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Orsay, June 26

On June 26, 1970, Grothendieck lectured at Orsay on scientific responsibility and the military apparatus. A typescript circulated under the title “Responsabilité du savant dans le monde d’aujourd’hui: Le savant et l’appareil militaire.” The hosted scan establishes the document’s existence and title, but its weak text layer has not been transcribed for quotation for this account.11Alexandre Grothendieck, “Responsabilité du savant dans le monde d’aujourd’hui,” Lecture at the Université d’Orsay, June 1970, https://webusers.imj-prg.fr/~leila.schneps/grothendieckcircle/Savant.pdf.

The Orsay lecture came after Grothendieck’s May 25 decision and before the October 1 effective departure confirmed on June 9. Mathematical and public activity therefore continued during a documented transition rather than after an instantaneous break.22Grothendieck, Aux membres du Comité scientifique [de l’IHÉS]; Grothendieck, Letter to the director of the IHÉS confirming his departure; Grothendieck, “Responsabilité du savant dans le monde d’aujourd’hui”.

An institutional home can organize a life more deeply than a job description. IHÉS had provided Grothendieck with freedom, visitors, publication, a seminar, and a community; his work had given the institute international mathematical standing. Leaving altered the conditions under which ideas, students, manuscripts, and daily work had been held together.

The familiar phrase “he left mathematics in 1970” compresses a process into an event. In Récoltes et Semailles, Grothendieck later described 1970 as a major turn and a change of milieu. That retrospective account records later meaning rather than each contemporaneous step. The month-by-month record shows mathematical lectures and political organization occupying the same summer.33Grothendieck, Récoltes et Semailles (Université des Sciences et Techniques du Languedoc and Centre National de la Recherche Scientifique, 1986), 38.

Jackson reports that the lecture drew hundreds. Nicholas Katz, then visiting IHÉS and surprised by news of the resignation, remembered Grothendieck arguing in terms far more radical than a demand for transparent budgets. According to Katz’s recollection, he questioned whether doing mathematical research was harmful in the face of threats to human survival. That formulation must remain attributed to Katz until the typescript page is verified.44Jackson, “As If Summoned from the Void, II,” 1198–99.

The change in scale was unmistakable. At IHÉS, the dispute concerned a particular source of money and a particular board decision. At Orsay, Grothendieck addressed the place of scientists within military systems and the danger of nuclear proliferation. Resignation had turned an internal condition into a public argument.

His established mathematical reputation amplified the Orsay intervention. That public authority did not establish the argument’s political conclusions, but it helped draw attention to them.

Authority also exposed contradiction. The lecture took place at a university within a state-funded scientific system. Its listeners included researchers whose institutions received complex streams of public money. A categorical refusal could identify complicity more easily than it could design a general system for sustaining research without it. Critics in the audience could agree about nuclear danger and reject his prescription.

Jackson says an appendix to the typescript recorded hostile reactions from students, including a flyer mocking Grothendieck as an establishment figure who produced obedient little schemes. The detail belongs to the document as summarized by Jackson; it is not a license to reconstruct the room. Its significance is that the recent dissident from IHÉS could still appear to younger militants as a mathematical mandarin. Leaving an elite institution did not erase the social identity formed there.55Jackson, “As If Summoned from the Void, II,” 1199.

This tension followed Grothendieck’s activism. His public position challenged the prestige hierarchy while the audience remained one that prestige supplied. He rejected the institute’s funding decision and retained the authority accumulated through decades of scientific work. The contradiction does not invalidate his warning; it describes the position from which he made it.

Mathematics in Montréal

William Messing later recalled that in July Grothendieck attended an algebraic-geometry summer school at the Université de Montréal, alongside lecture series by Shreeram Abhyankar, Michael Artin, and Masayoshi Nagata. Messing described Grothendieck lecturing on Barsotti–Tate groups, objects important in the study of abelian varieties and arithmetic geometry.66Artin et al., “Alexandre Grothendieck 1928–2014, Part 2,” 405–6.

Period sources call the subject Barsotti–Tate groups; modern English usually says $p$-divisible groups. The name identifies a compatible $p$-power torsion object in families, which is enough here to show that the Montréal series treated current arithmetic geometry rather than ceremonial reminiscence. Its definition, rank axioms, elliptic-curve examples, failure cases, Dieudonné-crystal mechanics, and detailed attribution belong to Chapter 47.77Artin et al., “Alexandre Grothendieck 1928–2014, Part 2,” 405–6.

At David Lieberman’s request, Messing recalled, Grothendieck also gave an extra lecture on motives. Scheduled for an hour, it lasted more than three. In it he carefully stated a variant of a conjecture about absolute Tate cycles. The exact mathematical wording should be checked against Messing’s account before technical reuse, but the temporal point is secure: motives still held Grothendieck’s sustained attention in July 1970.88Artin et al., “Alexandre Grothendieck 1928–2014, Part 2,” 406.

The Montréal record refutes an instantaneous conversion story. Mathematical exposition and political activity occupied the same period rather than two lives separated by May 25.

That overlap may have been unstable. A person can continue an activity while questioning its value. The evidence of lectures does not prove that his relation to mathematics was unchanged. It proves only that “abandonment” requires a longer chronology.

