Mathematician:Leopold Kronecker

Mathematician
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, who was exploring the mathematics of the transfinite. Solved the quintic equation using group theory, but this proof of course did not use radicals as this had been proved to be impossible by the Abel-Ruffini Theorem.

The first to provide an axiomatic formulation for the structure of an abstract group.

Nationality
Prussian, then German

History

 * Born: December 7, 1823, Liegnitz, Prussia (now Legnica, Poland)
 * Studied under
 * 1841: Became a student at Berlin University, studied under and
 * Summer of 1843: University of Bonn
 * winter semester of 1843-44: University of Breslau, studied under again
 * 1845: Submitted PhD thesis
 * Left academia, returned home to Liegnitz to attend to family business
 * 1848: Married Fanny Prausnitzer
 * 1855: Returned to Berlin independently wealthy, but did not hold any university appointment
 * 23 January 1861: Elected to the Berlin Academy
 * October 1862: Started lecturing at Berlin University
 * 1880: Took over control of Crelle's Journal as the editor
 * 1883: Became a codirector of the mathematical seminar at Berlin University (taking over from )
 * 31 January 1884: Elected a foreign member of the Royal Society of London
 * Died: December 29, 1891, Berlin, Germany

Theorems and Definitions

 * First Kronecker Limit Formula
 * Second Kronecker Limit Formula
 * Kronecker Delta
 * Kronecker Symbol
 * Kronecker Sum
 * Kronecker Product
 * Kronecker-Weber Theorem
 * Kronecker's Theorem in number theory
 * Kronecker’s Theorem in field theory
 * Kronecker's Lemma


 * Kronecker-Capelli Theorem (with ) as it is known in Russia; also known as:
 * Rouché-Fontené Theorem (after and ; priority actually goes to ) as it is known in France
 * Rouché-Frobenius Theorem (after and )
 * Rouché-Capelli Theorem (after and ) as it is known in Italy


 * Kronecker's Constant, also known as:
 * Meissel-Mertens Constant, for and
 * the Hadamard-de la Vallée-Poussin Constant, for and
 * the Prime Reciprocal Constant

Publications

 * 30 July 1845: De Unitatibus Complexis ("On complex units") (thesis)
 * 1850: On the Solution of the General Equation of the Fifth Degree
 * 1887: Über den Zahlbergriff

Notable Quotes

 * Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk. (translated loosely as: God made the integers; all else is the work of man.)
 * -- Quoted in:
 * They Say: What Say They? : Let Them Say
 * Introduction, also in section on $1$

Requoted

 *  said, "God is a geometer." changed this to, "God is an arithmetician." Then came  and fashioned the memorable expression, "God created the natural numbers, and all the rest is the work of man."
 * -- Quoted as an epigraph to the preface to
 * -- Quoted as an epigraph to the preface to


 * If, as Kronecker asserted, the integers are made by God and all the rest is the work of Man, then complex numbers are certainly one of Man's most intriguing mathematical artefacts.
 * -- Opening sentence of