Jean Dhombres

Jean Dhombres: Reading Old Mathematics as Mathematics

Well past the age at which most scholars are writing prefaces to other people's festschrifts, Jean Dhombres was preparing a comprehensive study of Joseph Fourier covering the years 1768 to 1830, reconstructing the mathematical libraries of Gilles Personne de Roberval and Nicolas-Claude Fabri de Peiresc, and had put a 2,200-page volume on mathematical knowledge from the Baroque through the Enlightenment into production. He is one of the very few people in the field with the equipment to do all three, and the reason is unusual: he arrived at the history of mathematics as a working mathematician, not as a historian who picked up some mathematics on the way.

Polytechnique, and the Other Career

Jean Guy Dhombres was born in Paris on 27 August 1942. He entered the École Polytechnique, graduating in 1962, and took his doctorate in mathematics at Pierre and Marie Curie University in 1970. From 1964 he taught across a scatter of French institutions — ENSICA among them — and became professor at the University of Nantes, holding the chair from 1980 to 1988. His itinerary was strikingly wide for a French academic of his generation: posts and long visits took him to Bangkok, Singapore, Waterloo, Ottawa, Wuhan, Berkeley in 1999, and Mexico in 2002–03 and again in 2008.

The Functional Equations Years

His mathematics proper was in functional analysis and, more specifically, functional equations — the study of equations whose unknown is not a number but a function, where the object is to determine what a function must be from the structural constraints it satisfies. It is a discipline of a particular temperament. Its practitioners spend their time asking what follows from a rule of composition alone, stripped of any assumption about smoothness or formula, which is precisely the habit of mind that later served him when reading a seventeenth-century proof that had no modern apparatus behind it.

Building an Institution at Nantes

From 1985 to 1995 Dhombres directed the Centre François Viète for the history and philosophy of science and technology at Nantes, and from 1988 to 1996 he directed the CNRS laboratory for the history of science. In 1988 he became director of studies in the history of the exact sciences at the École des hautes études en sciences sociales, remaining until retirement and continuing afterwards as an emeritus figure at the Centre Alexandre-Koyré. He had already served as president of the Société française d'histoire des sciences from 1983 to 1987 and chaired a UNESCO commission. The pattern is consistent: he did not merely publish in the history of science in France, he built and ran the places where it is done.

What He Actually Did to the Subject

Dhombres's historical writing ranges over Lazare Carnot, Laplace, Fourier, the fundamental theorem of algebra — studied at length with Carlos Alvarez — the history of mathematical proof, the treatment of the infinite, the theory of heat diffusion, the relationship between mathematics and art, and the ways mathematicians communicate with one another. Alongside this he produced critical editions of historical texts including Bernoulli and L'Hôpital.

The underlying commitment is a methodological one, and it explains why the seemingly unrelated topics belong to one project. Dhombres treats the cultural and social dimensions of scientific knowledge as inseparable from its technical content: a mathematician's library, the rhetorical form of a published proof, the audience a memoir was written for, and the theorem itself are all evidence about the same thing. His EHESS seminars pursued this into the present, examining philosophical positions on twenty-first-century mathematics, the history of mathematical modelling, and the competing narratives that scientific communities tell about their own discoveries.

Honours

He was made a Chevalier of the Ordre national du Mérite in 1978, doctor honoris causa of the University of Geneva in 1997, won a Prix de l'Académie des sciences in 1999, and took the Roberval prize in 2000.

Why Jean Is Called a Genius

No source in the accessible record applies the word to him, and the fair description of his gift is more interesting than the label. It is a genuinely rare double competence, and it is cognitive rather than merely biographical.

Most history of mathematics is written in one of two failing modes. Either the historian lacks the technical training to see what an old argument is actually doing, and so describes the sociology around a result while paraphrasing the result itself; or the mathematician translates the old proof into modern notation, at which point the historical object disappears — the very difficulty the original author was struggling against has been silently supplied by two centuries of subsequent machinery. Dhombres does neither. Trained as a research mathematician in functional equations, he can follow an eighteenth-century argument at full technical depth; trained and institutionally committed as a historian, he refuses to modernise it. That is the skill: holding a proof in its own conceptual vocabulary, seeing exactly where it is weak and why its author could not see that, without importing the answer.

The counter-case must be stated. No theorem carries his name, and his mathematical research, while entirely respectable, did not reshape functional analysis. The bulk of his major output is synthesis, critical edition, and institution-building — immensely valuable, but the work of a scholar rather than a discoverer. His prizes are book prizes and an honorary doctorate, the honours of a distinguished professional, not of a revolutionary. "Genius" is the wrong word; "the rarest kind of competence in his field" is the right one, and he would probably prefer it.

Legacy

Dhombres's influence sits in two places that outlast any single book. The first is institutional: the Centre François Viète, the CNRS history-of-science laboratory, the EHESS chair and the Société française d'histoire des sciences all passed through his hands, and French history of mathematics is largely staffed by people formed in the structures he directed. The second is methodological. The mathematicians' libraries project — asking what Roberval and Peiresc actually owned and read — is characteristic of the turn he pushed: treating mathematics as something done by particular people in particular rooms with particular books, without ever letting that dissolve the mathematics into mere context. He has spent sixty years insisting that the two halves of the phrase "history of mathematics" both have to be taken seriously by the same person. It remains an unusual position, and it is largely his.

Achievements

• Knight of the National Order of Merit
• Held posts at Nantes University, École Nationale des Ponts et Chaussées and University of Ottawa
• Fields: mathematics, functional analysis and history of mathematics