The same point appears in the IHÉS scientific-work inventory for 1970. The IHÉS inventory assigns entries to Grothendieck, Grothendieck with Verdier, Deligne, Katz, and others. The inventory does not establish how each text relates to current versus earlier seminar work; it records texts across the institutional break.99Institut des Hautes Études Scientifiques, Archives de l’IHÉS, “Travaux de mathématiques et de physique théorique, année 1970,” F3.2.2.1/4.

The July 20 founding and July 24 plenary meeting documented in Survivre no. 1 belong to Chapter 43.1010Survivre … et vivre (Paris, 1970–1975), no. 1, https://science-societe.fr/survivre/, cover and p. 2.

Nice

The 1970 International Congress of Mathematicians was held in Nice. Pierre Cartier later recalled Grothendieck distributing Survivre material there and setting up a table between publishers’ booths without official authorization. Jackson reproduces that account.1111Jackson, “As If Summoned from the Void, II,” 1199–200; Cartier, “A Mad Day’s Work,” 393 n.12.

In Cartier’s recollection, Jean Dieudonné had a leading organizational role, the unofficial booth produced a dispute, Cartier and others tried to mediate, the table moved outside, and police became involved because organizers had promised municipal authorities that there would be no street demonstrations. Cartier also remembered an argument over moving the table off the sidewalk. The exact sequence has no independent contemporary record in the sources consulted.

The account is a later recollection, not a police report or contemporaneous transcript. This chapter omits dialogue, exact gestures, and every claim about Grothendieck’s private intention, including the later interpretation that he wanted arrest.

The encounter exposed a dispute about mathematical space. Publisher booths were authorized within the congress; the Survivre table was not. Cartier’s account places Grothendieck’s political distribution against organizers’ agreements with local authorities.

Their older collaboration sharpened the conflict. Dieudonné had helped turn Grothendieck’s drafts into EGA and had defended the importance of his work. The disagreement at Nice should not be narrated as proof that their earlier friendship was false. It shows that shared mathematical labor did not settle how a congress should handle unauthorized political activity.

The dispute also concerned equal access and emergency. Allowing one famous participant an unofficial booth raised a general rule for other groups, while Survivre’s announced dangers challenged ordinary procedure. The record establishes conflict between unauthorized distribution and congress rules; it does not establish each participant’s private hierarchy of values.

Cartier later said the tactics alienated people who broadly agreed with parts of the politics. That is his A2 judgment, not a general finding about Grothendieck’s character or the movement’s effectiveness.1212Jackson, “As If Summoned from the Void, II,” 1199–200.

The Nice episode also prevents a clean story of withdrawal from the mathematical world. Grothendieck went to its largest congress and contested what it should count as relevant. He did not disappear. He tried to change the terms of participation.

The Collège de France account

In “Remous au Collège de France,” Grothendieck describes a two-year appointment to the newly created first professeur associé chair. He identifies Serre as proposing his appointment and later renewal. This contemporaneous first-person account replaces the earlier Jackson-only framing.1313Alexandre Grothendieck, “Remous au Collège de France,” Survivre … et vivre, 1971, 1–4, https://csg.igrothendieck.org/wp-content/uploads/2024/09/U59d.pdf.

Grothendieck’s “Remous au Collège de France” gives his account of status, duration, and Serre’s role. The formal appointment instrument has not been found, and this account does not reconstruct approval procedures or exact lecture-program decisions beyond what Grothendieck states.

The Collège position did not restore the IHÉS arrangement of permanent post, visitor network, publications, and weekly seminar. It does establish that departure from IHÉS did not end participation in an elite academic platform.

Messing later described a June 1971 Collège lecture on a lifting result using Illusie’s deformation formalism. That testimony supports continued technical work; the theorem itself is not stated here.1414Artin et al., “Alexandre Grothendieck 1928–2014, Part 2,” 405–6.

Serre’s role in Grothendieck’s account documents professional assistance across disagreement. It does not establish private reconciliation or agreement about the IHÉS funding decision.

The source’s genre matters. “Remous au Collège de France” is Grothendieck’s own contemporary public account, not the Collège’s appointment register. It directly establishes what he said about the chair and Serre’s initiatives. An official instrument would establish the institution’s exact title, dates, vote, remuneration, and conditions with a different authority. The account is therefore primary without being exhaustive.

Its description of the first newly created professeur associé chair also requires a narrow reading. “First” identifies the position in Grothendieck’s account; it does not rank him above the Collège’s permanent professors or prove that every institutional participant used the same terminology. The French title is retained because an unreviewed English equivalent might import a different employment category.

The two-year duration distinguishes this arrangement from the permanent IHÉS position. A fixed appointment could preserve teaching and professional visibility while leaving the former institutional alignment unrestored. That difference is documentary, not psychological: it does not show whether Grothendieck experienced the post as refuge, compromise, platform, or transition.

Grothendieck’s account also separates several acts that a compressed sentence could merge. Serre’s proposal concerns an appointment; a later renewal proposal concerns continuation; the account of those proposals does not by itself reproduce the relevant votes or administrative instruments. This account therefore attributes the initiatives to Serre through Grothendieck and does not state that Serre controlled the outcome.

