The Classroom and the World

The first page is headed by an institution, an academic year, a subject, and a name. “Université des Sciences et Techniques du Languedoc,” it says; “Mathématiques”; “Année Universitaire 1978–79.” At the center stands the title En guise de programme for A. Grothendieck’s C4 course Introduction à la recherche. The typewritten sheet is not an undated meditation mistakenly filed among mathematics. It is a university course document.11Grothendieck, “En guise de programme pour le cours de C4 « Introduction à la recherche » 1978/79”.

What follows refuses the normal brevity of a syllabus. It does not list weeks, textbooks, or percentages for assessment. It begins with curiosity. When intense curiosity animates research, Grothendieck writes, the researcher advances as if borne on impatient wings through a moving fog. The image opens toward questions about creation, childhood, work, and the deadening effects of education. On the second leaf he asks what teacher and students will do in the new academic year so as not to reproduce the fixed scenario of the schoolmaster speaking before pupils.22Grothendieck, “En guise de programme pour le cours de C4 « Introduction à la recherche » 1978/79”.

The language is expansive, but the material object holds it to earth. This was a course at a named university in a specified year. Students enrolled. The professor had taught for several years already. The page records an attempt to make a philosophy of inquiry answerable to a classroom.

Reading the two leaves

The first leaf moves through four stages. It begins with Grothendieck’s imagery for inquiry: fog, wings, a new enigma, and further mysteries generated by the first discovery. It then names ardent curiosity as creative and compares it to a seed from which immense growth can come. Next it considers the meaning of life or work in the absence of creation. Finally it turns against Grothendieck’s own teaching over the previous three years.

That turn is crucial. He does not first accuse students. He says he had taught like a blind man painting. He had spoken about things he was discovering to people brought there by an obligation foreign to them. The objects seemed to him tangible and simple enough for a curious child, but he addressed listeners concerned with notes and examinations. The mathematical content could be alive in the speaker and arrive as inert, heterogeneous objects in the students’ minds.33Grothendieck, “En guise de programme pour le cours de C4 « Introduction à la recherche » 1978/79”.

The self-critique should not be softened into a generic promise to improve. He judged that he had mistaken the life of a subject in himself for its communicability to others. He had spoken to an imagined child, including the child in himself, while actual students sat within an examination system. The fault, in this account, lay partly in the dialogue he imagined rather than the relation he had.

The next paragraph criticizes indifference. Here the tone shifts. In his account, effort without joy produced anxiety rather than understanding, and his prior teaching perpetuated old impotence in voiceless pupils. He reduced the outcome to end-of-year marks and one or two students he considered unreached. The severity belongs to his rhetoric, not to an independently verified assessment of harm.

Leaf two turns from confession to a new contract for the coming year. The academic year should not reproduce the immutable scenario of master and schoolchildren. He immediately asserts another severe proposition: all teaching is vain unless addressed to beings whose curiosity is already awake. Restoring curiosity becomes the first problem.

The proposed answer is mutual provocation. The principal aim will be to call the sleeping child into play in both pupil and master. Grothendieck then corrects his own hierarchy: perhaps it is not the schoolmaster’s special role to provoke; perhaps each person must provoke all the others, beginning with himself. This is the document’s most self-displacing move.44Grothendieck, “En guise de programme pour le cours de C4 « Introduction à la recherche » 1978/79”.

The final lines refuse to guarantee success. Teacher and pupils might become children absorbed in a fascinating game, or remain jumping puppets. The alternative is deliberately stark. A modern syllabus might specify methods for discussion, feedback, and student choice. Grothendieck supplied an existential test.

Close reading reveals why the document cannot serve as transparent evidence that his teaching was liberatory. It shows that he recognized a failure, identified passivity as the central danger, and proposed mutual inquiry as a remedy. The surviving program speaks only in Grothendieck’s voice; no comparable first-person student records establish whether students experienced it that way.

It also reveals continuity with his mathematics. A false image must be exposed; the right question precedes technique; a structure should emerge from sustained attention rather than external rule. A classroom, however, contains several centers of attention. Eloquence alone could not scale a method that had worked for one mathematician.

Three course documents

The 1978–79 program belongs to a sequence. The University archive preserves a 1976 examination subject for a maîtrise course, Théorie des surfaces topologiques. It also preserves or records a DEA course in 1977–78 titled Géométrie arithmétique des polygones réguliers. The 1978–79 introduction to research then addressed both the mathematics to be taught and the conditions under which a student might become an active discoverer.55Maronne and Toën, Le temps des réflexions, 13–15.

The titles mark an enlarging arc. Topological surfaces supplied basic objects and deformation problems. Regular polygons led from visual symmetry toward arithmetic and algebraic realization. Introduction to research made the method itself explicit. One should not infer that each course followed mechanically from the previous one or that the same students attended all three. The sequence establishes recurring themes and levels, not a single cohort.

Nor should the word “course” suggest only lectures. An activity report excerpted in the 2024 archive exhibition describes sessions of common reflection on subjects selected by students, with each participant pursuing individual work during the year. No themes were to be excluded in advance. A student might possess or develop an intuition that caught the professor unprepared, disturbing the usual active-passive distribution of roles. 66Maronne and Toën, Le temps des réflexions.77Maronne and Toën, Le temps des réflexions, 14.

This is the strongest evidence for the pedagogical contract. It states what the course was meant to be. The exhibition immediately adds a caution: by the participants’ own later admission, the vision was not always realized. The document is a program in both senses—a plan and a declaration—not a neutral report that every meeting achieved equality.88Maronne and Toën, Le temps des réflexions, 14–15.

The 1976 examination supplies the counterweight. However open the year’s inquiry, university work ended in assessable form. A paper had to determine whether students could state definitions, reason through surfaces, and solve prescribed questions. Freedom and examination occupied the same course. Grothendieck’s program did not abolish the institution; it tried to alter relations within it.

Curiosity as a condition, not a compliment

In En guise de programme, curiosity is not one desirable trait among others. It is the condition of meaningful teaching. A discourse addressed to people whose curiosity is not awake is, in his formulation, vain. The teacher’s first question is therefore not how to transmit a body of material but how curiosity might live again.99Grothendieck, “En guise de programme pour le cours de C4 « Introduction à la recherche » 1978/79”.

This claim has an attractive democratic side. It places creative capacity in every student rather than reserving it for a certified elite. The course sheet repeatedly invokes the child sleeping in the pupil and in the master. The teacher does not own creation; the teacher must also be provoked.

