Aux origines de l’analyse infinitésimale : un calcul certain aux principes incertains ?
Bibliographic record
Abstract
On attribue régulièrement aux mathématiques un statut privilégié, celui d’une science pouvant prétendre à une certitude qu’aucune autre forme de connaissance ne saurait atteindre. Pendant une longue période, cette certitude fut historiquement fondée sur la géométrie euclidienne et l’arithmétique des entiers naturels. Le développement de l’algèbre ordinaire, puis du calcul infinitésimal, firent toutefois apparaître des difficultés, voire des contradictions internes qui exigèrent de caractériser en termes nouveaux le caractère certain de ces algorithmes. Tout se passait comme si des résultats certains se trouvaient déduits de principes incertains, voire absurdes. Cet article se propose d’aborder la question de la certitude mathématique à l’aune de ses caractérisations historiques et de tenter de déterminer plus spécifiquement les modèles et les solutions qui se sont affrontés lors des débats et remises en question sur ce sujet, que la naissance du calcul infinitésimal a engendrés à la fin du xvii e siècle.
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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 | 0.003 | 0.011 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.015 |
| Scholarly communication | 0.004 | 0.009 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.004 |
| Insufficient payload (model declined to judge) | 0.004 | 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".