Prussian Academy of Sciences
What organization did Leopold Kronecker join in 1861?
Leopold Kronecker Leopold Kronecker ( ; 7 December 1823 – 29 December 1891 ) was a German mathematician who worked on number theory , algebra and logic . He criticized Georg Cantors work on set theory , and was quoted by as having said , ( God made the integers , all else is the work of man ) . Kronecker was a student and lifelong friend of Ernst Kummer . Biography . Leopold Kronecker was born on 7 December 1823 in Liegnitz , Prussia ( now Legnica , Poland ) in a wealthy Jewish family . His parents , Isidor and Johanna ( née Prausnitzep ) , took care of their childrens education and provided them with private tutoring at home—Leopolds younger brother Hugo Kronecker would also follow a scientific path , later becoming a notable physiologist . Kronecker then went to the Liegnitz Gymnasium where he was interested in a wide range of topics including science , history and philosophy , while also practicing gymnastics and swimming . At the gymnasium he was taught by Ernst Kummer , who noticed and encouraged the boys interest in mathematics . In 1841 Kronecker became a student at the University of Berlin where his interest did not immediately focus on mathematics , but rather spread over several subjects including astronomy and philosophy . He spent the summer of 1843 at the University of Bonn studying astronomy and 1843–44 at the University of Breslau following his former teacher Kummer . Back in Berlin , Kronecker studied mathematics with Peter Gustav Lejeune Dirichlet and in 1845 defended his dissertation in algebraic number theory written under Dirichlets supervision . After obtaining his degree , Kronecker did not follow his interest in research on an academic career path . He went back to his hometown to manage a large farming estate built up by his mothers uncle , a former banker . In 1848 he married his cousin Fanny Prausnitzer , and the couple had six children . For several years Kronecker focused on business , and although he continued to study mathematics as a hobby and corresponded with Kummer , he published no mathematical results . In 1853 he wrote a memoir on the algebraic solvability of equations extending the work of Évariste Galois on the theory of equations . Due to his business activity , Kronecker was financially comfortable , and thus he could return to Berlin in 1855 to pursue mathematics as a private scholar . Dirichlet , whose wife Rebecka came from the wealthy Mendelssohn family , had introduced Kronecker to the Berlin elite . He became a close friend of Karl Weierstrass , who had recently joined the university , and his former teacher Kummer who had just taken over Dirichlets mathematics chair . Over the following years Kronecker published numerous papers resulting from his previous years independent research . As a result of this published research , he was elected a member of the Berlin Academy in 1861 . Although he held no official university position , Kronecker had the right as a member of the Academy to hold classes at the University of Berlin and he decided to do so , starting in 1862 . In 1866 , when Riemann died , Kronecker was offered the mathematics chair at the University of Göttingen ( previously held by Carl Friedrich Gauss and Dirichlet ) , but he refused , preferring to keep his position at the Academy . Only in 1883 , when Kummer retired from the University , was Kronecker invited to succeed him and became an ordinary professor . Kronecker was the supervisor of Kurt Hensel , Adolf Kneser , Mathias Lerch , and Franz Mertens , amongst others . His philosophical view of mathematics put him in conflict with several mathematicians over the years , notably straining his relationship with Weierstrass , who almost decided to leave the University in 1888 . Kronecker died on 29 December 1891 in Berlin , several months after the death of his wife . In the last year of his life , he converted to Christianity . He is buried in the Alter St Matthäus Kirchhof cemetery in Berlin-Schöneberg , close to Gustav Kirchhoff . Scientific activity . Mathematics research . An important part of Kroneckers research focused on number theory and algebra . In an 1853 paper on the theory of equations and Galois theory he formulated the Kronecker–Weber theorem , without however offering a definitive proof ( the theorem was proved completely much later by David Hilbert ) . He also introduced the structure theorem for finitely-generated abelian groups . Kronecker studied elliptic functions and conjectured his liebster Jugendtraum ( dearest dream of youth ) , a generalization that was later put forward by Hilbert in a modified form as his twelfth problem . In an 1850 paper , On the Solution of the General Equation of the Fifth Degree , Kronecker solved the quintic equation by applying group theory ( though his solution was not in terms of radicals : that was already proven impossible by the Abel–Ruffini theorem ) . In algebraic number theory Kronecker introduced the theory of divisors as an alternative to Dedekinds theory of ideals , which he did not find acceptable for philosophical reasons . Although the general adoption of Dedekinds approach led Kroneckers theory to be ignored for a long time , his divisors were found useful and were revived by several mathematicians in the 20th century . Kronecker also contributed to the concept of continuity , reconstructing the form of irrational numbers in real numbers . In analysis , Kronecker rejected the formulation of a continuous , nowhere differentiable function by his colleague , Karl Weierstrass . Also named for Kronecker are the Kronecker limit formula , Kroneckers congruence , Kronecker delta , Kronecker comb , Kronecker symbol , Kronecker product , Kroneckers method for factorizing polynomials , Kronecker substitution , Kroneckers theorem in number theory , Kroneckers lemma , and Eisenstein–Kronecker numbers . Philosophy of mathematics . Kroneckers finitism made him a forerunner of intuitionism in foundations of mathematics . Honours . Kronecker was elected as a member of several academies : - Prussian Academy of Sciences ( 1861 ) - French Academy of Sciences ( 1868 ) - Royal Society ( 1884 ) . The 25624 Kronecker asteroid is named after him .