Differential Equations and Algebraic Transcendents : French efforts at the creation of a Galois Theory of Differential Equations 1880-1910
Bibliographic record
Abstract
— A “Galois theory” of differential equations was first proposed by Emile Picard in 1883. Picard, then a young mathematician in the course of making his name, sought an analogue to Galois’s theory of polynomial equations for linear differential equations with rational coefficients. His main results were limited by unnecessary hypotheses, as was shown in 1892 by his student Ernest Vessiot, who both improved Picard’s results and altered his approach, leading Picard to assert that his lay closest to the path of Galois. The subject became interesting to a number of French researchers in the next decade and more, most importantly Jules Drach, whose flawed 1898 doctoral thesis led to a further reworking of the subject by Vessiot. The present paper recounts these events, looking at the tools created and at the interpretation of the Galois legacy manifest in these different attempts. Resume (Equations differentielles et transcendants algebriques : les efforts francais sur la creation d’une theorie de Galois pour les equations differentielles 1880–1910) Une « theorie de Galois » pour les equations differentielles a ete creee pour la premiere fois par Emile Picard en 1883. Picard, a cette epoque un jeune mathematicien qui cherchait faire une reputation, a faconne une theorie analogue a celle des equations algebriques de Galois pour les equations differentielles lineaires a coefficients rationnels. Ses resultats etaient limites par des hypotheses superflues, un fait demontre en 1892 par son eleve Ernest Vessiot, qui a ameliore les resultats de Picard en modifiant son approche. Texte recu le 5 mai 2011, accepte le 16 juin 2011. T. Archibald, Dept. of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby, British Columbia V5A 1S6 (Canada). Courrier electronique : tarchi@math.sfu.ca Thanks are due to the Archives Henri Poincare of the Universite Nancy 2, Nancy, France, for hosting a visit during which most of this paper was written. I thank the referees and the comite de redaction of the RHM for helpful comments. Thanks are also due to my Department and Simon Fraser University for ongoing support. © SOCIETE MATHEMATIQUE DE FRANCE, 2011
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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 | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.004 | 0.002 |
| Science and technology studies | 0.003 | 0.009 |
| Scholarly communication | 0.004 | 0.003 |
| Open science | 0.000 | 0.002 |
| Research integrity | 0.001 | 0.004 |
| Insufficient payload (model declined to judge) | 0.003 | 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".