# Mathematician:Mathematicians/Sorted By Nation/Germany

For more comprehensive information on the lives and works of mathematicians through the ages, see the MacTutor History of Mathematics archive, created by John J. O'Connor and Edmund F. Robertson.

*The army of those who have made at least one definite contribution to mathematics as we know it soon becomes a mob as we look back over history; 6,000 or 8,000 names press forward for some word from us to preserve them from oblivion, and once the bolder leaders have been recognised it becomes largely a matter of arbitrary, illogical legislation to judge who of the clamouring multitude shall be permitted to survive and who be condemned to be forgotten.*- -- Eric Temple Bell:
*Men of Mathematics*, 1937, Victor Gollancz, London

- -- Eric Temple Bell:

## Contents

- 1 Holy Roman Empire
- 1.1 Nicholas of Cusa (1401 – 1464)
- 1.2 Johannes Müller von Königsberg (1436 – 1476)
- 1.3 Albrecht Dürer (1471 – 1528)
- 1.4 Ludolph van Ceulen (1540 – 1610)
- 1.5 Johannes Kepler (1571 – 1630)
- 1.6 Johann Faulhaber (1580 – 1635)
- 1.7 Nicholas Mercator (c. 1620 – 1687)
- 1.8 Johann Friedrich Pfaff (1765 – 1825)
- 1.9 August Leopold Crelle (1780 – 1855)
- 1.10 Georg Simon Ohm (1789 – 1834)
- 1.11 Wilhelm August Förstemann (1791 – 1836)
- 1.12 Karl Wilhelm Feuerbach (1800 – 1834)
- 1.13 Julius Plücker (1801 – 1868)
- 1.14 Wilhelm Eduard Weber (1804 – 1891)

- 2 Electoral Palatinate
- 3 Esslingen am Neckar
- 4 Bavaria
- 5 Württemberg
- 6 Saxony
- 6.1 Petrus Apianus (1495 – 1552)
- 6.2 Erasmus Reinhold (1511 – 1553)
- 6.3 Gottfried Wilhelm von Leibniz (1646 – 1716)
- 6.4 Ehrenfried Walther von Tschirnhaus (1651 – 1708)
- 6.5 Gustav Roch (1839 – 1866)
- 6.6 Erwin Papperitz (1857 – 1938)
- 6.7 Friedrich Engel (1861 – 1941)
- 6.8 Alwin Reinhold Korselt (1864 – 1947)

- 7 East Prussia
- 7.1 Christian Goldbach (1690 – 1764)
- 7.2 Johann Daniel Titius (1729 – 1796)
- 7.3 Friedrich Julius Richelot (1808 – 1875)
- 7.4 Hermann Günter Grassmann (1809 – 1877)
- 7.5 Gustav Robert Kirchhoff (1824 – 1887)
- 7.6 Daniel Friedrich Ernst Meissel (1826 – 1895)
- 7.7 Paul David Gustav du Bois-Reymond (1831 – 1889)
- 7.8 Rudolf Otto Sigismund Lipschitz (1832 – 1903)
- 7.9 Paul Albert Gordan (1837 – 1912)
- 7.10 Johann Gustav Hermes (1846 – 1912)
- 7.11 Kurt Wilhelm Sebastian Hensel (1861 – 1941)
- 7.12 Felix Hausdorff (1868 – 1942)
- 7.13 Arnold Johannes Wilhelm Sommerfeld (1868 – 1951)
- 7.14 Emanuel Lasker (1868 – 1941)

- 8 Hamburg
- 9 Duchy of Brunswick-Lüneburg
- 10 Prussia
- 10.1 Friedrich Wilhelm Bessel (1784 – 1846)
- 10.2 Heinrich Ferdinand Scherk (1798 – 1885)
- 10.3 Carl Gustav Jacob Jacobi (1804 – 1851)
- 10.4 Ernst Eduard Kummer (1810 – 1893)
- 10.5 Theodor Schönemann (1812 – 1868)
- 10.6 Heinrich Eduard Heine (1821 – 1881)
- 10.7 Ferdinand Gotthold Max Eisenstein (1823 – 1852)
- 10.8 Leopold Kronecker (1823 – 1891)
- 10.9 August Beer (1825 – 1863)
- 10.10 Elwin Bruno Christoffel (1829 – 1900)
- 10.11 Karl Hermann Amandus Schwarz (1843 – 1921)
- 10.12 Moritz Pasch (1843 – 1930)
- 10.13 Felix Christian Klein (1849 – 1925)
- 10.14 Ferdinand Georg Frobenius (1849 – 1917)
- 10.15 Alfred Pringsheim (1850 – 1941)
- 10.16 Arthur Moritz Schönflies (1853 – 1928)
- 10.17 Hans Carl Friedrich von Mangoldt (1854 – 1925)
- 10.18 Paul Rudolf Eugen Jahnke (1861 – 1921)
- 10.19 David Hilbert (1862 – 1943)
- 10.20 Charles Proteus Steinmetz (1865 – 1923)
- 10.21 Georg Wilhelm Scheffers (1866 – 1945)
- 10.22 Martin Wilhelm Kutta (1867 – 1944)

