La vision unificatrice de Grothendieck : au-delà de l’unité (méthodologique ?) des mathématiques de Lautman
Bibliographic record
Abstract
Dans sa thèse complémentaire intitulée « Essai sur l’unité des sciences mathématiques dans leur développement actuel » Albert Lautman analysa la question de l’unité des mathématiques en considérant différentes paires antithétiques de concepts mathématiques, notamment le continu et le discret. Dans le cadre de sa refonte de la géométrie algébrique abstraite, le mathématicien français Alexandre Grothendieck considéra également l’opposition traditionnelle du continu et du discret selon un cadre conceptuel fort similaire à celui de Lautman. En comparaison, l’introduction du concept de topos lui permit de donner une réponse strictement mathématique et parfaitement claire à cette question.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.003 | 0.025 |
| Scholarly communication | 0.007 | 0.014 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.002 | 0.007 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".