Mapping the Mind: Techniques for Structuring and Interpreting Grothendieck's Evolving Mathematical Thought in His Notes

 This paper presents a methodological framework for the systematic analysis and interpre
tation of complex, often unstructured and difficult-to-decipher handwritten mathematical
 notes, using Alexander Grothendieck’s personal manuscripts (notably the “Cote 115” pages
 on topos theory and functorial correspondences) as a primary case study. We propose a
 multi-stage pipeline combining (1) high-resolution imaging and legibility enhancement; (2)
 thematic coding and provenance tracing across drafts and marginalia; (3) diagrammatic
 reconstruction, using bicategorical and ∞-categorical templates when appropriate; (4) for
mal reconstruction of nascent concepts (for example, candidates for adjointability or span
 compositions); and (5) comparative validation against extant publications and archival scans.
 The framework emphasises concrete techniques for handling illegible passages (confidence
weighted transcription, multi-expert voting, and pen-stroke clustering), for identifying
 conceptual evolution (chronological layering and dependence graphs), and for tracing in
terconnections between marginalia and main text (cross-referential anchors, concordance
 indices). It further develops procedures for reconstructing nascent mathematical ideas — such
 as adjointability conditions, span-composition heuristics, and proto-bicategorical diagrams —
 by combining diagrammatic inference with minimal formalization hypotheses that can be
 iteratively refined.
 To demonstrate the methods we present a detailed case study of proposed adjointability
 and span-composition notes in Cote 115, showing step-by-step how fragmented notations and
 sketches can be turned into coherent bicategorical diagrams and working conjectures. Finally,
 we discuss the generalizability of these techniques to other working mathematicians’ archives
 and argue that the pipeline supports both historical interpretation and the identification
 of fertile leads for current mathematical development. The primary objective of this work
 is two-fold: to inspire academic inquiry into Grothendieck’s notes, and to provide a novel
 methodological technique to facilitate productive research of these materials. It is our goal
 that this paper will stimulate new research and provide a framework that allows scholars to
 analyze Grothendieck’s notes, yielding robust and insightful findings in the future.