- 11 Saxony-Anhalt
- 12 Free Imperial City of Rothenburg
- 13 North Rhine / Westphalia
- 14 Hesse
- 15 Ernestine Duchies
- 16 Hanover
- 17 Grand Duchy of Baden
- 18 Braunschweig
- 19 Lower Saxony
- 20 German Conferderation
- 21 Duchy of Mecklenburg-Schwerin
- 22 Bremen
- 23 Duchy of Holstein
- 24 German Empire
- 24.1 Ernst Friedrich Ferdinand Zermelo (1871 – 1953)
- 24.2 Fritz Emde (1873 – 1951)
- 24.3 Heinrich Dörrie (1873 – 1955)
- 24.4 Friedrich Moritz Hartogs (1874 – 1943)
- 24.5 Erhard Schmidt (1876 – 1959)
- 24.6 Heinrich Wilhelm Ewald Jung (1876 – 1953)
- 24.7 Edmund Georg Hermann Landau (1877 – 1938)
- 24.8 Georg Karl Wilhelm Hamel (1877 – 1954)
- 24.9 Felix Bernstein (1878 – 1956)
- 24.10 Leopold Löwenheim (1878 – 1957)
- 24.11 Albert Einstein (1879 – 1955)
- 24.12 Paul Koebe (1882 – 1945)
- 24.13 Emmy Noether (1882 – 1935)
- 24.14 Konrad Hermann Theodor Knopp (1882 – 1957)
- 24.15 Max Born (1882 – 1970)
- 24.16 Arthur Josef Alwin Wieferich (1884 – 1954)
- 24.17 Hermann Klaus Hugo Weyl (1885 – 1955)
- 24.18 Ludwig Georg Elias Moses Bieberbach (1886 – 1982)
- 24.19 Arthur Rosenthal (1887 – 1959)
- 24.20 Erich Hecke (1887 – 1947)
- 24.21 Richard Courant (1888 – 1972)
- 24.22 William Richard Maximilian Hugo Threlfall (1888 – 1949)
- 24.23 Abraham Halevi Fraenkel (1891 – 1965)
- 24.24 Rudolf Carnap (1891 – 1970)
- 24.25 Roland Percival Sprague (1894 – 1967)
- 24.26 Heinz Hopf (1894 – 1971)
- 24.27 Wilhelm Friedrich Ackermann (1896 – 1962)
- 24.28 Ernst Paul Heinz Prüfer (1896 – 1934)
- 24.29 Carl Ludwig Siegel (1896 – 1981)
- 24.30 Gregor Wentzel (1898 – 1978)
- 24.31 Hellmuth Kneser (1898 – 1973)
- 24.32 Helmut Hasse (1898 – 1979)
- 24.33 Karl Menninger (1898 – 1963)
- 24.34 Wolfgang Krull (1899 – 1971)
- 24.35 Richard Dagobert Brauer (1901 – 1977)
- 24.36 Kurt Otto Friedrichs (1901 – 1982)
- 24.37 Werner Karl Heisenberg (1901 – 1976)
- 24.38 Oskar Morgenstern (1902 – 1977)
- 24.39 Camillo Herbert Grötzsch (1902 – 1993)
- 24.40 Kurt Mahler (1903 – 1988)
- 24.41 Helmut Grunsky (1904 – 1986)
- 24.42 Hans Lewy (1904 – 1988)
- 24.43 Hans Freudenthal (1905 – 1990)
- 24.44 Max August Zorn (1906 – 1993)
- 24.45 Karl Johannes Herbert Seifert (1907 – 1996)
- 24.46 Theodore Samuel Motzkin (1908 – 1970)
- 24.47 Bernhard Hermann Neumann (1909 – 2002)
- 24.48 Gerhard Karl Erich Gentzen (1909 – 1945)
- 24.49 Fritz John (1910 – 1994)
- 24.50 Lothar Collatz (1910 – 1990)
- 24.51 Helmut Wielandt (1910 – 2001)
- 24.52 Walter Ledermann (1911 – 2009)
- 24.53 Theodor Schneider (1911 – 1988)
- 24.54 Ernst Witt (1911 – 1991)
- 24.55 Hans Julius Zassenhaus (1912 – 1991)
- 24.56 Karl Stein (1913 – 2000)
- 24.57 Paul Julius Oswald Teichmüller (1913 – 1943)
- 24.58 Hanna Neumann (1914 – 1971)
- 24.59 Abraham Robinson (1918 – 74)

- 25 Weimar Republic
- 25.1 Richard Friederich Arens (1919 – 2000)
- 25.2 Gerhard Ringel (1919 – 2008)
- 25.3 Gerd Edzard Harry Reuter (1921 – 1992)
- 25.4 Erwin O. Kreyszig (1922 – 2008)
- 25.5 Ernst Gabor Straus (1922 – 1983)
- 25.6 Paul Moritz Cohn (1924 – 2006)
- 25.7 Friedrich Ernst Peter Hirzebruch (1927 – 2012)
- 25.8 Alexander Grothendieck (1928 – 2014)
- 25.9 Wolfgang Haken (b. 1928 )
- 25.10 Jürgen Kurt Moser (1928 – 1999)
- 25.11 Erich Müller-Pfeiffer (b. 1930 )
- 25.12 Robert John Aumann (b. 1930 )
- 25.13 Reinhold Remmert (b. 1930 )
- 25.14 Karl Heinrich Hofmann (b. 1932 )
- 25.15 Uta Caecilia Merzbach (1933 – 2017)

- 26 3rd Reich
- 27 East Germany
- 28 West Germany

## Holy Roman Empire

##### Nicholas of Cusa (1401 – 1464)

German philosopher, theologian, jurist, and astronomer.

Believed he had calculated $\pi$ exactly, as $3 \cdotp 1423$, but then also gave a good trigonometrical approximation later used by Willebrord van Royen Snell
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##### Johannes Müller von Königsberg (1436 – 1476)

Better known under his Latinized name (**Johannes Müller**) **Regiomontanus**: both surnames mean **King's mountain**.

German mathematician, astronomer, astrologer, translator, instrument maker and Catholic bishop.

Pupil of Georg von Peuerbach, whose uncompleted work he continued.

Set up a printing press at Nuremberg in $\text {1471}$ – $\text {1472}$ for printing scientific works.

First publisher of such scientific literature.

Became internationally famous within his own lifetime.
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##### Albrecht Dürer (1471 – 1528)

German painter, printmaker and theorist whose theoretical treatises involve principles of mathematics, perspective and ideal proportions.
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##### Ludolph van Ceulen (1540 – 1610)

German-Dutch mathematician best known for his calculation of the the value of $\pi$.

