Bibliographic record
Abstract
The title of this lecture alludes to Ribenboim’s delightful treatise on Fermat’s Last Theorem [Rib1]. Fifteen years after the publication of [Rib1], Andrew Wiles finally succeeded in solving Fermat’s 350-year-old conundrum. That same year, perhaps to console himself of Fermat’s demise, Ribenboim published a second book, this time on Catalan’s conjecture that there are no consecutive perfect powers other than 8 and 9. As we have learned at this Congress, Preda Mihailescu has just disposed of this conjecture as well. His breakthrough comes only 8 years after the publication of Ribenboim’s book on Catalan’s equation. Such is the magic of Ribenboim’s books: the age-old problems which they treat have invariably been solved, in comparatively short order! So it is with some eagerness that we await the publication of Ribenboim’s next tome (hoping it will be devoted to the Riemann Hypothesis, or the Birch and Swinnerton-Dyer conjecture...) This “fourteenth lecture” is meant as a tribute both to Ribenboim and to the spirit of Fermat: the fascination with concrete Diophantine problems, especially those that draw us, seemingly inexorably, to central topics in the subject (cyclotomic fields, elliptic curves, reciprocity laws, modular forms...)
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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; both teacher heads agree on what is shown here.
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".