Some remarks on history and pre-history of Feynman path integral
Pith reviewed 2026-05-25 19:10 UTC · model grok-4.3
The pith
Wiener introduced the first path integral in physics to describe Brownian motion, with Buhl approaching the idea in the 1930s before Feynman's independent discovery.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
Wiener used the first path integral of the history of physics to describe the Brownian motion, inspired by the work of some French mathematicians, particularly Gateaux and Levy. Although Richard Feynman has independently found this notion, in the course of the 1930s another French mathematician, Adolphe Buhl, had himself been close to forge such a notion. The difficulties of this notion had to wait many years before being resolved, and it was only recently that the path integral could be rigorously established from a mathematical point of view.
What carries the argument
The path integral as a summation over all possible trajectories, first appearing in Wiener's functional integrals for Brownian motion.
If this is right
- Wiener's formulation predates and supplies an early concrete instance of the path integral technique.
- Buhl's 1930s work represents a parallel but overlooked approach tied to geometrizing quantum mechanics.
- Feynman's contribution remains an independent discovery despite the pre-history.
- Mathematical rigor for the path integral is a separate later achievement unrelated to the initial conceptual steps.
- Credit for the idea's origin must be shared across Wiener, his influences, and Buhl without diminishing Feynman's role.
Where Pith is reading between the lines
- Historians of physics could search for additional overlooked precursors in early probability theory and functional analysis.
- Textbook accounts of the path integral might shift emphasis toward incremental development across probability and quantum mechanics.
- Buhl's papers, noted by Bachelard, could be examined for further details on his specific formulations.
- Current rigorous constructions of path integrals might be compared directly to Wiener's original measures to trace unresolved technical issues.
Load-bearing premise
The paper's readings of Wiener, Buhl, and related historical sources correctly identify conceptual proximity to the path integral without anachronistic projection of later ideas onto earlier work.
What would settle it
A re-examination of the original texts demonstrating that Wiener's integrals for Brownian motion lack the essential structure of later path integrals or that Buhl's writings contain no anticipation of summing over paths.
read the original abstract
One usually refers the concept of Feynman path integral to the work of Norbert Wiener on Brownian motion in the early 1920s. This view is not false and we show in this article that Wiener used the first path integral of the history of physics to describe the Brownian motion. That said, Wiener, as he pointed out, was inspired by the work of some French mathematicians, particularly Gateaux and Levy. Moreover, although Richard Feynman has independently found this notion, we show that in the course of the 1930s, while searching a kind of geometrization of quantum mechanics, another French mathematician, Adolphe Buhl, noticed by the philosopher Gaston Bachelard, had himself been close to forge such a notion. This reminder does not detract from the remarkable discovery of Feynman, which must undeniably be attributed to him. We also show, however, that the difficulties of this notion had to wait many years before being resolved, and it was only recently that the path integral could be rigorously established from a mathematical point of view.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper claims that Norbert Wiener introduced the first path integral in physics while describing Brownian motion in the early 1920s, drawing inspiration from the French mathematicians Gateaux and Levy; that Adolphe Buhl came close to the same notion in the 1930s while pursuing a geometrization of quantum mechanics; that Feynman discovered the concept independently; and that full mathematical rigor for path integrals was achieved only recently.
Significance. If the historical readings are accurate, the paper usefully situates the path integral within a longer French mathematical tradition without diminishing Feynman's independent contribution, and it correctly notes the long delay before rigorous foundations were established.
major comments (2)
- [Abstract / Buhl discussion] Abstract and the section on Buhl: the claim that Buhl 'had himself been close to forge such a notion' while geometrizing QM is load-bearing for the pre-history narrative, yet the text must supply direct quotations or explicit comparisons showing that Buhl employed summation over trajectories or measures on path space, rather than standard variational or geometric language of the period; without this, the attribution risks anachronism.
- [Wiener discussion] Section on Wiener: while the paper states that Wiener 'used the first path integral,' it should clarify whether this rests on Wiener's 1920s measure-theoretic construction of Brownian motion or on a later reinterpretation; a concrete reference to the specific functional Wiener employed would strengthen the 'first' attribution.
minor comments (2)
- [Abstract] Abstract: the phrasing 'close to forge such a notion' is grammatically awkward and should be revised to 'close to forging' or equivalent.
- [Introduction] The paper should include a brief statement of the precise modern definition of the Feynman path integral against which earlier works are being compared, to make the historical proximity claims falsifiable.
Simulated Author's Rebuttal
We thank the referee for the careful reading and constructive suggestions. We address the two major comments point by point below.
read point-by-point responses
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Referee: [Abstract / Buhl discussion] Abstract and the section on Buhl: the claim that Buhl 'had himself been close to forge such a notion' while geometrizing QM is load-bearing for the pre-history narrative, yet the text must supply direct quotations or explicit comparisons showing that Buhl employed summation over trajectories or measures on path space, rather than standard variational or geometric language of the period; without this, the attribution risks anachronism.
Authors: We agree that stronger textual evidence is required to support the claim about Buhl and to avoid any risk of anachronism. The current manuscript relies on Bachelard’s commentary and a general description of Buhl’s geometrization program; it does not yet contain the direct quotations or side-by-side comparisons requested. In the revised version we will add verbatim passages from Buhl’s 1930s papers that illustrate his consideration of multiple trajectories, together with explicit comparisons to the notion of summation over paths or measures on path space. revision: yes
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Referee: [Wiener discussion] Section on Wiener: while the paper states that Wiener 'used the first path integral,' it should clarify whether this rests on Wiener's 1920s measure-theoretic construction of Brownian motion or on a later reinterpretation; a concrete reference to the specific functional Wiener employed would strengthen the 'first' attribution.
Authors: The attribution rests on Wiener’s original 1920s measure-theoretic work rather than any later reinterpretation. We will revise the relevant section to cite the specific paper (Wiener’s 1923 construction of the measure on the space of continuous functions) and to identify the functional explicitly as the Wiener integral that computes probabilities by integration over path space. This clarification will be added without altering the historical claim. revision: yes
Circularity Check
No circularity: linear historical narrative with no derivations or self-referential reductions
full rationale
The paper is a purely historical discussion of the origins of the path integral concept, citing Wiener's work on Brownian motion, influences from Gateaux and Levy, Feynman's independent discovery, and Buhl's 1930s efforts at geometrizing quantum mechanics. It contains no equations, no fitted parameters, no predictions derived from inputs, and no mathematical derivations that could reduce by construction to self-definitions or self-citations. All claims rest on external historical sources and linear narrative without load-bearing loops or uniqueness theorems imported from the author's prior work.
discussion (0)
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