Carl Gustav Axel Harnack (,

Dorpat Tartu is the second largest city in Estonia after the Northern European country's political and financial capital, Tallinn. Tartu has a population of 91,407 (as of 2021). It is southeast of Tallinn and 245 kilometres (152 miles) northeast o ...

(now ) – 3 April 1888,

Dresden Dresden (, ; Upper Saxon: ''Dräsdn''; wen, label=Upper Sorbian, Drježdźany) is the capital city of the German state of Saxony and its second most populous city, after Leipzig. It is the 12th most populous city of Germany, the fourth lar ...

) was a

Baltic German Baltic Germans (german: Deutsch-Balten or , later ) were ethnic German inhabitants of the eastern shores of the Baltic Sea, in what today are Estonia and Latvia. Since their coerced resettlement in 1939, Baltic Germans have markedly declined ...

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 O ...

who contributed to

potential theory In mathematics and mathematical physics, potential theory is the study of harmonic functions. The term "potential theory" was coined in 19th-century physics when it was realized that two fundamental forces of nature known at the time, namely gravi ...

Harnack's inequality In mathematics, Harnack's inequality is an inequality relating the values of a positive harmonic function at two points, introduced by . Harnack's inequality is used to prove Harnack's theorem about the convergence of sequences of harmonic function ...

applied to

harmonic function In mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f: U \to \mathbb R, where is an open subset of that satisfies Laplace's equation, that is, : \ ...

s. He also worked on the

real algebraic geometry In mathematics, real algebraic geometry is the sub-branch of algebraic geometry studying real algebraic sets, i.e. real-number solutions to algebraic equations with real-number coefficients, and mappings between them (in particular real polynomia ...

of plane curves, proving Harnack's curve theorem for real plane algebraic curves. He was the son of the

theologian Theology is the systematic study of the nature of the divine and, more broadly, of religious belief. It is taught as an academic discipline, typically in universities and seminaries. It occupies itself with the unique content of analyzing the s ...

Theodosius HarnackHarnack, Axel; George L. Cathcart
"An Introduction to the Study of the Elements of the Differential and Integral Calculus"
London: Williams and Norgate, 1891, p. 6. and the twin brother of theologian

Adolf von Harnack Carl Gustav Adolf von Harnack (born Harnack; 7 May 1851 – 10 June 1930) was a Baltic German Lutheran theologian and prominent Church historian. He produced many religious publications from 1873 to 1912 (in which he is sometimes credited ...

(who long outlived him) - all of them from

, now known as Tartu, in what is today

Estonia Estonia, formally the Republic of Estonia, is a country by the Baltic Sea in Northern Europe. It is bordered to the north by the Gulf of Finland across from Finland, to the west by the sea across from Sweden, to the south by Latvia, and ...

. After his studies at the

University of Dorpat The University of Tartu (UT; et, Tartu Ülikool; la, Universitas Tartuensis) is a university in the city of Tartu in Estonia. It is the national university of Estonia. It is the only classical university in the country, and also its biggest ...

(where his father was a professor), he moved to

Erlangen Erlangen (; East Franconian: ''Erlang'', Bavarian: ''Erlanga'') is a Middle Franconian city in Bavaria, Germany. It is the seat of the administrative district Erlangen-Höchstadt (former administrative district Erlangen), and with 116,062 inhabi ...

to become a student of

Felix Klein Christian Felix Klein (; 25 April 1849 – 22 June 1925) was a German mathematician and mathematics educator, known for his work with group theory, complex analysis, non-Euclidean geometry, and on the associations between geometry and group ...

. He published his Ph.D. thesis in 1875 and received the right to teach (venia legendi) at the University of

Leipzig Leipzig ( , ; Upper Saxon: ) is the most populous city in the German state of Saxony. Leipzig's population of 605,407 inhabitants (1.1 million in the larger urban zone) as of 2021 places the city as Germany's eighth most populous, as we ...

the same year. One year later he accepted a position at the Technical University of

Darmstadt Darmstadt () is a city in the state of Hesse in Germany, located in the southern part of the Rhine-Main-Area (Frankfurt Metropolitan Region). Darmstadt has around 160,000 inhabitants, making it the fourth largest city in the state of Hesse a ...

. In 1877 he married Elisabeth von Öttingen, and they moved to

, where he acquired a professorship in the Polytechnikum, which became a technical university in 1890. Harnack suffered from health problems from 1882 onwards, forcing him to spend long periods in a

sanatorium A sanatorium (from Latin '' sānāre'' 'to heal, make healthy'), also sanitarium or sanitorium, are antiquated names for specialised hospitals, for the treatment of specific diseases, related ailments and convalescence. Sanatoriums are often ...

. He published 29 scientific articles and was a well-known mathematician at the time of his death. The various Harnack inequalities in harmonic analysis and in related discrete and probabilistic contexts are named after him, as are Harnack's curve theorem and

Harnack's principle In the mathematical field of partial differential equations, Harnack's principle or Harnack's theorem is a corollary of Harnack's inequality which deals with the convergence of sequences of harmonic functions. Given a sequence of harmonic function ...

. The Harnack medal of the

Max Planck Society The Max Planck Society for the Advancement of Science (german: Max-Planck-Gesellschaft zur Förderung der Wissenschaften e. V.; abbreviated MPG) is a formally independent non-governmental and non-profit association of German research institutes. ...

is named after his brother,

Selected works

Die Grundlagen der Theorie des logarithmischen Potentiales und der eindeutigen Potentialfunktion in der Ebene
(Teubner, 1887)
An introduction to the study of the elements of the differential and integral calculus
Cathcart, George Lambert, tr. (Williams and Norgate, 1891)

References

External links

*
Axel Harnack at the mathematical genealogy project
* Moritz Kassman
Harnack Inequalities: An Introduction
Boundary Value Problems (2007), Article ID 81415. (An article on Harnack's inequality that contains a biography of Axel Harnack in the introduction). 1851 births 1888 deaths People from Tartu People from Kreis Dorpat Baltic-German people 19th-century German mathematicians German twins Estonian twins Academic staff of Technische Universität Darmstadt {{Germany-mathematician-stub

Selected works

See also

References

External links