The **Ludolphine number** is the expression of the value of $\pi$ to $35$ decimal places:

- $3 \cdotp 14159 \, 26535 \, 89793 \, 23846 \, 26433 \, 83279 \, 50288 \ldots$

##### Johannes Kepler (1571 – 1630)

German mathematician and astronomer best known nowadays for Kepler's Laws of Planetary Motion.

Inherited the papers of Tycho Brahe and spent many years analysing his observations, looking for patterns.

His most significant contribution to scientific thought was his deduction that the orbits of the planets are elliptical.

Also pre-empted the methods of integral calculus to find the volume of a solid of revolution by slicing it into thin disks, calculating the volume of each, and then adding those volumes together.
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##### Johann Faulhaber (1580 – 1635)

German surveyor and engineer who was also a mathematician of the cossist tradition.

A significant influence on several mathematicians, including René Descartes, Jacob Bernoulli and Carl Jacobi.

Best known for his work on series of powers.
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##### Nicholas Mercator (c. 1620 – 1687)

German mathematician who designed a marine chronometer for Charles $\text {II}$ of England, and designed and constructed the fountains at the Palace of Versailles.

Known for the Newton-Mercator Series.
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##### Johann Friedrich Pfaff (1765 – 1825)

German mathematician who was a precursor of the German school, being a direct influence on Carl Friedrich Gauss.
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##### August Leopold Crelle (1780 – 1855)

Self-educated and enthusiastic German mathematician whose most important work was founding *Journal für die reine und angewandte Mathematik*, better known as **Crelle's Journal**.
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##### Georg Simon Ohm (1789 – 1834)

German physicist and mathematician best remembered for Ohm's Law.
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##### Wilhelm August Förstemann (1791 – 1836)

German mathematician best known for his textbooks, which were standard German grammar schools texts for some considerable time.

Published a series of articles on on the task of rationalizing equations.
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##### Karl Wilhelm Feuerbach (1800 – 1834)

German geometer best known for Feuerbach's Theorem.

Introduced homogeneous coordinates in $1827$, independently of August Ferdinand Möbius.
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##### Julius Plücker (1801 – 1868)

German mathematician and physicist who fundamental contributions to the field of analytical geometry.

Pioneer in the investigations of cathode rays that led eventually to the discovery of the electron.

Vastly extended the study of Lamé curves.

Published the first complete classification of plane cubic curves.
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##### Wilhelm Eduard Weber (1804 – 1891)

German physicist who invented the first electromagnetic telegraph with Carl Friedrich Gauss.
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## Electoral Palatinate

##### Jakob Köbel (1462 – 1533)

German mathematician and state official about whom little can be found on the internet.
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##### Elisabeth of the Palatinate (1618 – 1680)

Princess of the Electorate of the Palatinate who studied (among other things) mathematics and philosophy with René Descartes.

Her correspondence with Descartes survives as a record of the nature of philosophical and religious debates in that period.

Renowned for her intelligence and humanism.
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##### Prince Rupert of the Rhine (1619 – 1682)

Prince of the lines of both the Electorate of the Palatinate and the House of Stuart, who later in life turned to science and mathematics.

Known for posing the question which is now known as Prince Rupert's Cube.

Renowned for his military flair, but also notorious for his heavy-handed treatment of defeated enemies.
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##### Andreas Freiherr von Ettingshausen (1796 – 1878)

German mathematician and physicist.

The first to build an electromagnetic machine.

Invented the notation $\dbinom n k$ for the binomial coefficient.
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##### Oskar Bolza (1857 – 1942)

German mathematician best known for his research in the calculus of variations, particularly influenced by Karl Weierstrass's $1879$ lectures on the subject.
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## Esslingen am Neckar

##### Michael Stifel (1487 – 1567)

German monk and mathematician who made significant advances in mathematical notation, including the juxtaposition technique for indicating multiplication.

The first to use the term exponent. Published rules for calculation of powers.

The first to use a standard method to solve quadratic equations.

Also an early adopter of negative and irrational numbers.
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## Bavaria

##### Adam Ries (1492 – 1559)

Influential German mathematician who wrote some important instructional works, including sets of tables for calculations.
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##### Simon Jacob (c. 1500 – 1564)

German reckoner about whom little is known.

Published a book demonstrating that he understood some facts about the Fibonacci numbers that were not rediscovered until centuries later.
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##### Christopher Clavius (1538 – 1612)

German jesuit and logician.

Best known for:

- Clavius's Law (also written as
**Clavius' Law**), otherwise known as the**Consequentia Mirabilis**, which states that if by assuming the negation of a proposition you can prove its truth, then that proposition is true. - Being instrumental in the development of the Gregorian calendar.
- Writing highly-acclaimed and well-received text-books.

##### Johann Georg von Soldner (1776 – 1833)

German mathematician, physicist and astronomer.

Calculated the Euler-Mascheroni constant to 24 places.

The first one to predict (100 years before Einstein) that light rays would be bent by the gravitational fields of stars.
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##### Walther Franz Anton von Dyck (1856 – 1934)

German mathematician who was one of the pioneers of group theory.

The first to define a group in the abstract sense. The first to study a group by generators.

A student of Felix Klein.
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## Württemberg

##### Johannes Scheubel (1494 – 1570)

German mathematician noted for his work in popularising the use of algebra throughout Europe.

Also published an edition of the first six books of Euclid's *The Elements*.
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##### Johann Wilhelm von Camerer (1763 – 1847)

German protestant theologian, mathematician, astronomer and historian of mathematics.

Also published an edition of the first six books of Euclid's *The Elements*.
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##### Wilhelm Jordan (1842 – 1899)

German geodesist who conducted surveys in Germany and Africa and founded the German geodesy journal.

Remembered for Gauss-Jordan elimination, a version of Gaussian elimination with improved stability, for minimizing the squared error in the sum of a series of surveying observations.
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##### Otto Ludwig Hölder (1859 – 1937)

German mathematician most famous for his work in analysis (in particular Fourier series) and group theory.
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##### Wilhelm Weinberg (1862 – 1937)

German obstetrician-gynecologist who expressed the concept that would later come to be known as the Hardy-Weinberg Principle.
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## Saxony

##### Petrus Apianus (1495 – 1552)

German humanist and mathematician.