The boundary matters because later conflict can tempt a biographer to make every professional relation binary. Assistance with an appointment is an identifiable act. It neither cancels disagreement nor proves an intact friendship. Conversely, the absence of a recovered private reconciliation does not justify describing the two mathematicians as wholly estranged.

The Collège evidence also limits the language of exile. Grothendieck left a permanent research institute but entered another prestigious academic setting. The settings were not interchangeable: IHÉS had organized long-term research, visitors, publications, and the Tuesday seminar, while the associate chair was bounded in duration. “Departure from IHÉS” is exact; “expulsion from academic life” is not.

The 1971 lecture remembered by Messing adds a separate evidentiary line. It does not verify the appointment instrument, but it supports the claim that the post included substantive mathematical activity. Because Messing’s account is retrospective and the theorem statement is technical, the event remains a recollection and the mathematics is not stated here.

Together Grothendieck’s account and Messing’s establish continuity at two levels: an appointment described by its holder and a later lecture remembered by a participant. They do not establish a complete teaching schedule. Missing course programs, attendance records, and institutional minutes remain unknown rather than being reconstructed from reputation.

That restraint preserves the chapter’s central distinction. A door closed at IHÉS on a documented date; another institutional opening did not reverse the funding decision. Continuity after rupture was real without making the rupture merely symbolic.

The cause closest to the event

Among competing explanations, the military-funding dispute has the strongest documentary claim as the proximate cause of the IHÉS resignation. The audit records the source, the April minutes record Grothendieck’s condition and the board’s contrary decision, and the May 25 and June 9 letters establish his decision and its October 1 effective date. No psychological hypothesis is required for the institutional sequence.1515Institut des Hautes Études Scientifiques, Archives de l’IHÉS, Price Waterhouse & Co., financial statements for 1969, February 27, 1970, A3.1.4.2.4/4; Institut des Hautes Études Scientifiques, Archives de l’IHÉS, minutes of the board meeting of April 22, 1970, A3.1.4.2.2/1; Grothendieck, Aux membres du Comité scientifique [de l’IHÉS]; Grothendieck, Letter to the director of the IHÉS confirming his departure.

Proximate cause does not mean complete explanation. It accounts for the documented institutional timing; broader later changes in work, public activity, and relationships remain separate subjects supported mainly by retrospective sources.

Scharlau presents the reasons as multiple, complementary, contradictory, and partly inaccessible. His further interpretations based on personality are not repeated.1616Scharlau, “Who Is Alexander Grothendieck?” 933–36.

Cartier proposed several possible biographical, professional, and political factors, marking many of them as conjecture. Jackson emphasized work intensity and connected the funding crisis, Vietnam, and 1968 to a broader shift. Both accounts were written with knowledge of the later outcome and remain attributed interpretations.1717Jackson, “As If Summoned from the Void, II,” 1197–99; Cartier, “A Mad Day’s Work,” 391–93.

The highest evidence threshold applies to precisely these attractive explanations. Childhood does not mechanically yield antimilitarism. Work intensity does not establish a contemporaneous health condition. Failure to complete a program does not prove despair. Turning forty does not prove belief in decline. May 1968 does not prove conversion. Each may belong to an attributed interpretation; none should be presented as an observed internal event without a dated statement.

A later self-assessment

In Récoltes et Semailles, Grothendieck later reassessed the degree to which mathematical research had occupied his life through 1969. The exact French wording is known for this account only through a secondary transcription and is therefore withheld. The source supports a claim about his later interpretation, not a contemporaneous account of his condition in 1970.

This distinction prevents two opposite errors. The mathematical record should not be narrated as cost-free triumph, but a later moral reassessment cannot be converted into a diagnosis or an exclusive cause of resignation. The funding decision remains the best-documented trigger.

Vietnam and 1968

The Vietnam journey supplies firmer evidence of political action before the break. In November 1967 Grothendieck taught during air raids and reported on the organization of mathematical education under bombardment. The experience did not force an immediate resignation; IHÉS had granted leave and support for the trip. It did place war and mathematical life in one documented field of vision.1818Grothendieck, La vie mathématique en République Démocratique du Vietnam, 1–4.

May 1968 transformed French public life through student protest, strikes, and confrontation with state authority. Later witnesses say the upheaval impressed Grothendieck deeply. The statement is credible, but “May caused him to leave” is too strong. His public refusal in Moscow and Vietnam visit came earlier; the military-funding crisis came later. 1968 belongs to an accumulating context.

Ecological and antimilitary concerns circulated widely by the late 1960s. Their later organization lies outside Part VII; this chapter establishes only that the public concerns overlapped with the IHÉS departure.

These contexts explain why a small funding line could become emblematic without making it a pretext. The Ministry of the Armies represented the institutional connection between science and organized violence that he increasingly rejected. The audited amount gave the emblem a material form.

Conflict with Motchane

The relationship with Motchane had its own history. The founder had helped create a position possible for a stateless mathematician and built the institution in which Grothendieck’s greatest program flourished. Over time, according to multiple accounts, conflict increased. The funding dispute was therefore both a principled disagreement and an episode in a damaged working relationship.

