ESHS/HSS Annual Meeting

'The Limits of Newton's Law': editing the manuscripts of Poincaré's course on 'Lorentz invariants' (1906–1907)

• In Event: Mathematics in Manuscripts 1

English Abstract

The publication of Henri Poincaré's scientific manuscripts provides an ideal opportunity to observe the gradual construction of mathematical and physical concepts. A significant example of this is the course entitled “The Limits of Newton's Law,” given by Poincaré in 1906-1907 at the Faculty of Sciences in Paris, as part of his chair in celestial mechanics and mathematical astronomy. This lecture – previously known only through an anachronistic revision published in 1953 – was one of the first public presentations of what Poincaré would call the “Lorentz invariants,” which are at the heart of his mathematical formulation of special relativity.
The corpus we are publishing today comprises two essential manuscript layers: notes taken by an auditor, Henri Vergne, and Poincaré's preparatory autograph notes, which remain unpublished. A comparison of these notes reveals discontinuities, conceptual adjustments, and the gradual development of a line of reasoning that uniquely articulates celestial mechanics, the crisis of Newton's law, and the emergence of relativistic mechanics. Thus, over 29 lessons, we observe a development in which 19 of them remain rooted in Newtonian astronomy (deviation of Encke's comet, Mercury's perihelion, lunar acceleration), before the transition to Lorentz invariants (lessons 20 to 26) reconfigures the framework of the analysis.
This exemplary case raises questions for both the historian of mathematics – whether it be reconstructing the context of discovery, differentiating between heuristic speculation and formalized architecture – and the scientific editor, who faces a dual challenge: to trace the layers of a text in flux and to produce a critical edition that reveals the processual dimension of mathematical development. In these preparatory notes, Poincaré highlights the fragile boundary between public justification and still uncertain exploration.

Author

• Philippe Katz, Nantes Université