One of his books significantly appears in the painting *The Ambassadors* by Hans Holbein the Younger.
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##### Erasmus Reinhold (1511 – 1553)

German astronomer and mathematician, considered to be the most influential astronomical pedagogue of his generation.
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##### Gottfried Wilhelm von Leibniz (1646 – 1716)

German mathematician and philosopher who is best known for being the co-inventor (independently of Isaac Newton) of calculus.

Took some of the first philosophical steps towards a system of symbolic logic, but his works failed to have much influence on the development of logic, and these ideas were not developed to any significant extent.

Invented the system of binary notation.
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##### Ehrenfried Walther von Tschirnhaus (1651 – 1708)

German mathematician more famous for inventing a brand of porcelain.

Worked on techniques in algebra, and also investigated catacaustic curves.

Published what he thought was a solution to the quintic equation in $1683$, but Gottfried Wilhelm von Leibniz pointed out that it was fallacious.
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##### Gustav Roch (1839 – 1866)

German mathematician who made significant contributions to the theory of Riemann surfaces.
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##### Erwin Papperitz (1857 – 1938)

German mathematician who worked on the hypergeometric differential equation.
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##### Friedrich Engel (1861 – 1941)

German mathematician specialising in partial differential equations.
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##### Alwin Reinhold Korselt (1864 – 1947)

German mathematician best known for Korselt's Theorem which provides a definition for Carmichael numbers.

Contributed an early result in relational algebra.
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## East Prussia

##### Christian Goldbach (1690 – 1764)

Prussian amateur mathematician who also studied law and medicine.

Best known for posing the Goldbach Conjecture, which also appears as Goldbach's Marginal Conjecture, and a similar weaker conjecture known as Goldbach's Weak Conjecture.
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##### Johann Daniel Titius (1729 – 1796)

German astronomer best known for formulating the Titius-Bode Law, and thence to predict the existence of a planet between Mars and Jupiter.

Also active in the field of biology.
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##### Friedrich Julius Richelot (1808 – 1875)

German mathematician best known for his construction of the regular $257$-gon.
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##### Hermann Günter Grassmann (1809 – 1877)

Prussian mathematician who pioneered the field of linear algebra and vector analysis.

His work was way ahead of its time, and did not receive the recognition it deserved until much later.

During his life he gained more recognition for his study of languages, including Gothic and Sanskrit, than as a mathematician.
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##### Gustav Robert Kirchhoff (1824 – 1887)

Prussian physicist contributed to the fundamental understanding of electrical circuits, spectroscopy, and the emission of black-body radiation by heated objects.
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##### Daniel Friedrich Ernst Meissel (1826 – 1895)

German astronomer who contributed to various aspects of number theory.
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##### Paul David Gustav du Bois-Reymond (1831 – 1889)

German mathematician who worked on the mechanical equilibrium of fluids, the theory of functions and in mathematical physics.

Also worked on Sturm–Liouville theory, integral equations, variational calculus, and Fourier series.

In $1873$, constructed a continuous function whose Fourier series is not convergent.

His lemma defines a sufficient condition to guarantee that a function vanishes almost everywhere.

Also established that a trigonometric series that converges to a continuous function at every point is the Fourier series of this function.

Discovered a proof method that later became known as the Cantor's diagonal argument.

His name is also associated with the Fundamental Lemma of Calculus of Variations, of which he proved a refined version based on that of Lagrange.
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##### Rudolf Otto Sigismund Lipschitz (1832 – 1903)

German mathematician who worked in many areas, including analysis, number theory and differential geometry.
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##### Paul Albert Gordan (1837 – 1912)

German mathematician who worked in invariant theory and algebraic geometry.

Best known for his proof of his finite base theorem.
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##### Johann Gustav Hermes (1846 – 1912)

German mathematician best known for his attempted construction of the regular $65 \, 537$-gon.

Recent research suggests that there may be mistakes in this construction.
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##### Kurt Wilhelm Sebastian Hensel (1861 – 1941)

German mathematician best known for his introduction of $p$-adic numbers.
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##### Felix Hausdorff (1868 – 1942)

German mathematician fundamental in the development of modern topology.

Also active in set theory, measure theory and function theory.

The first to formulate what is now known as the Generalized Continuum Hypothesis.
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##### Arnold Johannes Wilhelm Sommerfeld (1868 – 1951)

German theoretical physicist who pioneered developments in atomic and quantum physics.
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##### Emanuel Lasker (1868 – 1941)

German philosopher and mathematician who was also one of the greatest chess-players of all time.

Inventor of the game now known as Lasca.
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## Hamburg

##### Johann Elert Bode (1747 – 1826)

German astronomer known for his reformulation and popularization of the Titius-Bode Law.

Determined the orbit of Uranus and suggested the planet's name.
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##### Johann Martin Zacharias Dase (1824 – 1861)

German mental calculator famous for calculating $\pi$ to $200$ places in $1844$.
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## Duchy of Brunswick-Lüneburg

##### Carl Friedrich Gauss (1777 – 1855)

One of the most influential mathematicians of all time, contributing to many fields, including number theory, statistics, analysis and differential geometry.
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## Prussia

##### Friedrich Wilhelm Bessel (1784 – 1846)

Prussian mathematician best known for making a systematic study of what is now known as Bessel's equation.
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##### Heinrich Ferdinand Scherk (1798 – 1885)

German mathematician notable for his work on minimal surfaces and the distribution of prime numbers.
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##### Carl Gustav Jacob Jacobi (1804 – 1851)

Prolific Prussian mathematician, now most famous for his work with the elliptic functions.
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##### Ernst Eduard Kummer (1810 – 1893)

German mathematician mostly active in the field of applied mathematics.

Also worked in abstract algebra and field theory.

