Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
The authors have been using a largely algebraic form of "computational discovery" in various undergraduate classes at their respective institutions for some decades now to teach pure mathematics, applied mathematics, and computational mathematics.This paper describes what we mean by "computational discovery," what good it does for the students, and some specific techniques that we used.1 Setting the stage "The imparting of factual knowledge is for us a secondary consideration.Above all we aim to promote in the reader a correct attitude, a certain discipline of thought, which would appear to be of even more essential importance in mathematics than in other scientific disciplines."Pólya & Szegő vol I. [28, p. VII]The preface quoted above from the classic book cited, which is nearly a hundred years old now, opens with an epigraph which we further paraphrase, as follows: "What is good education?Giving students systematic opportunities to discover things for themselves."Indeed, Computational Discovery, also called "Experimental Mathematics," is also very familiar to the research mathematician, not just mathematics educators: nearly everyone uses it (even if they say that they don't, or don't say that they do).There can be no shame in it, if the likes of Gauss and Euler used the technique [6,7].See also the excellent book [14].The most basic idea is, after all, very simple: one computes a few cases, tries to guess a pattern, and if successful,
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.
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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it