It has a severe side. If curiosity is absent, the document leaves little value to dutiful learning, incremental practice, or knowledge pursued for reasons not yet felt as passion. An anxious, employed, underprepared, or cautious student can appear disengaged under this scale. The rhetoric risks converting one preferred mode of learning into a judgment on the whole person.

The archive makes that risk concrete. Grothendieck later described many students as concerned mainly with the diploma and unable to take up questions that seemed to him close at hand. He also praised the active participation he found in some first-year option courses and believed several such students had the capacity to become excellent mathematicians. These are observations by a participant with exceptional authority, not measurements made from the students’ accounts.1010Grothendieck, Récoltes et Semailles, ed. Carmona (1985), 221–23, 282–84.

A source-led biography must therefore report two propositions together. Grothendieck designed teaching around the assumption of broadly shared creative capacity. He often judged actual students against that ideal in language that could be unforgiving. Preserving only the first produces an idealized pedagogue; preserving only the second produces a caricature of contempt.

Can curiosity be taught?

The course program produces a paradox. If meaningful teaching requires awakened curiosity, but the first task is to awaken curiosity, teaching seems to require its own result as a precondition. Grothendieck did not solve the paradox theoretically. He tried to change the situation in which students met mathematics.

Choice of subject was one device. A question proposed by a student has a different relation to obligation than a chapter assigned in sequence. It may still be adopted to please the teacher, and a novice may not know what questions are tractable. Choice is therefore necessary to the program but not sufficient.

Common sessions were another device. Individual work did not mean isolation. A participant could bring a problem to the group, expose an intuition, and encounter objections. The group supplied reality-testing without requiring the professor to possess the answer. In the best case, a question became common while remaining personally owned.

Elementary objects were a third. A graph or polyhedron did not require permission from an advanced vocabulary before it could be inspected. Students could form conjectures from examples. When a conjecture failed, the need for a sharper invariant arose within the work. This “just-in-time” acquisition of technique differed from a curriculum that front-loaded years of language before any personally meaningful question.

The device had limits. Elementary objects can produce hard problems faster than they produce tools. A beginner who discovers a question about maps on surfaces may need topology, group theory, complex analysis, and algebraic geometry to move further. If the teacher reveals the entire horizon at once, liberation becomes overload.

Another limit is time. A semester or academic year ends. Research may spend months selecting the right definition. Degree programs cannot indefinitely certify intention without result. Grothendieck’s later demand for finished written work acknowledged that research initiation needed closure.1111Grothendieck, “Esquisse d’un Programme,” sec. 9.

The final limit is plurality. Not all mathematicians experience curiosity as exhilaration. Some work slowly, through routine, collaboration, or careful mastery of an inherited method. A pedagogy built around sudden fascination can fail to recognize quieter forms of engagement. Nothing in the sources gives Grothendieck authority to define those forms away.

These limitations do not nullify the experiment. They explain why its ideal and practice diverged. The program attacked a real problem: education can teach students to wait for the sanctioned move. Its proposed cure depended heavily on the teacher’s ability to listen, pace expansion, and accept modes of work unlike his own. The archive suggests that those were precisely the difficult tasks.

The active and the passive

The activity report’s most consequential sentence concerns roles. When a student’s intuition puts the teacher at a loss, the institution’s prescribed active-passive distribution can be overturned. The point is epistemic rather than informal: authority does not determine where an open problem is going.

In a standard exercise, the teacher knows both method and answer. The student’s activity is real but bounded. In research, neither may know. If the teacher silently converts every unknown problem into a guided route toward a result already possessed, the student practices problem solving but not the uncertainty of discovery.

Grothendieck wanted students to choose questions capable of surprising him. This made the teacher’s ignorance productive. It also demanded unusual confidence from students facing an established mathematician. They had to believe that an undeveloped intuition could deserve a year’s work even when Grothendieck could immediately reframe it in a larger language.

The asymmetry did not disappear by being denounced. The professor evaluated work, directed theses, and possessed a mathematical vocabulary vastly larger than that of most participants. The archive exhibition describes small groups in his office before common lunches and notes that he was most often the speaker and had difficulty occupying the position of listener.1212Maronne and Toën, Le temps des réflexions, 14.

This does not prove hypocrisy. An ideal can reveal the precise failure of a practice. The course documents are valuable because they preserve both. Grothendieck understood that research teaching required the teacher to be displaced. He did not reliably make himself easy to displace.

The problem was not unique to him. Any research adviser invites independence while controlling entry to a profession. The inequality becomes more intense when the adviser’s name carries a field’s authority. A student’s disagreement with Grothendieck could be mathematically healthy and institutionally daunting. An account of shared research should keep the stakes visible.

The child and the student

Grothendieck’s image of the child had a documented mathematical history. In Montpellier as an undergraduate, he had pursued a basic question about volume outside the course. In the 1970s, simple forms—polygons, polyhedra, graphs on surfaces—again became points of departure. The child signified attention unblocked by the convention that a problem was trivial, old, or improperly posed.1313Grothendieck, Récoltes et Semailles, ed. Carmona (1985), “Promenade, ” pp. P3–P5; Grothendieck, “Esquisse d’un Programme,” sec. 2.

An actual student is not an emblem. Students arrive with prior schooling, material pressures, different ambitions, and rights not to become characters in a teacher’s philosophy. The course sheet sometimes moves quickly from the “child” to judgments about pupils fixed at their desks. A modern biography should retain the metaphor as Grothendieck’s, not use it to classify individuals.

The same boundary applies to psychological language in his later report. He referred to blocks and obstacles in ways that belonged to his own theory of creativity. This book does not diagnose students from those phrases. It translates the pedagogical fact into ordinary terms: many participants found the proposed language or open-ended work difficult, and the professor found that difficulty frustrating.1414Grothendieck, “Esquisse d’un Programme,” sec. 8, pp. 41–42.

What can be said positively is that some first-year students engaged. Some research students completed acceptable or better written work. Ladegaillerie finished a state doctorate; Contou-Carrère developed work on relative Jacobians; Jean Malgoire remained a mathematical interlocutor and later custodian of manuscripts. The classroom did not reproduce the IHÉS school, but it did not contain only silence.1515Grothendieck, “Esquisse d’un Programme,” sec. 9; Maronne and Toën, Le temps des réflexions, 14–15, 31–33; Université de Montpellier, “À la recherche d’Alexandre Grothendieck”.

