ProofWiki: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."

Saxony

Petrus Apianus

1495 – 1552

Also known as Peter Apian. Born as Peter Bienewitz (or Bennewitz), he Latinized his name (Biene is German and Apis is Latin for "bee") while at Leipzig University.

German humanist and mathematician.

One of his books significantly appears in the painting The Ambassadors by Hans Holbein the Younger.
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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.
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Carl Friedrich Gauss

1777 – 1855

Full name: Johann Carl Friedrich Gauss.

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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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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Adolf Hurwitz

1859 – 1919

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

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.

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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 von Dyck

1856 – 1934

Walther Franz Anton von Dyck was a German mathematician who was one of the pioneers of group theory.

He was originally known as Walther Dyck: the von was added later when he was ennobled.

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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Holy Roman Empire

Johannes Kepler

1571 – 1630

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

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.
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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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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.

Related by marriage to Dirichlet.
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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 known both as Gotthold Eisenstein and Ferdinand Eisenstein, 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 Law.
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Hermann Amandus Schwarz

1843 – 1921

Full name: Karl Hermann Amandus Schwarz.

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

Often misspelt Schwartz.

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 Klein

1849 – 1925

Christian Felix Klein (also reoprted as Felix Christian Klein) was a 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 Klein four-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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Hans von Mangoldt

1854 – 1925

Full name: Hans Carl Friedrich von Mangoldt.

German mathematician who contributed towards the solution of the Prime Number Theorem.
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David Hilbert

1862 – 1943

One of the most influential mathematicians in the late 19th and early 20th 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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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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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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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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Rudolf Lipschitz

1832 – 1903

Full name: Rudolf Otto Sigismund Lipschitz.

German mathematician who worked in many areas, including analysis, number theory and differential geometry.
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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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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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Jürgen Kurt Moser

1928 – 1999

German mathematician mainly involved in dynamical systems.
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Electoral Palatinate

Andreas Freiherr von Ettingshausen

1796 – 1878

German mathematician and physicist.

The first to build an electromagnetic machine.

Invented the notation $\displaystyle \binom n k$ for the binomial coefficient.
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North Rhine / Westphalia

Johann Lejeune Dirichlet

1805 – 1859

Full name: Johann Peter Gustav Lejeune Dirichlet.

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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Hesse

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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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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Hanover

Georg Friedrich Bernhard Riemann

1826 – 1866

Most famous for the Riemann Hypothesis, which is (at time of writing, early 21st century) one of the most highly sought-after results in mathematics.
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Braunschweig

Richard Dedekind

1831 – 1916

Julius Wilhelm Richard Dedekind was a 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.
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Grand Duchy of Baden

Ernst Schröder

1841 – 1902

Ernst Schröder (or Schroeder) was a 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-Schroeder 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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Kingdom of Württemberg

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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Albert Einstein

1879 – 1955

German-born mathematician and physicist. Probably the most famous scientist of all time.
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German Empire

Ernst Zermelo

1871 – 1953

Ernst Friedrich Ferdinand Zermelo 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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Friedrich Moritz Hartogs

1874 – 1943

Friedrich Hartogs (known to his associates as Fritz) was a 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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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-Schroeder 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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Emmy Noether

1882 – 1935

Amalie ("Emmy") Noether was a 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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Hermann Klaus Hugo Weyl

1885 – 1955

German mathematician who worked in the fields of mathematical logic and mathematical physics.
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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 Threlfall

1888 – 1949

William Richard Maximilian Hugo Threlfall was a German mathematician whose main work was in topology.

Collaborated extensively with Herbert Seifert.
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Abraham Fraenkel

1891 – 1965

Abraham Halevi (Adolf) Fraenkel (in Hebrew: אברהם הלוי (אדולף) פרנקל) was a 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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Heinz Prüfer

1896 – 1934

Ernst Paul Heinz Prüfer was a 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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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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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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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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Herbert Seifert

1907 – 1996

Full name: Karl Johannes Herbert Seifert. Sometimes reported as Herbert Karl Johannes Seifert.

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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Bernhard Neumann

1909 – 2002

Full name: Bernhard Hermann Neumann.

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

Husband of Hanna Neumann and father of Peter M. Neumann.
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Gerhard Gentzen

1909 – 1945

Full name: Gerhard Karl Erich Gentzen.

German mathematician and logician who made progress in symbolic logic.

Proved that the Peano axioms are consistent.
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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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Hanna Neumann

1914 – 1971

Full maiden name: Johanna von Caemmerer.

German-born mathematician active in the field of group theory.

Wife of Bernhard Neumann and mother of Peter M. Neumann.
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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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Gerd Edzard Harry Reuter

1921 – 1992

Harry Reuter was a German-born mathematician who emigrated to Britain who worked mainly in the fields of probability theory and analysis.
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Alexander Grothendieck

b. 1928

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 Appel, proved the Four Color Theorem with the help of a computer.
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