Scharlau proposed that Motchane may have welcomed an opportunity to remove a disruptive professor. The April minutes complicate that interpretation because Motchane suggested a period of reflection when the board president treated Grothendieck’s committee withdrawal as cessation. Perhaps this was tactical; perhaps conciliatory. The record does not disclose motive.1919Institut des Hautes Études Scientifiques, Archives de l’IHÉS, minutes of the board meeting of April 22, 1970, A3.1.4.2.2/1, p. 3; Scharlau, “Who Is Alexander Grothendieck?” 933–35.

It is equally possible to overuse Motchane’s early support as a moral debt. Gratitude for an appointment does not require accepting every later policy. Institutions change; relationships acquire new facts. Grothendieck could owe IHÉS opportunity and still judge its funding intolerable.

The conflict does not require a villain. Motchane sought to finance an institute under pressure. Grothendieck refused a source he associated with military power. The board’s stated position separated use from source. Colleagues chose continuity. Later accounts describe some consequences in the language of betrayal, but no single perspective governs the record.

Fairness does not mean moral equivalence. The sources allow readers to judge the positions. Fairness means not manufacturing evidence to predetermine the judgment.

What did not close

The mathematical language remained. Schemes, topoi, étale cohomology, and derived methods did not depend on Grothendieck’s institutional presence once thousands of mathematicians had begun to use them. Motives and the standard conjectures continued as programs. SGA volumes moved toward publication. Deligne, Katz, Illusie, Verdier, Berthelot, and others pursued work that was connected to his and irreducibly their own.

Grothendieck’s influence also remained in habits: work relative to a base, define objects through functors, search for universal properties, and enlarge a problem’s habitat until its solution becomes natural. Such habits can become anonymous because they feel inevitable after adoption. Their survival was a kind of victory and, in his later view, sometimes a form of erasure.

Personal relations did not all close at once. Grothendieck’s account credits Serre with proposing the Collège position. Students and colleagues continued correspondence or visits in varying degrees. Grothendieck himself returned to mathematical writing repeatedly. The later image of total solitude belongs to another period.2020Grothendieck, “Remous au Collège de France,” 1–4.

What closed was a particular alignment: Grothendieck’s program, a permanent IHÉS chair, the Tuesday seminar as a center of direction, and the expectation that the institution would remain his lifelong home. Once separated, those elements followed different histories.

The institute survived and continued to flourish. Grothendieck’s departure did not prove that it had rejected his mathematical legacy. Its current history celebrates him as a foundational figure. Institutional commemoration, however, should not smooth away the funding decision that made continued membership impossible on his terms.

The later course and effectiveness of Grothendieck’s activism lie outside this chapter. Part VII records the initial public interventions without judging the movement’s subsequent influence.

What changed before the year ended

By the end of 1970, Grothendieck no longer held his permanent IHÉS position. He had delivered a public lecture on scientific responsibility, taught technical mathematics in Montréal, and, in Cartier’s later account, disputed congress rules while distributing Survivre material at Nice. These are separate events with separate source types.

The change in institutional role is the firmest boundary. His letter of June 9 fixes October 1 as the effective date, while the April board record establishes the conflict and decision that preceded the two letters. No later interpretation is needed to state that the permanent appointment ended.

The Orsay typescript documents a public argument extending beyond one institute.

The mathematical record changed less abruptly. Montréal lectures and the 1970 work inventory show active subjects and texts. The Collège de France appointment provided another academic setting. Later work on Barsotti–Tate groups confirms that technical mathematics continued beyond the summer.

Social relations changed at different rates. Deligne did not resign. Grothendieck’s account credits Serre with proposing the next appointment. Other former students continued redaction and research. The record does not support one date on which a mathematical community became entirely external to Grothendieck.2121Grothendieck, “Remous au Collège de France,” 1–4.

The distinction among employment, public activity, mathematics, and relationships explains why sources emphasize different records: a board decision, letters of departure, an Orsay typescript, and mathematical lectures.

None of those descriptions should govern the others. A later memoir supplies evidence about retrospective meaning. The audit and board minutes supply direct evidence about institutional acts. Participant memories supply evidence about events not preserved in official minutes. Published mathematics supplies its own chronology.

The year also changed the setting in which Grothendieck’s authority operated. At IHÉS it organized a specialist program; at Orsay and Nice it entered public and institutional argument. The standards governing agreement differed.

This transfer had practical limits. Mathematicians who accepted Grothendieck’s technical judgment could reject his institutional prescription. Jackson also reports students mocking his establishment status at Orsay. These are documented disagreements and audience responses, not a general psychological explanation.2222Jackson, “As If Summoned from the Void, II,” 1198–99.

Periodization should therefore use 1970 as a documented institutional and public turn. It should not make the year an endpoint for mathematical creation or the predetermined beginning of later seclusion.

This form of closure leaves several lines open by design. Motives and standard conjectures continue without Grothendieck’s weekly direction. Crystalline and Barsotti–Tate work continues with him and others. IHÉS continues after the professor who had helped establish its mathematical standing leaves.

The breach as historical scale

From a distance, the years 1966 to 1970 look like a designed arc: medal, motives, standard conjectures, military funding, resignation. The documents resist that neatness. The motives program began before the medal. Political action preceded the funding crisis. Mathematical work continued after resignation. The institute’s budget problem intersected with, but did not create, a larger moral change.