Regularity

A regular polygon in the Euclidean plane has equal sides and equal angles. A regular polyhedron has congruent regular polygonal faces and the same arrangement at every vertex. The five convex Platonic solids are the tetrahedron, cube, octahedron, dodecahedron, and icosahedron. Their familiar pictures made them suitable for an initiation course.

“Regular” can also be separated from metric appearance. A map on a surface is combinatorially regular when its automorphism group acts transitively on suitable flags—a flag being an incident vertex-edge-face triple. The object can then be encoded by generators and relations or by permutations that move among flags. Symmetry becomes group action rather than visual equality of lengths.1616Grothendieck, “Esquisse d’un Programme,” secs. 4, 8; Maronne and Toën, Le temps des réflexions, 14–15, 25–31.

For a convex polyhedron with $V$ vertices, $E$ edges, and $F$ faces, Euler’s formula gives

$$V-E+F=2.$$

If every face is a $p$-gon and $q$ faces meet at every vertex, then $pF=2E$ and $qV=2E$. Substitution gives

$$\frac{1}{p}+\frac{1}{q}>\frac{1}{2},$$

which leaves only the five Platonic possibilities in the convex spherical case. This calculation is elementary enough for a classroom and structural enough to invite generalization.

Changing the surface replaces the right side by its Euler characteristic. Nonconvex or algebraic realizations change the classification. Replacing the real or complex numbers by another field or a general ring makes metric language insufficient. Grothendieck’s later problem was to give “a regular polyhedron over a finite field” a scheme-theoretic or arithmetic meaning.1717Grothendieck, “Esquisse d’un Programme,” sec. 4, pp. 20–22.

The analogy has a limit. A polyhedron over a ring is not a solid one can rotate in ordinary three-dimensional space. The phrase may refer to algebraic configurations, reflection data, moduli, or realizations whose coordinates lie in the ring. Grothendieck explored several formulations; the surviving work did not become one canonical published theory during these years. The narrative should present the problem, not manufacture a settled object.

The icosahedron received special attention. Its rotations form the alternating group $A_5$, a group that also appears in algebra and Galois theory. Its combinatorics therefore offered a bridge from a tangible solid to finite groups and arithmetic questions. The bridge was mathematically real, but it did not mean that every classroom treatment of the icosahedron already contained the later Galois–Teichmüller program.

Regular polygons and polyhedra exemplified Grothendieck’s pedagogical wager. A student could count edges and symmetries. The same count could open into group actions, moduli, and arithmetic. Technical language was not discarded; it was postponed until the object demanded it.

Regularity without a ruler

The transition from visible symmetry to abstract symmetry deserves a slower look. A child recognizes a square by equal-looking sides and right-looking angles. A geometer can define it by distances and angles. A combinatorialist can forget the metric and retain a four-cycle with its incidences. A group theorist can study the dihedral group $D_4$ generated by a quarter-turn and a reflection.

Each description forgets something and makes something else portable. Metric geometry distinguishes a square from a non-square rectangle. Combinatorics sees the same incidence pattern in both. Group theory isolates transformations and can reproduce the pattern in settings without Euclidean distance. Arithmetic asks over which fields or rings coordinates and transformations can be realized.

The icosahedron makes the progression richer. It has twenty triangular faces, thirty edges, and twelve vertices, satisfying $12-30+20=2$. Five faces meet at each vertex. Its orientation-preserving symmetry group has sixty elements and is isomorphic to $A_5$, the alternating group on five letters. That group is simple and appears in the theory of polynomial equations.

Thus one solid connects several languages: triangular tessellation of the sphere, a finite group presentation, rotations in three dimensions, and Galois-theoretic behavior. The connection is not mystical. It consists of explicit actions and representations. A course can begin with counting faces and reach the structure of a nonabelian simple group.

Moving “over a field” requires another step. Coordinates for vertices and matrices for symmetries satisfy polynomial equations. If those equations make sense over another field or ring, one can ask for corresponding algebraic configurations. Degeneration may occur in special characteristics; division by two or five may fail; distinct vertices may collide. The arithmetic version is not the same solid viewed through tinted glass. It is a family of algebraic solutions whose geometry changes with the base.1818Grothendieck, “Esquisse d’un Programme,” sec. 4.

This is where Grothendieck’s earlier relative viewpoint reenters. Instead of defining an icosahedron separately over each field, seek a universal or moduli construction over a base such as the integers, then study its fibers. Automorphism group schemes can replace one fixed symmetry group. The exact object remained exploratory in his notes, but the form of the question was continuous with schemes.

The pedagogical advantage and danger coincide. A regular polyhedron genuinely permits all these views. It also tempts the teacher to traverse them faster than students can follow. The archive course title “Arithmetic Geometry of Regular Polygons” proves that arithmetic and elementary form were joined in 1977–78. It does not prove which definitions, examples, or theorems occupied each week.1919Maronne and Toën, Le temps des réflexions, 15.

The mathematical card therefore records the ladder but not a reconstructed syllabus:

1. visual polygon or polyhedron;
2. cellular map on a surface;
3. permutation or group encoding;
4. moduli of realizations;
5. arithmetic variation over fields or rings.

Every arrow requires hypotheses. Treating the ladder as an automatic ascent would repeat the very passivity the course opposed, replacing discovery with a grand tour narrated by the professor.

The missing side of the seminar table

Most surviving prose used in this chapter was written by Grothendieck or by later curators. The course sheet gives the teacher’s intention. Esquisse and Récoltes et Semailles give the teacher’s assessment. The examination gives the institution’s demand. None is a collective transcript of student experience.

The imbalance has consequences. When Grothendieck says a student lacked curiosity, the archive preserves his interpretation more readily than the student’s reason for hesitation. When he remembers an inspired exchange, the student may have remembered a monologue. When he calls a piece of work acceptable, the author’s own account of discovery may assign importance elsewhere.

Named mathematical outputs partly correct the imbalance. Ladegaillerie’s papers can be read as arguments rather than as a teacher’s report about him. Contou-Carrère’s publications establish a line of work with its own afterlife. Malgoire’s later public statements and archival role provide another perspective, though recollection decades later remains different from a contemporary diary.

Judgments about the cohort remain attributed to Grothendieck; mathematical results follow the students’ publications where available; course structure follows official artifacts; later oral recollections are not silently converted into contemporary fact. This preserves the difference between author, artifact, and later witness.