Proved that Fermat's Last Theorem holds for all exponents $p$ such that $p$ is a regular prime.
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##### Theodor Schönemann (1812 – 1868)

Also rendered as **Theodor Schoenemann**.

German mathematician who obtained some important results in number theory.

Obtained Hensel's Lemma before Hensel, and formulated Eisenstein's Criterion (also known as the Schönemann-Eisenstein Theorem) before Eisenstein.
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##### Heinrich Eduard Heine (1821 – 1881)

German mathematician who worked mainly in analysis.
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##### Ferdinand Gotthold Max Eisenstein (1823 – 1852)

German mathematician best known for his work in number theory.

Student of Carl Friedrich Gauss.

Died tragically young of tuberculosis.
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##### Leopold Kronecker (1823 – 1891)

German mathematician most notable for his view that all of mathematics ought to be based on integers.

Also a proponent of the mathematical philosophy of finitism, a forerunner of intuitionism and constructivism.

His influence on the mathematical establishment was considerable.

His views put him in direct opposition most notably to Georg Cantor, who was exploring the mathematics of the transfinite.
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##### August Beer (1825 – 1863)

German physicist and mathematician.

Contributed towards the Beer-Lambert-Bouguer Law.
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##### Elwin Bruno Christoffel (1829 – 1900)

German mathematician and physicist.

Introduced fundamental concepts of differential geometry, opening the way for the development of tensor calculus.

This later provided the mathematical basis for general relativity.
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##### Karl Hermann Amandus Schwarz (1843 – 1921)

German mathematician known for his work in the field of complex analysis.

Student of Weierstrass.

Best known for his contribution to the Cauchy-Bunyakovsky-Schwarz Inequality.
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##### Moritz Pasch (1843 – 1930)

German mathematician who specialized in the foundations of geometry.

His work served as the inspiration for work by Giuseppe Peano and David Hilbert in their work to re-axiomise the field of geometry.

Best known for his formulation of what is now known as Pasch's Axiom.
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##### Felix Christian Klein (1849 – 1925)

German mathematician best known for his work establishing the connections between geometry and group theory.

Architect of the Erlangen program, which classifies geometries according to their symmetry groups.

Noted for the Klein bottle and the Klein $4$-group.
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##### Ferdinand Georg Frobenius (1849 – 1917)

German mathematician best known for his work on differential equations and group theory.

Gave the first full proof of the Cayley-Hamilton Theorem.
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##### Alfred Pringsheim (1850 – 1941)

German mathematician and patron of the arts, best known for Pringsheim's Theorem.
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##### Arthur Moritz Schönflies (1853 – 1928)

German mathematician known for his contributions to the application of group theory to crystallography, and for work in topology.
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##### Hans Carl Friedrich von Mangoldt (1854 – 1925)

German mathematician who contributed towards the solution of the Prime Number Theorem.
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##### Paul Rudolf Eugen Jahnke (1861 – 1921)

German mathematician best known for his $1909$ *Funktionentafeln mit Formeln und Kurven*.
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##### David Hilbert (1862 – 1943)

One of the most influential mathematicians in the late $19$th and early $20$th century.

Most famous for the Hilbert $23$, a list he delivered in $1900$ of $23$ problems which were at the time still unsolved.
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##### Charles Proteus Steinmetz (1865 – 1923)

Prussian-born American mathematician and electrical engineer and professor at Union College.

Fostered development of alternating current that enabled expansion of electric power industry in United States.

Formulated mathematical theories for engineers.

Explained the phenomenon of hysteresis.
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##### Georg Wilhelm Scheffers (1866 – 1945)

German mathematician whose specialty was differential geometry.

Also a writer of several well-received textbooks.
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##### Martin Wilhelm Kutta (1867 – 1944)

German mathematician best known for co-developing (with Carl David Tolmé Runge) of the Runge-Kutta Methods in the field of numerical analysis.

Also known for the Zhukovsky-Kutta Aerofoil.
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## Saxony-Anhalt

##### August Ferdinand Möbius (1790 – 1868)

German mathematician and theoretical astronomer, active in geometry and number theory.

Best known for inventing the Möbius Strip, although this was actually invented independently by Johann Benedict Listing at around the same time.
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##### Hermann Hankel (1839 – 1873)

German mathematician who worked on complex numbers and quaternions.
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##### Leo August Pochhammer (1841 – 1920)

German mathematician known for his work on special functions.

Also known for the Pochhammer symbol.
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##### Eugen Otto Erwin Netto (1846 – 1919)

German mathematician known for his work in group theory.
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## Free Imperial City of Rothenburg

##### Karl Georg Christian von Staudt (1798 – 1867)

German mathematician best known for his book *Geometrie der Lage*, an important work in the development of the discipline of projective geometry.
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## North Rhine / Westphalia

##### Daniel Christian Ludolph Lehmus (1780 – 1863)

German mathematician best remembered for the Steiner-Lehmus Theorem.
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##### Johann Peter Gustav Lejeune Dirichlet (1805 – 1859)

German mathematician who worked mainly in the field of analysis.

Credited with the first formal definition of a function.
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##### Karl Theodor Wilhelm Weierstrass (1815 – 1897)

German mathematician whose main work concerned the rigorous foundations of calculus.

Known as "the father of modern analysis".
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##### Heinrich Menge (1838 – c. 1904)

German classical scholar and high school teacher, who contributed towards the documentation of the ancient history of mathematics.
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##### Wilhelm Karl Joseph Killing (1847 – 1923)

German mathematician who made important contributions to the theories of Lie algebras, Lie groups, and non-Euclidean geometry.
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## Hesse

##### Moritz Abraham Stern (1807 – 1894)

German mathematician known for formulating Stern's diatomic series.

Also known for the Stern-Brocot Tree which he wrote about in $1858$ and which Brocot independently discovered in $1861$.
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##### Johann Benedict Listing (1808 – 1882)

German mathematician and physicist who coined the term **topology** in a letter of $1836$.

