The origins and legacy of Kolmogorov's Grundbegriffe

TL;DR

This paper reviews the historical and philosophical significance of Kolmogorov's Grundbegriffe, highlighting its role in establishing modern probability theory and its philosophical implications, on the 70th anniversary of its publication.

Contribution

It analyzes the sources and influences that shaped Kolmogorov's foundational work, emphasizing its synthesis of prior ideas and its lasting legacy.

Findings

Identifies key influences on Kolmogorov's work.

Highlights the dual role of the Grundbegriffe in formalism and philosophy.

Reflects on the historical impact of the publication.

Abstract

April 25, 2003, marked the 100th anniversary of the birth of Andrei Nikolaevich Kolmogorov, the twentieth century's foremost contributor to the mathematical and philosophical foundations of probability. The year 2003 was also the 70th anniversary of the publication of Kolmogorov's Grundbegriffe der Wahrscheinlichkeitsrechnung. Kolmogorov's Grundbegriffe put probability's modern mathematical formalism in place. It also provided a philosophy of probability - an explanation of how the formalism can be connected to the world of experience. In this article, we examine the sources of these two aspects of the Grundbegriffe - the work of the earlier scholars whose ideas Kolmogorov synthesized.