This rule also limits collective nouns. “The students” did not all have one preparation or response. The course program’s own goal of individual questions argues against treating them as a passive mass. Where names and works are known, they are used. Where they are not, the prose reports the limit rather than inventing representative characters.

Oral history could add surviving participants, course notebooks, and departmental records, but it would require consent and separation of public professional memory from nonpublic recollection. No interviews are simulated here, and no contemporary participant testimony is thereby created.

The absence of equal testimony is not reason to abandon the pedagogical story. It is reason to write its grammar carefully: “Grothendieck proposed,” “the course document states,” “he later judged,” and “the exhibition concludes,” rather than “the students felt.”

Because no comparable set of student diaries has been located, the chapter cannot measure how participants understood the experiment at the time. It therefore separates the teacher’s stated aims, the institution’s documents, and the students’ published mathematics. That separation preserves disagreement without inventing a collective response and keeps later recollection from replacing contemporary evidence in the surviving written record.

The examination problem

Open research and assessment have different temporal structures. Research permits a month spent discovering that a question is wrong. An examination usually requires a solvable question within hours. The 1976 surface-theory paper proves that the course occurred and shows where exploratory material had to be converted into expected performance.

That conversion can be educative. To explain an isotopy invariant with precision or prove a classification in a controlled case tests understanding. It can also restore the active-passive order the course wanted to disturb: the examiner selects; the student responds; a grade follows.

Grothendieck’s 1978–79 program does not supply an administrative mechanism for resolving the tension. Its answer is ethical and relational: teacher and pupils must provoke themselves and one another. The absence of a grading design is telling. He was stronger at declaring what inquiry should feel like than at describing how a mass institution could certify it.

This gap should not be mocked. Many modern research-based courses retain it. Institutions want curiosity and standardized outcomes at once. Grothendieck’s prose is extreme because it refuses to smooth the contradiction into a list of “learning objectives.”

Lunch, office, and the scale of a group

The archive exhibition includes an illustration based on a 1979 photograph by Jean Malgoire, captioned Le déjeuner mathématique sur l’herbe. The caption should not be expanded into an invented picnic scene. Its evidentiary use is limited: a small group met around mathematical work and sometimes ate together.2020Maronne and Toën, Le temps des réflexions, 14.

Such meals can sustain a seminar culture. Conversation crosses the boundary of the scheduled hour; students ask what they would not ask in a formal room; a diagram returns over food. They can also intensify dependence on one central speaker. The source says Grothendieck usually spoke. It does not provide a transcript of who else did.

Scale mattered. A handful of students in an office could pursue a theme closely. The same scale was vulnerable: if a few people left, no institutional seminar remained. Grothendieck’s later claim that he had not created a durable site of common research should be read against this evidence of meetings. He did create occasions. He believed they did not become self-renewing.2121Grothendieck, “Esquisse d’un Programme,” sec. 9, pp. 42–43.

The distinction between occasion and place is useful. An occasion depends on the presence and energy of particular people. A place develops routines, archives, shared authority, and successors. SGA had become a place in this sense even as its volumes required years of editing. The Montpellier lunches remained occasions centered on Grothendieck.

The dependence extended beyond local conditions. His cessation of publication meant that students could not easily point outsiders to a current body of work under development. Course notes and unpublished pages lacked the public scaffolding that attracts visitors and lets new entrants prepare. A seminar without a circulating text must repeatedly begin in the speaker’s voice.

The world in the classroom

The course sheet does not mention defense funding, nuclear weapons, or ecological crisis. It would be false to claim that Grothendieck continued the exact political lectures of the Collège de France inside Introduction à la recherche. The surviving document concerns the structure of teaching and creativity.

Its institutional critique nevertheless belongs to the same ethical field. The master who speaks and the pupil who obeys reproduce a hierarchy. Work pursued only for credentials loses intrinsic meaning. A university can deaden curiosity just as a research system can subordinate inquiry to power. Grothendieck connected these concerns in his broader writings, but the specific Montpellier course should be cited for what it says.

The world also entered through students’ lives. Research training in the late 1970s occurred amid a constrained employment market. In Esquisse, Grothendieck noted that few of those who persevered would have the chance to earn a living in the profession. This material limit complicates his criticism of diploma-seeking. For a student, the diploma could determine access to work as well as symbolize conformity.2222Grothendieck, “Esquisse d’un Programme,” sec. 9.

Grothendieck recognized the employment problem even while demanding disinterested curiosity. His proposed move to the CNRS in 1984 would likewise be weighed against the fact that a post awarded to him could be unavailable to a younger researcher. The contradiction was not invisible to him. It remained unresolved.

The safest philosophical conclusion is therefore not that true research ignores careers. It is that curiosity and livelihood must coexist, and the university often asks one to masquerade as the other. Grothendieck’s course tried to protect curiosity. Students still had to live.

Hospitality and law

Pierre Cartier’s 1998 account describes a prosecution connected with Grothendieck’s public defense of hospitality. The Bibliothèque nationale de France catalogs his published plea under the title Plaidoirie sur le délit d’hospitalité: 1978. Because the checked sources differ by a year and no court record has been inspected, the chapter uses only “the 1977–78 hospitality case.” It does not reproduce the reported penalty, a procedural date, or a detailed legal characterization from the single secondary dependency chain.2323Cartier, “La folle journée, de Grothendieck à Connes et Kontsevich,” 27; Alexandre Grothendieck, Plaidoirie sur le délit d’hospitalité: 1978, with Giorgio Agamben and Hervé Le Tellier, Tracts 75 (Gallimard, 2026), https://catalogue.bnf.fr/ark:/12148/cb48746393q.

The title phrase délit d’hospitalité supplied Grothendieck’s public framing. The BnF summary indicates that the plea presented the act as ordinary human welcome and challenged the law applied to it. The short 2026 Gallimard edition includes the plea and selected letters; the catalog record verifies the edition’s documentary identity and 1978 subtitle, not the charge language or procedural details of the underlying case.2424Grothendieck, Plaidoirie sur le délit d’hospitalité: 1978.

Cartier interpreted the case as a decisive step in Grothendieck’s rupture with scientific society. That is Cartier’s retrospective judgment, not a judicial fact. Mathematics continued; seminars, letters, and manuscripts followed. The case can be treated as evidence of public dissent and legal consequence without turning it into the psychological cause of later withdrawal.2525Cartier, “La folle journée, de Grothendieck à Connes et Kontsevich,” 27; Grothendieck and Brown, Correspondance Grothendieck–Brown; Maronne and Toën, Le temps des réflexions, 16–23.

