ARC Corpus · Volume 6

The History of Proof

The trial, the lineage of zero, the two Eulers, Gauss's drawer and the undecidable why

« Le comment contient le pourquoi. »

Filipe Bastos

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Abstract

What the ARC corpus says about proof: what it is, what it forgot, how it was received, who showed their proofs and who kept them in a drawer, and why the question of why never receives an answer. The volume follows the line of ten moves, from Hippasus to Copenhagen, through Aristotle, Stevin, Viète, Descartes, Newton and Leibniz, Gauss, Napoleon, Fourier and Boltzmann. Its main piece, The Trial of Proof, is given in full: indictment, investigation, judgement, numbered exhibits and falsifiable predictions. It continues with the undecidable why, the lineage of zero, the two Eulers, Gauss's drawer and the problem that created the problem. The author's rule governs every page: the corpus dates moves, it does not judge people.

Keywords: history of mathematics, proof, zero, Euler, Gauss, Stevin, epistemology

The chapters themselves are in French. Open any chapter and use the Translate links in the header for a machine translation; the abstract and the table of statements on this page are translated by hand.

Résumé (français)

Ce que le corpus ARC dit de la preuve : ce qu'elle est, ce qu'elle a oublié, comment elle a été reçue, qui a montré ses preuves et qui les a gardées dans un tiroir, et pourquoi la question du pourquoi ne reçoit jamais de réponse. Le volume suit la lignée des dix gestes, d'Hippase à Copenhague, en passant par Aristote, Stevin, Viète, Descartes, Newton et Leibniz, Gauss, Napoléon, Fourier et Boltzmann. Sa pièce maîtresse, le Procès de la Preuve, est versée en entier : acte d'accusation, instruction, jugement, dossier coté et prédictions falsifiables. Suivent le pourquoi indécidable, la lignée du zéro, les deux Euler, le tiroir de Gauss et le problème qui a créé le problème. La règle de l'auteur gouverne chaque page : le corpus date des gestes, il ne juge pas des hommes.

Keywords: histoire des mathématiques, preuve, zéro, Euler, Gauss, Stevin, épistémologie

