Definition

Proper noun: A German mathematician who lived from 1823 to 1891. He made significant contributions to number theory and algebra. He is famously associated with the statement, "God made the integers, all else is the work of man," reflecting his philosophical views on mathematics.

Usage

• Leopold Kronecker was a contemporary of other great 19th-century mathematicians like Karl Weierstrass and Georg Cantor.
• The Kronecker delta, a function used in mathematics and physics, is named after Leopold Kronecker.

Advanced Usage

• Kronecker's finitism: This refers to his mathematical philosophy, which was skeptical of non-constructive methods and concepts (like certain aspects of set theory developed by Cantor) that could not be built in a finite number of steps from the integers.
• In historical context, the Kronecker-Weber theorem in algebraic number theory, which he helped prove, connects abelian extensions of the rational numbers with cyclotomic fields.

Variants and Related Words

• Kroneckerian (adj): Pertaining to the work or views of Leopold Kronecker.
  • His approach to the problem was decidedly Kroneckerian.
• Kronecker delta (n): A function of two variables, usually integers, which is 1 if they are equal and 0 otherwise. It is a fundamental tool in linear algebra and tensor analysis.
• Kronecker product (n): An operation on two matrices of arbitrary size resulting in a block matrix. It is also known as the tensor product of matrices.

Synonyms

• German mathematician (context-specific descriptor)

Related Phrases

• "God made the integers...": This famous quotation is almost always attributed to Leopold Kronecker when discussing the foundations of mathematics.

Noun

1. German mathematician (1823-1891)