The attendance of former colleagues also complicates a story of total abandonment. Récoltes et Semailles specifically remembers Dieudonné traveling to Montpellier to testify. Broader attendance should be checked against the primary edition before use. The attributed recollection shows that a professional relationship could become civic solidarity.2626Grothendieck, Récoltes et Semailles, ed. Carmona (1985), 297 note 17.

The classroom and courtroom were not the same arena. Yet both raised the relation between an institution’s rule and a person’s judgment. In the course, Grothendieck asked whether teacher and pupil would submit to a mechanical ritual. In court, he challenged the application of an ordinance. The parallel is interpretive and limited: it does not make mathematics a legal allegory. It shows a consistent willingness to expose rules to first-principles criticism.

The legal episode in Cartier’s account

Cartier’s later account gives the legal episode a dramatic outline, which makes precision especially important. The chapter reports his account as testimony and does not convert it into an official court record.

Cartier’s article is a recollection by a mathematical colleague, published two decades later. It gives a year and procedural and penalty details that the checked corpus does not independently corroborate. Those particulars remain in the internal evidence record and do not enter the body as reported facts. The article also surrounds the episode with judgments about Grothendieck’s character and later life that this biography does not adopt.2727Cartier, “La folle journée, de Grothendieck à Connes et Kontsevich,” 27.

The BnF catalog is a bibliographic record for a primary text published in 2026. It gives the title, the date “1978” as subtitle, the publisher, series, extent, ISBN, and the fact that selected letters appear in an appendix. Its summary quotes the plea’s attack on laws requiring routine collaboration with the police. The record verifies the existence and documentary identity of the edition, not every procedural date.2828Grothendieck, Plaidoirie sur le délit d’hospitalité: 1978.

The year difference may have a simple explanation: investigation or charge in 1977, hearing and plea in 1978. It may instead reflect an error in one source. Without the judgment or edition in hand, choosing one year would create false certainty. The range 1977–78 communicates what is known and makes the gap visible.

The numerical penalty and detailed procedure remain single-source claims in the checked corpus because later summaries may depend on Cartier. They are withheld from body use until an official record or an independent reliable account corroborates the terms.

Finally, the case does not prove total social isolation. A prosecution involved authorities, legal participants, witnesses, and supporters. Former mathematical colleagues appeared in another role. Whatever distance existed from routine research institutions, Grothendieck remained involved in relations carrying public obligation.

This evidence changes the meaning of “world.” In the classroom he questioned authority through pedagogy. Outside it, hospitality placed an ethical choice under law. Neither event should be romanticized. Both show that the Montpellier years were not a retreat into solitary mathematical eccentricity.

What remains public

Withholding the reported penalty changes the legal passage in a useful way. The chapter still has a documented public object: a plea cataloged with a 1978 subtitle, a later colleague’s recollection of the case, and Grothendieck’s public framing of hospitality. What disappears is numerical and procedural detail that only one checked dependency chain carries.2929Cartier, “La folle journée, de Grothendieck à Connes et Kontsevich,” 27; Grothendieck, Plaidoirie sur le délit d’hospitalité: 1978.

This is not a claim that Cartier’s account is false. It is a judgment about threshold. A serious legal allegation requires more than attribution when exact punishment, status, or procedure is reported. The official record or an independent reliable account may later corroborate those particulars. Until then, the range “1977–78 hospitality case” establishes the public conflict without overstating the file.

The BnF catalog has a different competence. It can identify an edition, title, subtitle, publisher, extent, and appended letters. Its summary can show how the published plea frames the act. It cannot substitute for a judgment, docket, or contemporaneous police and court record. The revised prose no longer asks bibliographic metadata to do judicial work.

The chapter retains Cartier where his role is strongest: as a named later witness to a public episode and as an interpreter whose judgments are visibly his. It rejects his account as a sole basis for the exact penalty and rejects character diagnosis altogether. This separation lets testimony remain useful without becoming an official file.

Pedagogy and law are then compared at the proper level. Both involve rules and Grothendieck’s public criticism of them. The course document does not prove a legal philosophy, and the plea does not prove a teaching method. Their relation is interpretive and bounded, not a hidden causal mechanism connecting classroom frustration to prosecution.

The evidence boundary is itself part of the chapter’s theme. Grothendieck urged students to question inherited authority. The biography applies a related discipline to its sources: institutional labels, participant recollection, and catalog metadata are tested rather than merely repeated. The result is less dramatic and more accountable.

The body can still convey consequence without the withheld numbers. A prosecution, a published plea, testimony by a former colleague, and a public challenge to the law are substantial facts. Removing a fine and sentence does not neutralize the event; it prevents precision from becoming a substitute for corroboration. The legal history remains open to a court-file check rather than being closed by literary confidence.

The same economy governs quotation. The title of the plea is verified, while the longer courtroom wording awaits a page-checked edition and rights review. Paraphrase can identify the public moral argument without presenting an unverified sentence as exact speech. If the primary edition is later inspected, a short located quotation may replace the paraphrase; until then, the chapter does not simulate the authority of a transcript. Legal sensitivity, translation status, and quotation rights are related controls but not interchangeable ones.

The revised passage therefore keeps the chapter’s public-world function intact. It shows teaching inside an institution and dissent before another institution, while refusing to turn an underchecked penalty into narrative emphasis. Evidence of conflict remains; unsupported precision does not.

That balance preserves both public accountability and the minimum-necessary treatment owed to people whose circumstances are not the chapter’s subject.

Mathematics in several registers

The course documents show Grothendieck moving quickly between elementary objects and research horizons. The pedagogical issue is the pace and distribution of authority, not a mathematical ladder.3030Grothendieck, “Esquisse d’un Programme,” secs. 4, 8–9.

No surviving weekly syllabus establishes which definitions or examples carried that movement.

A social movement ends, concerns remain

The final issue of Survivre et vivre appeared in spring 1975, just before the course sequence considered here. Its end did not mean that ecological and antimilitarist concerns ended in Grothendieck’s life. It meant that one collective publication and organizational form had run its course.3131Pessis, “Les années 1968 et la science: Survivre … et Vivre, des mathématiciens critiques à l’origine de l’écologisme”, appendix entry for no. 19.