In $1858$ he invented the Möbius strip at about the same time that August Ferdinand Möbius did.
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##### Gustavus Frankenstein (1827 – 1893)

German-American clock maker, artist, mathematician and writer.

Best known now for being the first to discover a perfect magic cube of order 8.
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##### Alexander Wilhelm von Brill (1842 – 1935)

German mathematician best known for his involvement with Felix Klein in the reform of the teaching of mathematics.

Made significant contributions to the field of algebraic geometry.
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##### August Otto Föppl (1854 – 1924)

German mathematician credited with introducing Föppl-Klammer theory and the Föppl-von Kármán Equations.
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##### Paul Friedrich Wolfskehl (1856 – 1906)

German physician with an interest in mathematics.

He bequeathed $100\,000$ marks (equivalent to $£ 1\,000\,000$ pounds in $1997$ money) to the first person to prove Fermat's Last Theorem.

By the time the prize was finally awarded to Andrew John Wiles on $27$ June $1997$, the monetary value of the award had dwindled to $£30\,000$.
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## Ernestine Duchies

##### Carl Anton Bretschneider (1808 – 1878)

German mathematician who worked in geometry, number theory, and history of geometry.

He also worked on logarithmic integrals and mathematical tables.

Probably the first mathematicians to use the symbol $\gamma$ for the Euler-Mascheroni constant, which he published in a paper of $1837$.
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## Hanover

##### Georg Friedrich Bernhard Riemann (1826 – 1866)

German mathematician most famous for the Riemann Hypothesis, which is (at time of writing, early $21$st century) one of the most highly sought-after results in mathematics.
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##### Carl Louis Ferdinand von Lindemann (1852 – 1939)

German mathematician who made his mark by publishing a proof in $1882$ that $\pi$ is transcendental.
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## Grand Duchy of Baden

##### Moritz Benedikt Cantor (1829 – 1920)

German historian of mathematics.
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##### Friedrich Wilhelm Karl Ernst Schröder (1841 – 1902)

German mathematician active mainly in the field of algebraic logic.

He is best known for his contribution to what is now known as the Cantor-Bernstein-Schröder Theorem.
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##### Heinrich Martin Weber (1842 – 1913)

German mathematician who worked in algebra, number theory, analysis and applications of analysis to mathematical physics.

Formulated the ring axioms.
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##### Max Noether (1844 – 1921)

German mathematician (also occasionally rendered **Nöther**) notable for his work in algebraic geometry and algebraic functions.

Father of Emmy Noether.
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## Braunschweig

##### Julius Wilhelm Richard Dedekind (1831 – 1916)

German mathematician who worked in the fields of abstract algebra, and algebraic number theory.

Most noted for his work on the foundations of the real numbers.

Used the thinking behind the resolution of Galileo's Paradox to underpin the definition of an infinite set.
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## Lower Saxony

##### Karl Theodor Reye (1838 – 1919)

German mathematician who contributed to geometry, particularly projective geometry and synthetic geometry.
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##### Adolf Hurwitz (1859 – 1919)

German mathematician who was an early master of the theory of Riemann surfaces.
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## German Conferderation

##### Georges Pfeffermann (1838 – 1914)

German amateur mathematician who did a lot of work on magic squares and multiplicative magic squares.
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## Duchy of Mecklenburg-Schwerin

##### Friedrich Ludwig Gottlob Frege (1848 – 1925)

German philosopher, logician, and mathematician, one of the founders of modern logic.

Made major contributions to the foundations of mathematics.
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## Bremen

##### Carl David Tolmé Runge (1856 – 1927)

German mathematician, physicist, and spectroscopist.

Best known as the co-developer (with Martin Wilhelm Kutta) of the Runge-Kutta Methods in the field of numerical analysis.

Also known for his work on the Zeeman effect.

His work paved the way for the Thue-Siegel-Roth Theorem in the field of Diophantine equations.
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## Duchy of Holstein

##### Max Karl Ernst Ludwig Planck (1858 – 1947)

German theoretical physicist whose discovery of energy quanta won him the Nobel Prize in Physics in $1918$.
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## German Empire

##### Ernst Friedrich Ferdinand Zermelo (1871 – 1953)

German mathematician best known for his work on the foundations of mathematics.

Laid the groundwork (later to be enhanced by Abraham Fraenkel) for what are now known as the Zermelo-Fraenkel axioms of axiomatic set theory.
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##### Fritz Emde (1873 – 1951)

German electronic engineer and high school teacher, best known for his co-authorship with Eugen Jahnke of *Funktionentafeln mit Formeln und Kurven*.
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##### Heinrich Dörrie (1873 – 1955)

German teacher of mathematics and author of several specialist books.
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##### Friedrich Moritz Hartogs (1874 – 1943)

German mathematician who made advances in set theory and complex analysis.

Killed himself as a result of the treatment he had received from the government of his country at the time.
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##### Erhard Schmidt (1876 – 1959)

Baltic German mathematician whose work significantly influenced the direction of mathematics in the twentieth century.
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##### Heinrich Wilhelm Ewald Jung (1876 – 1953)

German mathematician who specialized in geometry and algebraic geometry.
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##### Edmund Georg Hermann Landau (1877 – 1938)

German mathematician who worked in the fields of number theory and complex analysis.
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##### Georg Karl Wilhelm Hamel (1877 – 1954)

German mathematician with interests in mechanics, the foundations of mathematics and function theory.
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##### Felix Bernstein (1878 – 1956)

German mathematician active mainly in the field of algebraic logic.

He is best known for his $1897$ contribution to what is now known as the Cantor-Bernstein-Schröder Theorem.
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##### Leopold Löwenheim (1878 – 1957)

German mathematician whose work pioneered the field of model theory.

Much of his unpublished work was lost when the British brutally bombed his house in $1943$, an act of unforgivable barbarism for which the Brits have never delivered appropriate recompense.
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##### Albert Einstein (1879 – 1955)

German-born mathematician and physicist. Probably the most famous scientist of all time.
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##### Paul Koebe (1882 – 1945)

German-born mathematician who dealt exclusively with the complex numbers.

