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Record W4391845938 · doi:10.1090/bull/1826

Proof in the time of machines

2024· article· en· W4391845938 on OpenAlexafffund
Andrew Granville

Bibliographic record

VenueBulletin of the American Mathematical Society · 2024
Typearticle
Languageen
FieldComputer Science
TopicLogic, programming, and type systems
Canadian institutionsUniversité de Montréal
FundersNatural Sciences and Engineering Research Council of Canada
KeywordsMathematical proofComputer-assisted proofProof of conceptProof complexityComputer scienceAnalytic proofProof assistantBurden of proofProof theoryStructural proof theoryTheoretical computer scienceCalculus (dental)MathematicsAutomated theorem provingMedicine

Abstract

fetched live from OpenAlex

We are concerned here with the nature of proof and what proof will become in this age of machines. We do so by comparing the values associated with (traditional) community based proof verification to those associated with computer proof verification. We finish by proposing ways that computer proofs might incorporate successful strategies from human experiences.

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 imitation

Not 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.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.873
Threshold uncertainty score0.206

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0010.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

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.

Opus teacher head0.012
GPT teacher head0.248
Teacher spread0.236 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it

Classification

machine, unvalidated

Machine predicted; a candidate call from one teacher head, not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
Study designTheoretical or conceptual
Domainnot available
GenreEmpirical

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".

Quick stats

Citations4
Published2024
Admission routes2
Has abstractyes

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