The title of this Part, “The Summit and the Breach,” should therefore be read as overlapping conditions. The summit contained refusal: Moscow and Vietnam. The breach contained continuity: Montréal and the Collège de France. There was no pure before and after.

This overlap is not narrative indecision. It is the historical form of transformation. People often act in a new direction while continuing old obligations. Institutions can lose a central figure while preserving his work. A mathematical program can become most influential as its originator withdraws from directing it.

The next Part follows the political movement and its participants. Part VII ends with the effective IHÉS departure and preserves the coexistence of technical mathematics and public intervention.

For Part VII, the final sequence is bounded. The board accepted the grant on April 22; Grothendieck announced his decision on May 25, confirmed it on June 9, spoke at Orsay on June 26, and left the permanent position effective October 1. Montréal mathematics and the Nice dispute show continued activity during that interval.2323Institut des Hautes Études Scientifiques, Archives de l’IHÉS, minutes of the board meeting of April 22, 1970, A3.1.4.2.2/1; Grothendieck, Aux membres du Comité scientifique [de l’IHÉS]; Grothendieck, Letter to the director of the IHÉS confirming his departure; Grothendieck, “Responsabilité du savant dans le monde d’aujourd’hui”; Artin et al., “Alexandre Grothendieck 1928–2014, Part 2,” 406; Jackson, “As If Summoned from the Void, II,” 1199–200.

Each date belongs to a different documentary act. The April 22 minutes record the board’s discussion and vote while reporting back on the April 6 conflict. They do not contain Grothendieck’s later decision. The May 25 letter addresses the Scientific Committee and announces that decision with a probable effective date. The June 9 letter addresses the director and confirms October 1. The sequence is assembled from records, not from one retrospective narrative.

The change from a probable date to a confirmed date is small in wording and large in chronology. It marks a move from announced intention to fixed institutional timing. Calling May 25 the day Grothendieck “left IHÉS” erases the interval that the second letter expressly preserves.

That interval is not empty. The Orsay title and date are documentary; Katz’s report of the lecture’s argument is recollection. Messing’s Montréal account is another recollection, independently attached to a named mathematical event. Cartier’s Nice account is a third. Their different source types cannot be combined into a day-by-day diary, but they establish activity between decision and effective departure.

The letters do not specify every employment consequence. They do not establish from the text inspected here when salary, office access, seminar responsibility, or administrative privileges changed. October 1 governs the effective departure stated in his letter of June 9; it should not be made to answer questions the letter does not address.

Nor do the documents create a resignation scene. No source consulted places the participants in one room on May 25 or supplies gestures, weather, spoken exchanges, or a final exit from Bois-Marie. The surviving act is written notification. Its documentary plainness is more reliable than a reconstructed confrontation.

The sequence also prevents the opposite compression, in which the April vote automatically produces a departure with no agency or delay. The board chose acceptance. Grothendieck then communicated his own decision and later confirmed its effective date. Causation is strongly supported at the institutional level without turning separate acts into one mechanical instant.

The May letter’s allegation about assurances remains another layer. It explains how Grothendieck framed the prior dispute at the moment of decision. It does not transform his account into the missing written assurances or the record of the alleged oral promise. The fact of allegation is F; the full agreement and alleged breach remain C/U.

The result is more than a corrected date. It changes the narrative form from a sudden conversion to an interval of overlapping commitments. That conclusion depends on actions and documents rather than an inferred state of mind.

“Effective departure” is consequently the preferred phrase in this chapter. “Resignation” is useful shorthand for the decision, but without a modifier it can make announcement and effect appear simultaneous. “Dismissal” would contradict the form of the surviving letters, while “walkout” would invent an event. The controlled phrase preserves both Grothendieck’s agency and the interval recorded in his two letters.

The interval also distributes evidentiary responsibility. The April minutes establish what the board decided; his letter of May 25 establishes what Grothendieck announced and alleged; his letter of June 9 establishes when departure took effect. “Responsabilité du savant,” Messing, and Cartier establish different activities before that endpoint at different confidence levels. No source is made to carry the whole sequence.

This method leaves legal details open. The letters can establish a communicated decision without resolving every contractual question about notice, tenure, or institutional procedure. Such matters would require employment records and formal instruments not present among the sources consulted. The historical claim needs no stronger vocabulary: a permanent relationship ended effective October 1 after the documented funding conflict and written notice.

That boundary is sufficient for the chronology assigned to this Part.

The summit had not vanished. It had become a resource he could use, a history others could continue, and a standard against which his rejection of scientific prestige would be measured. The breach did not erase the architecture. It changed who would inhabit it.

From a specialist proof to a public warning

The Orsay typescript marks a change of audience and standard of proof. In algebraic geometry, Grothendieck could specify a category, hypotheses, and a theorem. In a lecture on military systems and survival, evidence came from nuclear arsenals, institutional finance, ecological risk, and political judgment. No axiomatic framework could compel one response.

His mathematical reputation may have encouraged listeners to expect theorem-like certainty. That expectation was both asset and trap. A scientist can explain technical danger with authority; political choices still require values and collective consent. The prestige of proof does not transfer automatically to a program of action.

