Why did Leopold Kronecker oppose Georg Cantor’s theories about infinite numbers?

Leopold Kronecker’s opposition to Georg Cantor’s work on infinite sets and transfinite numbers was rooted in his strict philosophy of mathematics, which prioritized constructivism and finitism.12

Kronecker famously asserted that "God made the integers, and all the rest is the work of man," believing that only the positive whole numbers had true mathematical existence. His primary objections to Cantor’s theories included:13

• Metaphysical Nature: Kronecker viewed Cantor’s treatment of infinity as overly metaphysical, rejecting the idea that infinite sets could have an "actual" existence rather than merely a "potential" one.324
• Lack of Constructivity: Kronecker was a pioneer in doubting the validity of nonconstructive existence proofs—proofs that assert an object exists without providing a specific method to construct or identify it.12
• Methodological Rigor: Because Cantor’s set theory relied on abstract concepts and nonconstructive arguments, Kronecker felt it lacked the necessary rigor and foundational grounding in arithmetic.12

This fundamental disagreement led Kronecker to vehemently reject Cantor’s papers and block his professional advancement at the University of Berlin.3