His most important results were on the uniformization of Riemann surfaces.
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##### Emmy Noether (1882 – 1935)

German-born mathematician who made considerable contributions to abstract algebra and theoretical physics.

Most famous for Noether's Theorem which makes the fundamental connection between symmetry and various laws of conservation.

Her philosophy and outlook were fundamental in the development of ideas that led to the establishment of the field of category theory.

Daughter of Max Noether.
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##### Konrad Hermann Theodor Knopp (1882 – 1957)

German mathematician who worked on generalized limits and complex functions.
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##### Max Born (1882 – 1970)

German-Jewish physicist and mathematician who was instrumental in the development of quantum mechanics.

Also made contributions to solid-state physics and optics.

Supervised the work of a number of notable physicists in the 1920s and 1930s.
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##### Arthur Josef Alwin Wieferich (1884 – 1954)

German mathematician who contributed briefly to the field of number theory before concentrating on a career in teaching.
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##### Hermann Klaus Hugo Weyl (1885 – 1955)

German mathematician who worked in the fields of mathematical logic and mathematical physics.
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##### Ludwig Georg Elias Moses Bieberbach (1886 – 1982)

German mathematician working mostly in analysis.
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##### Arthur Rosenthal (1887 – 1959)

German mathematician working in geometry, in particular the classification of regular polyhedra and Hilbert's axioms.

Also made contributions in analysis, including to Carathéodory's theory of measure.

With Michel Plancherel, made contributions in ergodic theory and dynamical systems.
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##### Erich Hecke (1887 – 1947)

German mathematician working mainly in functional analysis.
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##### Richard Courant (1888 – 1972)

German mathematician best known for his writings.

Made considerable contributions to the field numerical analysis.
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##### William Richard Maximilian Hugo Threlfall (1888 – 1949)

German mathematician whose main work was in topology.

Collaborated extensively with Karl Johannes Herbert Seifert.
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##### Abraham Halevi Fraenkel (1891 – 1965)

German-born Israeli Hungarian mathematician best known for his work on axiomatic set theory.

He improved Ernst Zermelo's axiomatic system, and out of that work came the Zermelo-Fraenkel axioms.

He also wrote on topics in the history of mathematics.
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##### Rudolf Carnap (1891 – 1970)

German-born philosopher who was active in Europe before 1935 and in the United States thereafter.
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##### Roland Percival Sprague (1894 – 1967)

German mathematician, known for the Sprague-Grundy Theorem and for being the first mathematician to find a perfect squared square.
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##### Heinz Hopf (1894 – 1971)

German mathematician who worked on the fields of topology and geometry.
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##### Wilhelm Friedrich Ackermann (1896 – 1962)

German mathematician, best known for the Ackermann function.
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##### Ernst Paul Heinz Prüfer (1896 – 1934)

German mathematician who worked on abelian groups, algebraic numbers, knot theory and Sturm-Liouville theory.

Provided an ingenious proof of Cayley's Formula.
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##### Carl Ludwig Siegel (1896 – 1981)

German mathematician specialising in analytic number theory.
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##### Gregor Wentzel (1898 – 1978)

German physicist best known for development of quantum mechanics
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##### Hellmuth Kneser (1898 – 1973)

German mathematician, who made notable contributions to group theory and topology.

Derived the theorem on the existence of a prime decomposition for $3$-manifolds.

Originated the concept of a normal surface.
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##### Helmut Hasse (1898 – 1979)

German mathematician who worked mainly in algebraic number theory and class field theory.
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##### Karl Menninger (1898 – 1963)

German teacher of and writer about mathematics.
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##### Wolfgang Krull (1899 – 1971)

Made significant contributions to many areas of commutative algebra.

Much of his work was influenced by Felix Klein and Emmy Noether.
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##### Richard Dagobert Brauer (1901 – 1977)

German / American mathematician who worked mainly in abstract algebra.

Made important contributions to number theory.

Founder of modular representation theory.
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##### Kurt Otto Friedrichs (1901 – 1982)

German applied mathematician whose major contribution was his work on partial differential equations.
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##### Werner Karl Heisenberg (1901 – 1976)

German theoretical physicist who was one of the key pioneers of quantum mechanics.
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##### Oskar Morgenstern (1902 – 1977)

German-born economist notable for founding the field of game theory in collaboration with John von Neumann, and applying it to economics.
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##### Camillo Herbert Grötzsch (1902 – 1993)

German mathematician working mainly in graph theory
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##### Kurt Mahler (1903 – 1988)

German mathematician working mainly in analysis and number theory.

Proved the Prouhet-Thue-Morse constant and Champernowne constant to be transcendental.
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##### Helmut Grunsky (1904 – 1986)

German mathematician who worked in complex analysis and geometric function theory.
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##### Hans Lewy (1904 – 1988)

German born American mathematician, known for his work on partial differential equations and on the theory of functions of several complex variables.
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##### Hans Freudenthal (1905 – 1990)

German born Dutch mathematician, made substantial contributions to algebraic topology.

Took an interest in literature, philosophy, history and mathematics education.

One of the most important figures in mathematics education in the $20$th century.
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##### Max August Zorn (1906 – 1993)

German-born American mathematician who worked in algebra, set theory and numerical analysis.

Best known for Zorn's Lemma, which he discovered in 1935. This is also known as the Kuratowski-Zorn Lemma, thereby acknowledging the work of Kazimierz Kuratowski who had published a version of it in 1922.
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##### Karl Johannes Herbert Seifert (1907 – 1996)

German mathematician who worked mainly in topology and knot theory.

Collaborated extensively with William Threlfall.

One of the few who managed to weather the 2nd World War without upsetting either the Nazis or the Allies.
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##### Theodore Samuel Motzkin (1908 – 1970)

German-born Israeli-American mathematician who was one of the pioneers of linear programming.

Also published in the fields of algebra, graph theory, approximation theory, combinatorics, numerical analysis, algebraic geometry and number theory.