Grothendieck’s response, as later accounts describe it, was not to lower urgency. He widened the claim: researchers had to consider how institutions connected their work to military power and whether scientific activity diverted attention from survival. The argument challenged the professional division under which a mathematician proves theorems and a citizen votes or protests elsewhere.

The French title centered the scientist’s responsibility in the contemporary world. Its exact English translation remains unverified, so this account uses a descriptive gloss rather than a quoted translation. The argument, as summarized by later sources, concerned participation in laboratories, grants, prestige, education, and state policy as well as the content of particular research.2424Grothendieck, “Responsabilité du savant dans le monde d’aujourd’hui”, title; Jackson, “As If Summoned from the Void, II,” 1198–99.

This institutional idea connects the Orsay lecture to the IHÉS conflict without reducing one to the other. The board defended nondirected research. Grothendieck questioned whether nondirection exhausted responsibility. His lecture generalized the provenance test from one grant to a scientific system.

The typescript’s appendices, as Jackson summarizes them, also show that public communication was adversarial. Students mocked the celebrated geometer as part of the establishment. Their response denied him the outsider position he may have sought. He could leave IHÉS but could not instantly leave the social authority his mathematics had produced.

The mismatch is historically revealing. Grothendieck saw elite mathematics as a milieu he was leaving. Some activists saw him as a personification of its power. Social identity is relational: one cannot resign from how every audience locates one.

The lecture therefore began an apprenticeship as demanding as SGA redaction but with different feedback. A failed proof can be repaired by mathematics. A hostile audience may reject the premise, messenger, tactic, or institution. There is no unique correction.

Crystals after the breach

The Montréal thread continued into Messing’s work on crystals attached to Barsotti–Tate groups and interacted with Illusie’s deformation machinery and Berthelot’s crystalline theory. This chapter uses that chain only as evidence that mathematical work crossed the IHÉS departure; Chapter 47 gives the definitions, an example, and the attribution among Illusie, Messing, and Berthelot.2525Artin et al., “Alexandre Grothendieck 1928–2014, Part 2,” 405–6.

The congress as contested institution

An ICM is not only a collection of lectures. It allocates rooms, official booths, program time, and symbolic legitimacy. Publishers belong because books are part of professional exchange. Political groups may seek entry because assembled mathematicians are also workers, citizens, and recipients of public funds.

At Nice, the Survivre material placed war and ecological collapse inside a professional mathematical gathering. Organizers could share some concerns and still insist that unauthorized use of exhibition or street space violated commitments; Cartier’s recollection records precisely that tension.

Dieudonné’s role connected the institutional conflict to an earlier collaboration. He had spent years helping make Grothendieck’s mathematical program publishable and now held congress responsibilities tied to municipal arrangements. The sources establish those roles and the dispute, not a complete account of either man’s reasoning.

Later retellings delight in the dramatic contrast and can caricature both. Grothendieck becomes the pure rebel eager for arrest; Dieudonné the bureaucrat defending publishers. Cartier’s actual recollection is more complicated. He and others sympathetic to the politics tried to negotiate, and frustration arose because tactics endangered arrangements they had made.

The episode can be read beside the unsuccessful call for collective resignation as two documented cases in which colleagues who shared some concerns did not follow Grothendieck’s proposed action. This is a bounded comparison of outcomes, not a claim of identical motives.

The unofficial booth entered later memory through Cartier’s account. That persistence establishes the episode’s place in reception history; it does not measure political success.

Causes by type

The evidence supports organizing causes by type rather than selecting one.

Trigger: the April board decision to accept Ministry of the Armies funds contrary to Grothendieck’s stated condition. This is documented at high confidence.2626Institut des Hautes Études Scientifiques, Archives de l’IHÉS, minutes of the board meeting of April 22, 1970, A3.1.4.2.2/1.

Institutional background: budget pressure, mixed funding, a deteriorated relationship with Motchane, and disagreement over governance. Budget is documented; relationship deterioration has multiple testimonies; private motives remain uncertain.

Political trajectory: Moscow protest, Vietnam visit, antimilitarism, May 1968, nuclear danger, and emerging ecology. Actions and public events are documented; their relative causal weights are not.

Work trajectory: extensive investment, unfinished EGA/SGA/motives programs, and Grothendieck’s later critical account of that investment. Output and retrospective testimony are documented; no contemporaneous health conclusion follows.

Life history: statelessness, wartime displacement, his father’s anarchism, and solidarity with outsiders. Biographical facts are documented elsewhere in the book; their use as causal mechanisms requires Grothendieck’s own connection or cautious interpretation.

Interpersonal style: categorical standards, conflict, disappointment when colleagues did not follow, and tactics criticized by allies. Specific acts and recollections are documented; psychological diagnosis is prohibited.

The matrix prevents one level from swallowing another. The trigger explains timing. Political trajectory explains intelligibility. Work trajectory may explain readiness for revaluation. Life history offers background. Interpersonal style affects form. None is a universal motive beneath the others.

The categories also interact. Budget pressure made the grant practical; political trajectory made it intolerable; damaged trust made compromise harder; work intensity increased the stakes of leaving. “Interaction” is still interpretation, but it preserves plurality without claiming randomness.