The distinction matters for teaching. There is no evidence that Introduction à la recherche was a disguised continuation of the bulletin. Its critique of passive education, however, belonged to a wider post-1968 field in which scientific authority, expertise, institutions, and everyday life were contested. Pessis’s study documents similar experiments and debates across French universities and scientific groups.3232Pessis, “Les années 1968 et la science: Survivre … et Vivre, des mathématiciens critiques à l’origine de l’écologisme”, chapters on university teaching and scientific critique.

Grothendieck’s position was no longer that of an organizer at the center of a small national movement. He was a professor in a southern university, pursuing local courses and intermittent projects. The scale had changed from public lectures about civilization to typed pages for a course. The ethical intensity had not necessarily diminished; it attached to the relation between people in a room.

That relocation of scale is one meaning of “the classroom and the world.” The world did not enter because every geopolitical question appeared on the blackboard. It entered because the form of teaching was treated as a social relation with consequences: obedience or initiative, credential or inquiry, authority or shared risk.

The post-1968 context also changed the audience’s expectations. Students had seen or inherited critiques of professorial authority. Alternative seminars, collectively organized curricula, and political discussion about science were not peculiar to Grothendieck. His program belonged to that history while using his distinctive vocabulary of child, creation, and game.

This wider field prevents two exaggerations. He did not invent participatory teaching in Montpellier. Nor was his course only a local echo of 1968. The mathematical choice of surfaces, polyhedra, and student-generated problems came from his own developing research as well as contemporary institutional criticism.

Pessis documents debates over whether scientific expertise itself reproduced social power. In Survivre et vivre, some participants moved from warning the public as scientists toward questioning the right of scientists to speak as a new priesthood. The 1978–79 program’s attack on the master’s monologue carries a related suspicion: expertise can turn a relation into obedience.3333Pessis, “Les années 1968 et la science: Survivre … et Vivre, des mathématiciens critiques à l’origine de l’écologisme”.

The professor could not renounce expertise. Students needed him to know topology, test arguments, and identify false generalizations. A classroom without authoritative claims is not automatically free; it may leave the least prepared students most dependent on confidence and informal status. The problem was to make expertise answerable without pretending it did not exist.

Grothendieck’s documents are strongest as a record of this unsolved problem. They do not offer a reusable method that another university could install. They show a mathematician trying to prevent knowledge from becoming domination while relying on the extraordinary force of his own knowledge.

The surviving classroom

The classroom survives first as paper made for different institutional purposes. The 1978–79 program names USTL, the academic year, Grothendieck, the C4 level, and Introduction à la recherche. Its two leaves state an intention and a self-critique. The 1976 examination sheet belongs to assessment, while the recorded 1977–78 DEA title places arithmetic geometry and regular polygons inside an advanced course. The archive exhibition adds an activity-report excerpt about common reflection and student-chosen subjects. None of these objects is a transcript. Together they establish course identity, sequence, stated method, and the coexistence of open inquiry with formal evaluation.3434Grothendieck, “En guise de programme pour le cours de C4 « Introduction à la recherche » 1978/79,” 1–2; Maronne and Toën, Le temps des réflexions, 13–15.

Material form helps control interpretation. A heading is strong evidence for the institution and year because those details were needed to administer the course. A manifesto-like paragraph is strong evidence for what its author wanted to declare, but not for how every meeting unfolded. An examination is strong evidence that students faced assessed questions, but not for the full range of discussion during the year. An activity report describes a planned or remembered practice through an institutional genre. The chapter assigns each object the claim it can carry rather than using the most vivid sentence as a substitute for the whole classroom.3535Grothendieck, “En guise de programme pour le cours de C4 « Introduction à la recherche » 1978/79,” 1–2; Maronne and Toën, Le temps des réflexions, 13–15.

For a general reader, the four objects resemble four camera positions trained on the same course: the title card, the instructor’s statement, the assessment desk, and a later institutional summary. The analogy is useful because no view contains the room. It also has a firm limit. Documents are not photographs, and their authors selected language for administrative, persuasive, or retrospective purposes. Combining them does not create a panoramic recording or authorize dialogue. It produces a bounded reconstruction in which intention, requirement, and later description can agree or remain in tension.3636Grothendieck, “En guise de programme pour le cours de C4 « Introduction à la recherche » 1978/79,” 1–2; Maronne and Toën, Le temps des réflexions, 13–15.

Important records remain absent. No opened enrollment list fixes the number or identities of participants in 1978–79. No weekly syllabus allocates subjects by date. No marked script shows how Grothendieck evaluated one response. No student notebook records the sequence of definitions, and no comparable set of contemporary student accounts supplies a collective reaction. The missing evidence prevents a scene-led narrative, but it does not erase the surviving course. It tells the biography where to stop: at documented aims, institutional forms, named mathematical outputs, and explicitly attributed later assessments.3737Grothendieck, “En guise de programme pour le cours de C4 « Introduction à la recherche » 1978/79,” 1–2; Maronne and Toën, Le temps des réflexions, 13–15.

Printed pagination, rather than browser filename order, fixes the sequence of the two program leaves. The Grothendieck Circle’s hosting establishes that the scans can be inspected; it does not establish physical custody or reproduction rights.3838Grothendieck, “En guise de programme pour le cours de C4 « Introduction à la recherche » 1978/79,” 1–2; Maronne and Toën, Le temps des réflexions, 13–15.

The program’s typography is evidence only at a modest scale. Typewriting, headings, and two-leaf length show a prepared course statement, not spontaneous speech. Handwritten additions, stamps, or filing annotations would need separate visual verification before use. A reproduction can let readers inspect institutional form, but a caption must not claim that the displayed copy was the one held by every student. Object identity and distribution remain different questions.3939Grothendieck, “En guise de programme pour le cours de C4 « Introduction à la recherche » 1978/79,” 1–2.

The page break is part of the document’s argument. The first leaf ends inside a balance sheet of the preceding teaching years; the second completes that reckoning and then turns to the question of the new academic year. Printed sequence, not browser filename order, therefore carries a movement from retrospective judgment to a prospective course. The two images are consecutive leaves of one prepared statement, not separate manifestos assembled later.4040Grothendieck, “En guise de programme pour le cours de C4 « Introduction à la recherche » 1978/79”.

