Carl Gustav Axel Harnack (,

Dorpat Tartu is the second largest city in Estonia after Tallinn. Tartu has a population of 97,759 (as of 2024). It is southeast of Tallinn and 245 kilometres (152 miles) northeast of Riga, Latvia. Tartu lies on the Emajõgi river, which connects the ...

(now ) – 3 April 1888,

Dresden Dresden (; ; Upper Saxon German, Upper Saxon: ''Dräsdn''; , ) is the capital city of the States of Germany, German state of Saxony and its second most populous city after Leipzig. It is the List of cities in Germany by population, 12th most p ...

) was a

Baltic German Baltic Germans ( or , later ) are Germans, ethnic German inhabitants of the eastern shores of the Baltic Sea, in what today are Estonia and Latvia. Since Flight and expulsion of Germans (1944–1950), their resettlement in 1945 after the end ...

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 ...

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 the two fundamental forces of nature known at the time, namely g ...

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 functions ...

applied to

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

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 polynomi ...

plane curve In mathematics, a plane curve is a curve in a plane that may be a Euclidean plane, an affine plane or a projective plane. The most frequently studied cases are smooth plane curves (including piecewise smooth plane curves), and algebraic plane c ...

s, proving Harnack's curve theorem for real plane algebraic curves.

Biography

He was the son of the

theologian Theology is the study of religious belief from a religious perspective, with a focus on the nature of divinity. It is taught as an academic discipline, typically in universities and seminaries. It occupies itself with the unique content of ...

Theodosius Harnack Theodosius Andreas Harnack (; , St. Petersburg – , Dorpat (now )) was a Baltic German theology, theologian. A professor of Divinity, he started his career as a Privatdozent for church history and homiletics at the University of Dorpat (in wha ...

Harnack, 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 the

Russian Empire The Russian Empire was an empire that spanned most of northern Eurasia from its establishment in November 1721 until the proclamation of the Russian Republic in September 1917. At its height in the late 19th century, it covered about , roughl ...

. After his studies at the University of Dorpat (where his father was a professor). In 1873 he moved to

Erlangen Erlangen (; , ) is a Middle Franconian city in Bavaria, Germany. It is the seat of the administrative district Erlangen-Höchstadt (former administrative district Erlangen), and with 119,810 inhabitants (as of 30 September 2024), it is the smalle ...

to become a student of

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

. 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 States of Germany, German state of Saxony. The city has a population of 628,718 inhabitants as of 2023. It is the List of cities in Germany by population, eighth-largest city in Ge ...

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

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

. 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'), also sanitarium or sanitorium, is a historic name for a specialised hospital for the treatment of specific diseases, related ailments, and convalescence. Sanatoriums are often in a health ...

. 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. The Harnack medal of the

Max Planck Society The Max Planck Society for the Advancement of Science (; abbreviated MPG) is a formally independent non-governmental and non-profit association of German research institutes. Founded in 1911 as the Kaiser Wilhelm Society, it was renamed to the M ...

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 Scientists from Tartu People from Kreis Dorpat Baltic-German people from the Russian Empire Emigrants from the Russian Empire Mathematicians from the Russian Empire 19th-century German mathematicians Academic staff of Technische Universität Darmstadt Academic staff of Leipzig University University of Erlangen–Nuremberg alumni {{Germany-mathematician-stub

Biography

Selected works

See also

References

External links