[Paper Review] The emergence of French statistics. How mathematics entered the world of statistics in France during the 1920s

Rémi Catellier, Laurent Mazliak|arXiv (Cornell University)|Jun 23, 2009

Philosophy and History of Science3 citations

TL;DR

This paper traces the emergence of mathematical statistics in France during the 1920s, focusing on Émile Borel’s foundational role in establishing the Statistical Institute of Paris University (ISUP, 1922) and the Institut Henri Poincaré (IHP, 1928), which institutionalized probability theory and statistical methodology. It demonstrates how Borel, Maurice Fréchet, and Georges Darmois forged a theoretical framework linking probability and statistics, culminating in the launch of the *Annales de l’Institut Henri Poincaré* in 1931, marking the formal institutionalization of mathematical statistics in France and challenging Stigler’s 1933 origin thesis by showing earlier, deliberate development in France.

ABSTRACT

This paper concerns the emergence of modern mathematical statistics in France after the First World War. Emile Borel's achievements are presented, and especially his creation of two institutions where mathematical statistics was developed: the {\it Statistical Institute of Paris University}, (ISUP) in 1922 and above all the {\it Henri Poincaré Institute} (IHP) in 1928. At the IHP, a new journal {\it Annales de l'Institut Henri Poincaré} was created in 1931. We discuss the first papers in that journal dealing with mathematical statistics.

Motivation & Objective

• To analyze the institutional and intellectual mechanisms that enabled mathematical statistics to emerge in France during the 1920s.
• To examine Émile Borel’s role in founding key institutions—ISUP (1922) and IHP (1928)—dedicated to mathematical statistics.
• To investigate how probability theory, particularly Borel’s measure-theoretic approach, was integrated into statistical practice in France.
• To challenge Stephen Stigler’s hypothesis that mathematical statistics began in 1933 by demonstrating its earlier, deliberate development in France.
• To highlight the filiative relationship between probability and mathematical statistics as envisioned by Borel, Fréchet, and Darmois.

Proposed method

• Historical analysis of archival sources, including institutional records and correspondence, collected during a research stay at University Paris 6 in 2008.
• Examination of the founding of the Statistical Institute of Paris University (ISUP) in 1922 as a site for early mathematical statistics education.
• Study of the creation of the Institut Henri Poincaré (IHP) in 1928 as a center for advanced research in mathematical statistics.
• Analysis of the first issues of the *Annales de l’Institut Henri Poincaré* (1931), particularly papers on mathematical statistics, to trace the discipline’s formalization.
• Comparative analysis of French developments with international trends, especially Anglo-Saxon and Soviet statistical theory.
• Use of biographical and institutional data to reconstruct the intellectual network centered on Borel, Fréchet, and Darmois within the Paris Statistical Society (SSP).

Experimental results

Research questions

• RQ1 How did Émile Borel institutionalize mathematical statistics in France during the 1920s?
• RQ2 What role did the creation of ISUP (1922) and IHP (1928) play in advancing mathematical statistics in France?
• RQ3 How did Borel, Fréchet, and Darmois conceptualize the relationship between probability theory and statistics?
• RQ4 In what ways did the *Annales de l’Institut Henri Poincaré* (1931) mark the formal emergence of mathematical statistics in France?
• RQ5 How does the French development of mathematical statistics between 1920 and 1950 challenge Stigler’s 1933 origin thesis?

Key findings

• Émile Borel founded the Statistical Institute of Paris University (ISUP) in 1922, establishing one of the first formal institutions for mathematical statistics in France.
• The Institut Henri Poincaré (IHP), founded in 1928, became the central hub for mathematical statistics in France, institutionalizing the field through research and publication.
• The launch of the *Annales de l’Institut Henri Poincaré* in 1931 provided a dedicated platform for publishing foundational work in mathematical statistics, signaling the discipline’s formal recognition.
• Borel, Fréchet, and Darmois explicitly framed probability theory as the 'father' of mathematical statistics, establishing a filiative rather than complementary relationship between the two fields.
• The paper demonstrates that mathematical statistics in France was institutionally and intellectually established by the 1920s, predating Stigler’s 1933 milestone and challenging its universality.
• The three mathematicians were the only ones elected President of the Paris Statistical Society (SSP) between 1920 and 1950, underscoring their central role in shaping the field.