Kronecker
Kronecker's primary contributions were in the theory of equations. He
made major contributions in elliptic functions and the theory of
algebraic numbers.
Kronecker was taught mathematics at school by Kummer and it was due to
him that Kronecker became interested in mathematics. Kronecker became
a student at Berlin University in 1841 where he studied under Jacobi,
Dirichlet and Eisenstein. After spending time at Bonn and Breslau he
returned to Berlin to write a Ph. D. thesis on algebraic number theory
under Dirichlet's supervision.
Kronecker then left Berlin and returned to Silesia where he was to
make a private fortune as a banker. He remained there until 1855 when
he returned to Berlin where he was to remain for the rest of his life.
In 1855 Kummer came to Berlin to fill the vacancy left when Dirichlet
left for Göttingen. Kronecker was not to become a professor until
Kummer retired in 1883.
Kronecker was of very small stature and extremely selfconscious about
his height. In fact he attacked vigorously anyone whose mathematics he
disapproved.
His primary contributions were in the theory of equations and higher
algebra. His major contributions were in elliptic functions, the
theory of algebraic equations, and the theory of algebraic numbers.
Kronecker led the opposition to Cantor's view of set theory and the
foundations of mathematics. He believed in the reduction of all
mathematics to arguments involving only the integers and a finite
number of steps. Kronecker is well known for his remark
God created the integers, all else is the work of man.
Kronecker believed that mathematics should deal only with finite
numbers and with a finite number of operations. The value of set
theory, particularly in analysis and topology, made sure that it was
accepted into mathematics despite initial opposition to the idea of
the infinite.
Kronecker views were not put aside, however, and were developed by
Poincaré and Brouwer, who placed particular emphasis upon intuition.
Intuitionism stresses that mathematics has priority over logic, the
objects of mathematics are constructed and operated upon in the mind
by the mathematician, and it is impossible to define the properties of
mathematical objects simply by establishing a number of axioms.
Biographies of mathematicians are from the
History of
Mathematics archive at the University of St. Andrews, and are
used with permission.