A book may assign narrative emphasis while showing this hierarchy of confidence. The military-funding decision should carry the account of resignation. Broader causes should appear as attributed attempts to understand the larger life change.

Dates against mythology

Exact dates resist several myths.

The Moscow absence in 1966 resists the myth that politics began in 1970.

The April 1967 motives poster resists the myth that every great idea already existed in a finished book.

The November 1967 Vietnam report resists the myth that May 1968 alone awakened concern.

The December 10, 1969 budget and February 27, 1970 audit resist the myth that the grant conflict was purely symbolic.

The April 6 and April 22 sequence resists the myth of a one-day resignation.

The June 26 Orsay lecture resists the myth of slow, private withdrawal.

The July mathematical lectures resist the myth of instantaneous abandonment.

Dates do not explain; they prevent explanations from violating sequence. A cause must precede or coincide with what it causes. A retrospective interpretation must be labeled later. A publication date must not replace a seminar date.

Chronology is particularly important when a life is described through conversion. Conversion stories reorder earlier events as signs. The record instead shows commitments accumulating, coexisting, and changing weight.

The first afterlife of the summit

Grothendieck’s mathematical authority became political capital. Audiences came because of the summit. Journalists and students could not treat him as an unknown activist. The capital was not fully convertible: mathematical respect did not guarantee political agreement.

Former collaborators became custodians and independent creators. Their work ensured that the summit continued without its organizer. The result could look to Grothendieck like appropriation or abandonment and to them like mathematics proceeding.

IHÉS incorporated his legacy into its scientific identity while surviving his ethical rejection. Institutional memory can honor a departed critic without resolving the criticism. The archive’s publication of the April minutes now permits readers to see both.

The Fields Medal itself gained another afterlife. It became part of the contrast by which biographies measured his refusal of prestige. But he had accepted the award even while refusing the ceremony. Later he would decline the Crafoord Prize. These were different acts at different times and should not be collapsed into one timeless hostility to honors.

The motives program gained an afterlife through categories and conjectures. The standard conjectures remained open. Deligne proved Weil. Each development altered what “unfinished” meant.

These afterlives began before 1970 ended. The breach distributed one life into several histories that no longer moved together: IHÉS, algebraic geometry, motives, ecology, and Grothendieck’s later writings.

An ending without a scene

A conventional ending would place Grothendieck outside Bois-Marie, turn him away from the door, and describe a new road. No source supplies that scene, and the metaphor would be false. He returned to IHÉS on occasion. He occupied other elite posts. Mathematics continued. Relationships thinned unevenly.

The archival ending is less visual and more exact: a board resolution, two letters, a typescript title, and a summer-school memory. Paper follows paper while institutional belonging changes.

This Part has treated the summit through its products and the breach through its records. That symmetry is intentional. Fame and conflict both generate legends. Bibliography and administration give them friction.

The central mathematical works ask how different realizations relate to a common source. The central biographical lesson is that the sources do not collapse. Grothendieck’s memoir, a colleague’s recollection, an audit, and a board minute each retain their form.

The central ethical disagreement asks whether scientific work can be separated from the money and institutions supporting it. The record contains no shared answer. Grothendieck acted as though provenance made separation impossible. The board acted as though nondirection preserved it. Colleagues occupied positions between.

The central chronological correction is that rupture and continuity overlapped. Between the May decision and October departure, Grothendieck gave mathematical and public lectures. One history did not wait for the other to finish.

Part VIII begins inside that overlap. It will follow the movement rather than repeat the resignation, and it will let activism acquire its own evidence, collaborators, conflicts, and failures. The mathematician remains present, not as a credential pasted onto politics but as a person carrying a method into a domain where methods answer differently.

The door that closed was real. It had an institutional name, a budget, a board, and a date. The person who passed through it remained unfinished.

Rupture in slow time

Historians use rupture to mark a change in pattern. The word does not require every thread to snap simultaneously. Geological faults can move suddenly after long pressure; social lives can move visibly while old structures persist.

For Grothendieck, several clocks ran.

The employment clock changed in weeks: April conflict, May resignation.

The public clock changed in months: the June Orsay lecture and the later Nice congress dispute documented new public interventions.

The mathematical clock changed over years: continued lectures, Collège work, later intermittent research, and major manuscripts in the 1980s.

The professional-relations clock changed unevenly: some colleagues remained in contact, while later writings criticized others. The available sources do not support one date for a complete social break.

The retrospective clock appears in later writings that reorganize the meaning of earlier decades; it is not contemporaneous evidence for 1970.

Calling 1970 the turning point is accurate at the scale of employment and public priority. Calling it the end of mathematics is inaccurate at the scale of practice. Both statements can appear in sources because their temporal units differ.

This model also prevents pathologizing suddenness. The funding conflict supplied a concrete institutional trigger after documented political actions in 1966–1968; no mental-health explanation is required.

It prevents the opposite error of dissolving rupture into gradualism. The resignation had real consequences. Tuesday seminars no longer revolved around his permanent presence. The institute and mathematician could not return to the previous alignment simply because he still proved theorems.

The sources emphasize different records: board minutes document institutional conflict, the Orsay typescript documents public intervention, mathematical testimony documents continued lectures, and Grothendieck’s later memoir supplies retrospective meaning. The chapter identifies the scale and date of each claim rather than merging them.

