...more

I used to arrive early (I always arrive early), to sit almost at the top of the ‘amphi,’ nearly in line with the door, in the ‘Mountain’ section of this assembly (to use the political terminology of 1793), or perhaps of this fake Convention whose supposedly studious students, who sat further down in the front rows, made up the Marsh. My preference was a place at the end of a row, on a narrow uncomfortable bench, where I would have just one neighbor to my right, and where the neighbor to my left was not the wall, as it would have been further down, but a glass panel.
The lecture hall filled up, the noise of conversations gradually gave way to that of paper and the scratching of chalk on the board while, through the steam formed by breath, behind the filthy glass, I could see the night, almost attentive, nearby, slowly evaporating in its dampness to give way to a pale, dull daylight.
Between the beginning and end of the lecture, the nocturnal darkness abandoned the city and was replaced by a gray, wintry penumbra. But at the instant when I sat down, taking my uncomfortable narrow place inside that collegiate volume made up of trapezoidal sections (inverted rectangular trapezoids, their bases up towards the sky), which was still almost empty, and while the pane was still clear of misty breathing, I could see myself, looking outside, almost outside of myself, just next to the night, contiguous with its ever-impenetrable, blue, somber mass.
Outside, the sunrise was slow and feeble, penetrating that studious hum barely, insufficiently, surmounting with difficulty that pallid, cold, electric light. This was a difficult period, during the 1954–55 academic year; the place: Institut Henri Poincaré – in the Hermite lecture hall; certificate: Differential and Integral Calculus, taught by Monsieur G(ustave) Choquet.
I turned to see my image take form somewhere in the air outside, thus obeying the most basic and unvarying laws of geometric optics (General Physics Certificate), then become covered with steam, before misting, fading and disappearing. It was nighttime in winter. It was cold: cold outside, and cold in the ill-heated amphi. I placed my hand on the bare glass, I pressed my palm on it to wipe away the steam and see my face better, as well as those of my studious neighbors, but above all to wonder numbly at the enigmatic quality of that paradoxical light, bathing those suspended faces in the outside air, without any support, a yellow light both electric & virtual, illuminating this pocket of icy space, excavated from unbending night.
So I listened absent-mindedly, lazily taking notes in my exercise book, jotting down almost illegible scraps of some definition or other that did not seem too off-putting, or some obvious corollary to a theorem which remained thoroughly mysterious in itself. If, that is, there were some decipherable traces of the explanations still left on the board.
But "Choquet" – we said “Choquet” as you might say “Schwartz” or “Bouligand,” with audibly implicit inverted commas, which are less a mark of off-handed familiarity than a form of citation, an apparently individualized but in fact impersonal naming of the “professor function,” which would become colored only subsequently, as the “year” advanced and the month of exams (June) approached, with a collective halo of reaction, be it of rejection or acceptance, or else with concerns and anecdotes, before, as becomes an oral tradition being classified, refined, complicated, deformed then handed down to the following year’s students, in this way gradually building up professional legends attached to names and becoming distinctly singular “portraits” of their bearers – so, as I was saying, “Choquet” rarely wrote anything on the board. He talked through his mathematics, without notes, sometimes making geometric gestures in the air with his hands.
Mathematicians, in the typical, spontaneous representations of people when they first meet you and learn that you are someone who does “math” (coming just after the ritualistic statement: “I was useless at math at school”), are individuals who express themselves in a language which is incomprehensible to almost everyone else, and thus prestigious, defining truths that are at once essential and obscure. The reaction of the listeners in the Calculus lecture hall in 1954 to Choquet’s opening words, as he spoke for the first time in this role (in this function) in this place (he had just taken over from “Valiron,” one of the last representatives of the old “French” school of analysis), was extraordinarily similar to the general reaction of non-mathematicians: alarm. Whatever their mathematical past had been, they had not been expecting this.