Contents

  1. Foreword
  2. Chapter 1. The thread of the volume: the lineage of the ten gestures
    • 1.1 The single charge
    • 1.2 The lineage read backwards, as the author found it
    • 1.3 The lineage read forwards
    • 1.4 The four gestures this volume does not detail elsewhere
    • 1.5 What the lineage does not say
  3. Book One. The Trial of Proof
  4. Chapter 2. Preface and indictment (Part 0)
    • Preface: how to read this trial
    • §0.1 The reversal, stated as fact
    • §0.2 The door: the 1-9 is not a base
    • §0.3 The attraction: the how drawn in by the why
    • §0.4 The single charge
    • §0.5 The scope: the amputation did not stay within mathematics
    • §0.6 The second door: the Fundamental Figure
  5. Chapter 3. What a proof is, and what it has forgotten (Part 1)
    • §1.1 What proof claims to be
    • §1.2 What proof has forgotten
    • §1.3 Coherence is prior to the tool
    • §1.4 The admission: proof signed its own dismissal
  6. Chapter 4. The false calibrations: anatomy of a dismemberment (Part 2)
    • §2.1 Why an anatomy, not a history
    • §2.2 The smiths: Aristotle and Euclid
    • §2.3 The circle: Pythagoras, Gauss
    • §2.4 The triangle: Hippasus, and the lineage of substantification
    • §2.5 The number: Stevin, Newton
    • §2.6 Reality: Galileo and Descartes, Darwin, Copenhagen
    • §2.7 The complete anatomy
  7. Chapter 5. Proof judged by coherence (Part 3)
    • §3.1 The criterion of the trial
    • §3.2 Where "dismissed" becomes "literally false"
    • §3.3 The key exhibit: the formulas of chaos
    • §3.4 Consequences unfolded: the restored grammar makes the mysteries trivial
    • §3.5 The structural verdict on Copenhagen
    • §3.6 The last defense: the objection of success
    • §3.7 Synthesis of the judgment: the unified law
  8. Chapter 6. The grammar that precedes proof (Part 4)
    • §4.1 What was there before, and survives
    • §4.2 The seven derivations of k_arc
    • §4.3 The Fundamental Figure: √2 links 2π and reveals φ
    • §4.4 The three rails
    • §4.5 The two-faced object: "Theorem 4.1"
    • §4.6 Why this grammar cannot be proved, and why that is its strength
  9. Chapter 7. Inversion as method (Part 5)
    • §5.1 Judging the judge is not a trick: it is φ
    • §5.2 The tested precedent
    • §5.3 The death of the why with intention
    • §5.4 The bare why, saudade, and the posture that does not cut
  10. Chapter 8. What the restoration opens (Part 6)
    • §6.1 Not a correction of modernity: a restoration
    • §6.2 Consciousness
    • §6.3 Tension
    • §6.4 Energy: E = Dc², the inversion applied to Einstein
    • §6.5 The cosmological descents
    • §6.6 The living and the world of 6
    • §6.7 The paving, medicine, institutions, death
    • §6.8 The end of the integral: weighing the beach
    • §6.9 Four enigmas the grammar reorganizes
  11. Chapter 9. The pathogenic trinity, and the closing before the jury (Parts 7 and 8)
    • §7.1 Substantification is an epistemic inflammation
    • §7.2 The pathogenic trinity: unknown, fear, inflammation
    • §7.3 The Portuguese, masters of the unknown: the model of peace
    • §7.4 Happiness is a path, not an address
    • §7.5 Peace as restoration of the how
    • §8 Closing: the jury
  12. Chapter 10. The numbered file and the predictions of the Trial
    • 10.1 Appendix A of the Trial: the file references
    • 10.2 Appendix B of the Trial: the falsifiable predictions
  13. Book Two. The why and the walk
  14. Chapter 11. The undecidable why: an anthology of the philosophy of how
    • I. The question without an object: the undecidable why
    • II. The grammar of knowledge: the philosophy of how
    • III. Proofs while walking
    • IV. Death and nothingness: the same error
    • V. Closing: what the anthology demands
    • What the anthology's script verifies
  15. Chapter 12. The problem that created the problem: Hippasus, the undecidable why, and the two objects never touched
    • I. The incident: what really happened
    • II. The undecidable why: anatomy of the demand
    • III. The how: learning while walking
    • IV. The two objects never touched: death and nothingness
    • V. The junction: a single matrix, five monsters
    • VI. Statuses and prediction
  16. Book Three. The dates reread
  17. Chapter 13. The lineage of zero: eight dates reread
    • 13.1 628, Brahmagupta, *Brāhmasphuṭasiddhānta*, chapter 18
    • 13.2 1202, Fibonacci, *Liber Abaci*
    • 13.3 1494, Luca Pacioli, *Summa de arithmetica*
    • 13.4 1585, Simon Stevin, *De Thiende*
    • 13.5 1748, Leonhard Euler, *Introductio in analysin infinitorum*
    • 13.6 1801, Carl Friedrich Gauss, *Disquisitiones Arithmeticae*, article 1
    • 13.7 1889, Giuseppe Peano, *Arithmetices principia, nova methodo exposita*
    • 13.8 1908, Giuseppe Peano, *Formulario mathematico*
    • 13.9 The lineage in one line
    • 13.10 What this piece does not say
    • 13.11 Engravings for the Register of Errors (version 1.2)
  18. Chapter 14. The two Eulers: what he counted, what he let slip
    • Recto. Euler the counter
    • Verso. Euler who lets slip
  19. Chapter 15. Gauss's drawer: a dated file of priorities claimed without proof shown
    • 15.1 The criterion
    • 15.2 The six files
    • 15.3 What the file establishes
    • 15.4 What the file does not settle, and what would settle it
    • 15.5 Sources of the dates
  20. Chapter 16. The book of zero and remainders: plan and readings
    • 16.1 Prologue: zero and its disciples
    • 16.2 First part: the world before the cut
    • 16.3 Second part: six gestures
    • 16.4 Third part: the consequences
    • 16.5 Fourth part: the restoration
  21. Book Four. The genealogy and the defense
  22. Chapter 17. The civilizational butchery: Pythagoras, Heraclitus, Parmenides, Nāgārjuna, Hume, and the ghosts that remain
    • 17.1 Pythagoras and the native reading
    • 17.2 The post-Pythagorean bifurcation
    • 17.3 Hume and the resolution of causality
    • 17.4 The ontological chain restored
    • 17.5 Desire as recognition, and the true engines
    • 17.6 The active butchery and its ghosts
    • 17.7 Coda: genealogy as regularization
  23. Chapter 18. Killing the sophisms: a manual for neutralizing the operations that castrate
    • 18.1 Why a book against the sophists
    • 18.2 Anatomy of the sophism
    • 18.3 Twenty standard sophisms
    • 18.4 The psychology of the sophist
    • 18.5 The sophisms expected against the corpus
    • 18.6 The riposte
    • 18.7 Silence: when the sophism deserves no answer
    • 18.8 The sacrificed generations
  24. Chapter 19. The technical file of the Quantum Bible, recalculated
    • 19.1 The seven derivations of k_arc according to the Quantum Bible
    • 19.2 The verification tables, redone
    • 19.3 The annotated bibliography
    • 19.4 The six falsifiable validation protocols
  25. Appendix A: Table of statements
  26. Appendix B: Withdrawals and corrections
    • B.1 Corrections carried by the sources
    • B.2 Contradictions between sources, settled
    • B.3 Withdrawals from the old table of contents (chapter 16)
    • B.4 Statuses downgraded or requalified
    • B.5 Figures corrected after recalculation
    • B.6 Historical facts corrected
    • B.7 Withdrawals of form
  27. Appendix C: Merged sources
  28. Appendix D: Verifications redone
  29. Colophon

Version 1.0, octobre 2026 · 73 419 mots · 170 pages · Licence CC BY 4.0