Leopold Kronecker
modernMathematical Constructivism / Finitism1823 – 1891
Leopold Kronecker (1823-1891) was a German mathematician who worked on number theory, algebra, and the foundations of mathematics. He is known for his constructivist philosophy of mathematics, famously asserting that 'God made the integers; all else is the work of man,' and for his opposition to Cantor's set theory and non-constructive methods.
Notable Achievements
1
Pioneered mathematical constructivism, insisting all mathematics be grounded in finite operations on integers
2
Proved the Kronecker-Weber theorem on abelian extensions of the rationals
3
Developed foundational work in algebraic number theory and the theory of elliptic functions
4
Introduced the Kronecker delta and Kronecker product in linear algebra
5
Famously opposed Cantor's transfinite set theory, shaping early 20th-century foundational debates