Worked as a cryptographer for the British government during World War II.
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##### Bernhard Hermann Neumann (1909 – 2002)

German-born mathematician who was one of the leaders in the field of group theory.

Husband of Hanna Neumann and father of Peter Michael Neumann.
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##### Gerhard Karl Erich Gentzen (1909 – 1945)

German mathematician and logician who made progress in symbolic logic.

Proved that the Peano axioms are consistent.
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##### Fritz John (1910 – 1994)

German mathematician best known for his work on partial differential equations and ill-posed problems.
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##### Lothar Collatz (1910 – 1990)

German mathematician best known for posing the Collatz Conjecture.
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##### Helmut Wielandt (1910 – 2001)

German mathematician whose main work was in group theory, especially permutation groups.
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##### Walter Ledermann (1911 – 2009)

German mathematician best known for his work in homology, group theory and number theory.
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##### Theodor Schneider (1911 – 1988)

German mathematician best known for providing a proof of the Gelfond-Schneider Theorem.
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##### Ernst Witt (1911 – 1991)

German mathematician working mainly in the field of quadratic forms and algebraic function fields.
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##### Hans Julius Zassenhaus (1912 – 1991)

German mathematician who did significant work in abstract algebra, and also pioneered the science of computer algebra.
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##### Karl Stein (1913 – 2000)

German mathematician well known for complex analysis and cryptography.
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##### Paul Julius Oswald Teichmüller (1913 – 1943)

German mathematician who introduced quasiconformal mappings and differential geometric methods into complex analysis.

Usually known as **Oswald Teichmüller**.
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##### Hanna Neumann (1914 – 1971)

German-born mathematician active in the field of group theory.
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##### Abraham Robinson (1918 – 74)

German-American mathematician who is most widely known for development of non-standard analysis.
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## Weimar Republic

##### Richard Friederich Arens (1919 – 2000)

German-born American mathematician who worked in the fields of functional analysis and topology.
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##### Gerhard Ringel (1919 – 2008)

German mathematician who was one of the pioneers in the field of graph theory.
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##### Gerd Edzard Harry Reuter (1921 – 1992)

German-born mathematician who emigrated to Britain who worked mainly in the fields of probability theory and analysis.
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##### Erwin O. Kreyszig (1922 – 2008)

German-Canadian applied mathematician best known for his text books.
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##### Ernst Gabor Straus (1922 – 1983)

German-American mathematician who helped found the theories of Euclidean Ramsey theory and of the arithmetic properties of analytic functions.

Worked as the assistant to Albert Einstein.
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##### Paul Moritz Cohn (1924 – 2006)

German-born mathematician renowned as an expert in abstract algebra, in particular non-commutative rings.
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##### Friedrich Ernst Peter Hirzebruch (1927 – 2012)

German mathematician, working in the fields of topology, complex manifolds and algebraic geometry.
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##### Alexander Grothendieck (1928 – 2014)

Sometimes rendered **Alexandre Grothendieck**.

German-born mathematician of semi-Ukrainian ancestry who is usually credited with creating the modern field of algebraic geometry.

His collaborative seminar-driven approach had the result of making him one of the most influential thinkers of the 20th century.
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##### Wolfgang Haken (b. 1928 )

German mathematician mainly involved in topology where the bulk of his work has been on 3-dimensional manifolds.

In $1976$, along with Kenneth Ira Appel, proved the Four Color Theorem with the help of a computer.
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##### Jürgen Kurt Moser (1928 – 1999)

German mathematician mainly involved in dynamical systems.
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##### Erich Müller-Pfeiffer (b. 1930 )

German mathematician best known for his text book.
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##### Robert John Aumann (b. 1930 )

German-born Israeli-American mathematician noted for his work on conflict and cooperation through game-theory analysis.
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##### Reinhold Remmert (b. 1930 )

German mathematician whose work has mainly been in developing the theory of complex spaces.
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##### Karl Heinrich Hofmann (b. 1932 )

German mathematician working in the fields of topological algebra and functional analysis, especially topological groups and semigroups and Lie theory.
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##### Uta Caecilia Merzbach (1933 – 2017)

German-born American historian of mathematics.
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## 3rd Reich

##### Stefan Oscar Walter Hildebrandt (1936 – 2005)

German mathematician concerned mainly with the calculus of variations and nonlinear partial differential equations.
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##### Bernd Fischer (b. 1936 )

German mathematician best known to his contributions to the classification of finite simple groups.

Discovered several of the sporadic groups:

- Introduced 3-transposition groups
- Constructed the three Fischer groups
- Described the Baby Monster and computed its character table
- Predicted the existence of the Fischer-Griess Monster.

##### Wilfrid Keller (b. 1937 )

German mathematician best known for his activity in number theory, including the hunt for titanic primes.
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##### Jürgen Neukirch (1937 – 1997)

German mathematician known for his work on algebraic number theory.
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##### Heiko Harborth (b. 1938 )

German mathematician whose work is mostly in the areas of number theory, combinatorics and discrete geometry, including graph theory..
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##### Peter Schreiber (b. 1938 )

German mathematician and historian of mathematics who deals with the foundations of mathematics and geometry.
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##### Christoph Bandelow (1939 – 2011)

German mathematician mainly working in probability theory.

Also known as the author of books on Rubik's cube and other mathematical recreations.
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##### Eberhard Freitag (b. 1942 )

German mathematician known for his work in function theory and modular forms.
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## East Germany

##### Ingmar Lehmann (b. 1946 )

German mathematician, university lecturer and non-fiction author.
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##### Gerd Rudolph (b. 1950 )

German mathematician and physicist specialising in gauge theory.
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## West Germany

##### Andreas Raphael Blass (b. 1947 )

German mathematician who works in mathematical logic, particularly set theory, and theoretical computer science.
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##### Dietmar Arno Salamon (b. 1953 )

German mathematician.
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##### Gerd Faltings (b. 1954 )

German mathematician known for his work in arithmetic algebraic geometry.
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