The pronouns carry part of the proposed change. The failed past is narrated chiefly as what “I” did: speaking, discovering, and failing to notice the monologue. The projected year shifts toward “we,” the new protagonists, while “master” and “pupil” appear as institutional roles that both parties might repeat. This grammar does not prove that authority was shared in practice. It proves that the program framed the problem as one involving the teacher’s conduct as well as the students’ curiosity, rather than simply blaming passive listeners.4141Grothendieck, “En guise de programme pour le cours de C4 « Introduction à la recherche » 1978/79”.

The exhibition supplies an earlier institutional frame for the later program. It dates Grothendieck’s appointment to the autumn 1973 academic opening and describes an original form of research teaching based on the topological intuition of surfaces with deliberately modest prerequisites. The 1976 examination and the 1977–78 DEA title then show assessed and advanced-course artifacts before the 1978–79 program. This sequence establishes changing course forms across several years; it does not turn the 1978 manifesto into a transcript of the first year.4242Maronne and Toën, Le temps des réflexions, 13–15.

Assessment is present inside the program’s self-criticism, not added only by a later exam sheet. Near the end of the first leaf Grothendieck describes pupils taking notes for the examination and then evokes end-of-year marking as part of the poor balance he assigns to the preceding three years. The second leaf begins by asking what the participants will do differently while still acknowledging an official course. The source therefore documents a critique formed from within teaching and grading, not a declaration that institutional assessment had ceased.4343Grothendieck, “En guise de programme pour le cours de C4 « Introduction à la recherche » 1978/79”.

A method of teaching

The stated method can be reconstructed as a sequence of choices rather than as a personality portrait. Begin from a question capable of engaging a participant. Permit students to propose themes. Use common sessions to expose individual intuitions to objections. Require individual work over the year. Accept the possibility that a student sees something the professor does not. These elements come from the program and activity-report excerpt. They describe an intended redistribution of initiative. They do not show that authority disappeared, because the professor still organized the course, spoke with exceptional prestige, and remained connected to assessment.4444Grothendieck, “En guise de programme pour le cours de C4 « Introduction à la recherche » 1978/79,” 1–2; Maronne and Toën, Le temps des réflexions, 14–15.

The source record also supplies a correction from within the experiment. The archive exhibition says the participatory vision was not always realized and reports difficulty with listening and transmission. Grothendieck’s later account judged his research teaching harshly while naming particular students whose work mattered. Those statements must remain attributed and situated. They do not license a diagnosis, a composite failed student, or an imagined confrontation. They do establish that the program’s author recognized a gap between declaring an active-active relation and sustaining it in practice.4545Schneps and Lochak, Geometric Galois Actions 1, 7–48, 41–43; Maronne and Toën, Le temps des réflexions, 14–15.

The examination makes the method’s institutional limit visible. An open problem may change shape or end in a useful failure; an examination needs a question that can be answered and judged within a fixed time. The 1976 paper proves that surface material entered assessment, not that every research session became an exam drill. Its presence shows two standards operating together: exploratory ownership during work and accountable written performance at an endpoint. Grothendieck’s later insistence on something acceptable “black on white” belongs to the same tension. The chapter describes the tension without claiming that one document reveals how it was resolved for each student.4646Grothendieck, “Esquisse d’un Programme,” 42–43; Maronne and Toën, Le temps des réflexions, 13–15.

Method also changes with scale. A professor can let one research student pursue a question for years, but a course has an academic endpoint and several participants with different preparation. The program proposes mutual inquiry; it does not specify how topics were selected when interests conflicted, how prerequisite gaps were addressed, how speaking time was shared, or how incomplete work was graded. Those omissions are not proof that no practice existed. They mark the difference between a declaration of pedagogical values and an operational course record. The archive exhibition’s report that Grothendieck was often the speaker and had difficulty listening supplies one later check on implementation, while named student work supplies evidence that some long projects reached rigorous form. A responsible account holds both: the method sought a real displacement of the teacher’s knowledge, and the surviving evidence does not show that institutional asymmetry or unequal preparation disappeared.4747Grothendieck, “Esquisse d’un Programme,” 42–43; Maronne and Toën, Le temps des réflexions, 14–15.

Student choice also needs evidence at the level of process. The activity report says subjects were chosen by students and pursued individually, but no surviving list maps names to topics for the year. The narrative can describe the rule and its intended reversal of roles; it cannot invent an example of a student surprising Grothendieck. Named outputs enter only where a paper, thesis, or later public record identifies them.4848Grothendieck, “Esquisse d’un Programme,” 41–43; Maronne and Toën, Le temps des réflexions, 14–15.

The program places its rebellion inside, not outside, an official course. On the second leaf Grothendieck explicitly refers to the new academic year and to satisfying the requirements of an official course, then asks whether the old schoolmaster’s performance will simply recur. The juxtaposition is evidence of an institutional experiment by a professor still answerable to a curriculum. It is not evidence that USTL endorsed every judgment in the program or suspended its examinations.4949Grothendieck, “En guise de programme pour le cours de C4 « Introduction à la recherche » 1978/79”.

His proposed first question is not a mathematical topic but how curiosity might be awakened where it is absent. Only after that question, the leaf says, would a shared voyage of discovery have meaning. The order explains why the sheet contains no weekly sequence of theorems: it is a program for a relation to inquiry, not a syllabus. The limit is equally clear. A declaration that curiosity should precede teaching does not tell us how a hesitant student was invited to speak, how disagreement was handled, or whether the new order lasted beyond the page.5050Grothendieck, “En guise de programme pour le cours de C4 « Introduction à la recherche » 1978/79”.

Near its close, the document turns the familiar contrast between active master and passive pupil against both roles. Teacher and pupils can become performers in the same mechanical ritual; alternatively, both can recover the absorbed attention associated in the text with play. That is Grothendieck’s metaphor, not a developmental theory about real children. Its pedagogical force lies in making the professor subject to the same criticism as the class, while the surviving examination record shows that institutional judgment did not vanish.5151Grothendieck, “En guise de programme pour le cours de C4 « Introduction à la recherche » 1978/79”; Maronne and Toën, Le temps des réflexions, 13–15.

The public artifacts show that exploration and assessment coexisted rather than replacing one another. The exhibition reproduces a 1976 maîtrise examination in topological surface theory and identifies a 1977–78 DEA course in arithmetic geometry of regular polygons. The exam proves that a bounded written task entered university evaluation; the DEA label proves an advanced course identity. Neither object supplies attendance, grades, a weekly timetable, or a student’s response. Their value is precisely institutional: open-ended rhetoric remained attached to courses that also generated titles, levels, and assessed documents.5252Maronne and Toën, Le temps des réflexions, 13–15.

