Bibliographic record
Abstract
Computer Algebra Systems (CAS) provide sophisticated functionality to assist with mathematical problem solving. Despite their widespread adoption, however, little work in the HCI community has examined the extent to which these computational tools support domain experts. In this paper, we report findings from a qualitative study investigating the work practices and tools of nine mathematicians in a research setting. Counter to our expectations, our data suggests that computational tools play only a minor role in their workflow, with the limited use of CAS owing primarily to four factors: (1) the need for transparency in CAS's reasoning to explain computed results; (2) the problem of rigidity and formality in CAS's input/output style dialogue; (3) the need for 2D input to support a wide range of annotations, diagrams, and in-place manipulation of objects of interest; and (4) the need for collaboration, particularly in early stages of problem solving. While grounded in the study of mathematicians, these findings (particularly the first) have implications for the design of computational systems intended to support complex problem solving.
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 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 | 0.020 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.006 | 0.004 |
| Scholarly communication | 0.006 | 0.008 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.096 | 0.036 |
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".