John Wallis's 1685 history of algebra used Mabillon-style documentary evidence to rule for Harriot over Descartes in a priority dispute

diplomaticsmabillonhistoriographyhistory-of-mathematicspriority-disputewallisharriotdescartes

G.I. Sinkevich's 2017 historiography-of-mathematics preprint states that "Voss' and Mabillon's works influenced subsequent researchers and J. Wallis, in the first place" — naming Jean Mabillon's 1681 diplomatics as a direct influence on John Wallis's 1685 Treatise of Algebra both Historical and Practical, in which, per the source, the history of algebra was "for the first time presented as a history of ideas," and which took a side in a live scholarly dispute: whether Descartes derived his method from Thomas Harriot's posthumous 1631 Artis Analyticae Praxis. Wallis's text, reproduced in the source, marshals textual comparison — chapters 53 and 55 accuse Descartes of borrowings, setting Harriot's 1631 book against Descartes' 1637 Geometry — and a secondhand anecdote ("a short Story which Dr. John Pell lately told me he had from Sir Charles Cavendish"): Cavendish showing Harriot's book to Roberval in Paris, who exclaims "Il l'aveu! Il l'aveu!" ("He had seen it! He had seen it!") — as documentary proof against the received Cartesian attribution. The source's own narration concludes: "Wallis was right about the seniority of Herriot. Descartes had Herriot's treatise when he was writing his Geometry."

This is the same methodological act as documentary source criticism — authenticating an origin-claim against dated documents rather than the received account — applied by name-checked inheritance from Mabillon, decades before Ranke, and via a route the vault's open question about a Mabillon-to-priority-adjudication descent did not anticipate: straight into 17th-century historiography of mathematics, bypassing Quellenkritik entirely.