Sage (version 3.4); The Princeton Companion To Mathematics
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
To the uninitiated, this statement might sound unimpressive, or even obvious, but the readers of SIAM Review will clearly recognize the challenges of representing the infinite and the continuous in a machine that is finite and discrete.For example, consider just the vagaries of floating-point arithmetic.A better description, which concisely captures the essence of Sage, comes from the project's mission: "Creating a viable free open-source alternative to Magma, Maple, Mathematica and Matlab."While Sage continues to improve and expand at a dramatic pace, it has come a long way toward meeting its goals.Stable and fast algorithms are provided for much of the mathematical universe, including symbolic, exact, numerical, and graphical capabilities.A notebook interface runs in a web browser and provides a convenient and productive environment for using all of Sage's features.The user and developer communities have also expanded dramatically.All of this is based on open-source software, open standards, and an open development process.Borne of his frustration with proprietary programs providing similar functionality, William Stein founded Sage in 2005 and continues to lead the project.He wondered how one could rely on software for research in mathematics with little or no knowledge of the algorithms and code producing those results.He believed rapid progress in scientific research had always been predicated on an open exchange of ideas, and so should it be with software for mathematics.Since 2005 the project has attracted a very large user community, as measured by these recent monthly statistics provided by Harald Schilly, the Sage web site and forum manager: 2,000 forum posts generated and viewed by the 2,000 forum members, 6,000 downloads of the program, and 60,000 visits to the web site.Contributors to the code are an international group numbering 150, while at any one time roughly 40 of these developers are working assiduously on projects or improvements.
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 | 0.001 | 0.001 |
| 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 | 0.000 |
| Research integrity | 0.000 | 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