic form in the variables ...
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 (group), lattice in \mathbb R^n, and the study of these lattices provides fundame ...
'', 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 integer An integer is the number zero (), a positive natural number (, , , etc.) or a negative intege ...
. 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 Greek may refer to: Greece Anything of, from, or related to Greece, a country in Sou ...
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 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 event (philosophy), events that occurs in an apparently irreversible process, irreversible succession from the past, through the present, into the future. It is a component quantity of various me ...
and
space Space is the boundless Three-dimensional space, three-dimensional extent in which Physical body, objects and events have relative position (geometry), position and direction (geometry), direction. In classical physics, physical space is often ...
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 $x^2 + y^2 + z^2 - c^2 t^2$ (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 of
hyperbolic space In mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in m ...
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 transformation, linear coordinate transformation, transformations from a Frame of Reference, coordinate frame in spacetime to another frame that moves at a constant velo ...
, 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 A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical ...
(1881), Homersham Cox (1881),
Alexander Macfarlane Alexander Macfarlane FRSE Fellowship of the Royal Society of Edinburgh (FRSE) is an award granted to individuals that the Royal Society of Edinburgh, Scotland's national academy of science and Literature, letters, judged to be "eminently ...
(1894) and others (see History of Lorentz transformations). 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.

* List of things named after Hermann Minkowski * Abraham–Minkowski controversy * Brunn–Minkowski theorem * Hasse–Minkowski theorem * Hermite–Minkowski theorem *
Minkowski addition In geometry, the Minkowski sum (also known as Dilation (morphology), dilation) of two set (mathematics), 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 ...
* Minkowski (crater) * Minkowski distance *
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 number, real or Complex number, ...
*
Minkowski inequality In mathematical analysis, the Minkowski inequality establishes that the Lp space, 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 ha ...
* Minkowski model * Minkowski plane * Minkowski problem * Minkowski problem for polytopes * Minkowski's second theorem *
Minkowski space In mathematical physics, Minkowski space (or Minkowski spacetime) () is a combination of Three-dimensional space, three-dimensional Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two Event (rel ...
* Minkowski's bound * Minkowski's theorem in geometry of numbers * Minkowski–Hlawka theorem * Minkowski–Steiner formula * Smith–Minkowski–Siegel mass formula *
Proper time In theory of relativity, 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 p ...
* Separating axis theorem *
Taxicab geometry A taxicab geometry or a Manhattan geometry is a geometry whose usual distance function or Metric (mathematics), metric of Euclidean geometry is replaced by a new metric in which the distance between two points is the sum of the absolute differences ...
*
World line The world line (or worldline) of an object is the path (topology), 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 disti ...