Neither document is a neutral timetable. The activity report translates the experiment into institutional prose—sessions, chosen subjects, individual work, and redistribution of roles. The program uses metaphor, first-person failure, questions, and an appeal to play. Their genres explain why one can establish a course method while the other establishes the teacher’s public argument about it. Combining them broadens the record, but it still does not produce student testimony, observed classroom dialogue, or a success rate.5353Grothendieck, “En guise de programme pour le cours de C4 « Introduction à la recherche » 1978/79,” 1–2; Maronne and Toën, Le temps des réflexions, 14–15.5454Grothendieck, “En guise de programme pour le cours de C4 « Introduction à la recherche » 1978/79,” 1–2; Maronne and Toën, Le temps des réflexions, 14–15.

The chronological order also matters. The 1976 examination precedes the 1977–78 DEA label and the 1978–79 program; the exhibition’s activity-report excerpt interprets a practice whose exact date and file context require the archive. Later self-assessment in Esquisse belongs to 1984. The evidence thus contains contemporary course paper, assessed artifacts, an institutional report, and retrospective judgment. Their agreement on recurring difficulty does not make them one contemporaneous witness.5555Grothendieck, “Esquisse d’un Programme,” 41–43; Grothendieck, “En guise de programme pour le cours de C4 « Introduction à la recherche » 1978/79,” 1–2; Maronne and Toën, Le temps des réflexions, 13–15.

The published plea

The BnF record identifies Gallimard, the Tracts series, number 75, a fifty-two-page extent, ISBN 978-2-07-316366-0, and selected letters in an appendix. Those fields establish the later edition’s documentary identity. They do not establish a filing date, hearing date, statutory elements, judgment, or sentence for the underlying case. The chapter therefore attributes the broad word “prosecution” to Cartier and supplies no more technical procedural verb.5656Cartier, “La folle journée, de Grothendieck à Connes et Kontsevich,” 23–42, 27; Grothendieck, Plaidoirie sur le délit d’hospitalité: 1978.

No court docket, judgment, hearing record, or contemporaneous official notice has been inspected, and the body of the 2026 edition has not been page-checked here. Its catalog summary can identify the plea’s public framing but not the context of every sentence. “Trial,” “hearing,” “charge,” and “conviction” are therefore withheld because each could imply a procedural stage the sources consulted do not establish. The date range is not asserted to be a two-year proceeding.5757Cartier, “La folle journée, de Grothendieck à Connes et Kontsevich,” 27; Grothendieck, Plaidoirie sur le délit d’hospitalité: 1978.

Hospitality as public argument

The biographical relevance lies in a public act and a public argument. Grothendieck used the language of hospitality to challenge the law applied in the episode, and a former mathematical colleague later remembered appearing in its orbit. That evidence is enough to place civic dissent beside university teaching. The chapter keeps the institutional conflict and supplies no individual circumstances beyond the public record.5858Grothendieck, Récoltes et Semailles, ed. Carmona (1985), 17; Cartier, “La folle journée, de Grothendieck à Connes et Kontsevich,” 27; Grothendieck, Plaidoirie sur le délit d’hospitalité: 1978.

Minimization also improves the comparison with pedagogy. The course document and the plea both show Grothendieck questioning rules, but they address different institutions and different kinds of obligation. One concerns who may speak and discover in a class; the other concerns a public challenge framed through hospitality. The parallel is analytical and limited. It does not prove that one event caused the other, that a mathematical idea encoded a legal position, or that a single disposition explains both.5959Grothendieck, “En guise de programme pour le cours de C4 « Introduction à la recherche » 1978/79,” 1–2; Cartier, “La folle journée, de Grothendieck à Connes et Kontsevich,” 27; Grothendieck, Plaidoirie sur le délit d’hospitalité: 1978.

The same limit bars psychological inference about Grothendieck. A public plea can show how he framed an act and a law; it cannot prove that the episode caused his later mathematical choices or institutional distance. Cartier’s interpretation may be reported as Cartier’s. Continued teaching, correspondence, and manuscripts provide independent chronological evidence against a simple rupture story. Public consequence and an unsupported causal mechanism remain separate claims.6060Wikiquote, “Alexandre Grothendieck,” 1982–84; Maronne and Toën, Le temps des réflexions, 16–23; Cartier, “La folle journée, de Grothendieck à Connes et Kontsevich,” 27; Grothendieck, Plaidoirie sur le délit d’hospitalité: 1978.

The grammar of the documents

The chapter’s evidence is strongest when it preserves grammar. The course sheet says what Grothendieck proposed. The activity report says how work was intended to proceed. The examination shows an assessed artifact. Student publications show authored mathematical results. Grothendieck later judged the experiment, and curators later interpreted the archive. Cartier recalled a public episode; the BnF identified an edition. Changing all those verbs to the narrator’s flat “was” would erase source differences and manufacture consensus.6161Grothendieck, “Esquisse d’un Programme,” 41–43; Grothendieck, “En guise de programme pour le cours de C4 « Introduction à la recherche » 1978/79,” 1–2; Maronne and Toën, Le temps des réflexions, 13–15; Cartier, “La folle journée, de Grothendieck à Connes et Kontsevich,” 27; Grothendieck, Plaidoirie sur le délit d’hospitalité: 1978.

What the documents cannot say is equally specific. They do not provide a collective student voice, a continuous classroom record, a complete legal file, or a causal explanation for Grothendieck’s choices. These are not philosophical mysteries placed at the chapter’s end. They are defined research gaps with identifiable next sources: course files, student-facing artifacts, official legal records, and a page-checked primary text. Until those appear, uncertainty remains local rather than spreading into every established fact.6262Grothendieck, “En guise de programme pour le cours de C4 « Introduction à la recherche » 1978/79,” 1–2; Maronne and Toën, Le temps des réflexions, 13–15; Grothendieck, Plaidoirie sur le délit d’hospitalité: 1978.

The move at the end of the decade

The two-page program and the bounded hospitality record leave two public institutional objects: one states a pedagogical wager, and one documents legal dissent. Neither authorizes a residence replay or an advance mathematical lesson.

Chapter 51 ends with courses, unequal authority, public law, and source limits; Chapter 52 begins from its dated 1978 letter.