What persistence proves

Evidence that Grothendieck continued mathematics has a limited logical role. It disproves immediate cessation. It does not prove that resignation was only symbolic, that activism was secondary, or that he intended a normal research career.

Evidence that IHÉS continued using and publishing his work disproves institutional erasure in a simple sense. It does not settle later complaints about credit or personal relation.

Grothendieck’s account that Serre proposed the position is evidence against total professional estrangement at that date. It does not prove agreement on the funding issue.2727Grothendieck, “Remous au Collège de France,” 1–4.

Evidence that Deligne remained and later proved Weil disproves dependence of the program on one person. It does not make Grothendieck’s departure mathematically inconsequential.

These limited inferences are a discipline against narrative totalization. Each fact closes one false path without dictating the whole road.

Persistence can itself change meaning. A mathematics lecture given while questioning science is not identical in personal significance to one given at the summit. A former collaboration continued through a text may no longer be a living relationship. Institutional memory can preserve work while excluding the critic’s policy demand.

The task is therefore to write continuity with verbs, not essences: he lectured, corresponded, proved, organized, criticized, returned. “He remained a mathematician” may be philosophically true and historically too broad.

What can be concluded

It can conclude that Grothendieck’s international mathematical standing was at its height in the late 1960s. Award, publications, seminar records, and testimony converge.

It can conclude that motives and standard conjectures were active, public programs, not later legends. It cannot conclude that their finished modern forms existed in his lectures.

It can conclude that EGA and SGA were collective works organized under unequal authority. It cannot settle every later claim of inadequate credit.

It can conclude that military-origin money formed a small documented share of IHÉS income and a material share of its immediate planning gap. It cannot infer a weapons project.

It can conclude that Grothendieck made refusal a condition, the board accepted the grant, the two letters recorded his decision and confirmation, and departure took effect October 1.

It can conclude that he continued serious mathematics after the decision and made documented public interventions. It cannot assign an exact date to the end of his identity as a mathematician.

It can conclude that colleagues differed. It cannot assign cowardice, betrayal, pathology, or venality without evidence.

These conclusions are intentionally bounded. A complete biography earns scope through limits.

A final measure of the breach

The breach can be measured in changed relations. At the summit, Grothendieck belonged to a shared seminar, institute, set of volumes, and program, even when authority was unequal. After resignation, the institute, former students, and mathematical world increasingly became entities he addressed from elsewhere.

Pronouns are not primary evidence unless quoted from exact texts. The observation is structural: institutional membership changed the relation between speaker and collective.

The former mathematical collective did not disappear. Mathematics continued to use his language, and he continued to speak to mathematicians. A person can belong to a history he rejects as a present milieu.

This doubleness is the final meaning of the door. It separated roles without sealing memory. Grothendieck stood outside the permanent institution and inside the mathematics it continued to house.

End date, not endpoint

The calendar end of this Part is 1970. The historical processes cross it. SGA volumes would appear later, Deligne’s proof lay ahead, and Grothendieck’s mathematical returns and later writings belonged to subsequent decades.

An endpoint would falsely settle those processes. An end date simply hands them to the next chronological owner.

Part X will eventually return to credit disputes in Récoltes et Semailles. It should refer back to the 1960s contribution ledger rather than reconstruct it from accusation. Part IX will treat teaching and intermittent mathematics after the activist years. Part VII has established the baseline those later parts need.

The last verified actions of 1970 belong to several worlds: a mathematical congress, public argument, a visiting academic position, and continued technical work. Any one used as the final image would oversimplify.

The proper ending is a chronology still branching. The permanent IHÉS line stops. Mathematical, political, relational, and spiritual lines continue at different speeds.

That is not refusal to conclude. It is the conclusion the evidence permits.

The year’s last significance lies in coexistence. A public critic of scientific institutions still depended on scientific audiences, taught motives, and moved through elite appointments while no longer remaining at IHÉS.

Coexistence looks inconsistent only under an expectation of instantaneous change. The documents instead show new public obligations stated while older mathematical practices continued.

The next years would resolve some overlaps through sharper withdrawal and create others through teaching and intermittent research. Those developments need their own dates. In 1970, the breach is complete at IHÉS and incomplete everywhere else.

The Part ends there: not with disappearance, but with institutional separation made durable. Mathematics continues in other hands and still in his; public protest broadens; the reasons remain layered. The door is historical because the records show what stood on each side.

One further caution belongs at the boundary. Later readers know the solitary village, the unpublished manuscripts, the spiritual writings, and the accusations against former colleagues. None was fully present in the summer of 1970. Hindsight can make the resignation the first scene of an ending already scripted. The documents instead show open alternatives: another prestigious appointment, live mathematical programs, new political allies, and continuing correspondence.

Open alternatives do not mean that every future was equally likely. They mean evidence at the date cannot borrow certainty from the outcome. A chronological biography must let 1970 remain a year whose participants did not know 2014.

Grothendieck’s own later narrative is part of that future knowledge. It gives the break meaning and names a turning point. The contemporary records give sequence and institutional fact. Holding them together without merging them is the final method of this Part.

The next Part may show paths narrowing. This one ends while they are still plural.