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Notes on a Path to AI Assistance in Mathematical Reasoning

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Alex Kontorovich

History and Overview · Submitted 4 Oct 2023

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The goal is to think through a path by which we might arrive at AI that is useful for the research mathematician.

how it is stated · speculative 0.66 read the record →

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arXiv ID2310.02896 (version 1)
Pith IDCLOVFOIW, Pith's permanent record of this paper and its review
CitationAlex Kontorovich. "Notes on a Path to AI Assistance in Mathematical Reasoning." arXiv:2310.02896 (2023). https://pith.science/paper/CLOVFOIW
Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,286 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.33 · human participants 0.11 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.02 · compares with prior results 0.02 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

These informal notes are based on the author's lecture at the National Academies of Science, Engineering, and Mathematics workshop on "AI to Assist Mathematical Reasoning" in June 2023. The goal is to think through a path by which we might arrive at AI that is useful for the research mathematician.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 These informal notes are based on the author's lecture at the National Academies of Science, Engineering, and Mathematics workshop on "AI to Assist Mathematical Reasoning" in June 2023. background 0.97 0.64 0.02 asserted 0.99
s1 The goal is to think through a path by which we might arrive at AI that is useful for the research mathematician. contribution 0.49 0.17 0.11 speculative 0.66

What kind of paper the classifier reports this is: position or commentary 1.00 · evidence from argument 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

These informal notes are based on the author's lecture at the National Academies of Science, Engineering, and Mathematics workshop on "AI to Assist Mathematical Reasoning" in June 2023. The goal is to think through a path by which we might arrive at AI that is useful for the research mathematician.

Human review

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How the literature uses it

What this paper does with the arXiv papers it cites

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

What it cites · 5 sentences without a confident label

Cites as support 2 papers
  • Three vignettes to illustrate this are: * It took two years from Ellenberg-Gijswijt's 2017 solution [ref] of the Cap Set Conjecture to its 2019 formalization [ref] . * It took one year from Gardam's 2021 counterexample [ref] to Kaplansky's unit conjecture for group rings to its 2022 formalization [ref] . * The formalization [ref] of Bloom's solution [ref] to the Edros-Graham density conjecture on Egyptian unit fractions arrived before its referee reports!

    On a density conjecture about unit fractions · Paths to Large Datasets of Formalized Mathematics · 0.96

  • AI has also already proved somewhat effective here; see, e.g., [ref] , and the more recent discovery [ref] of murmurations in the Fourier coefficients of elliptic curves.

    Murmurations of elliptic curves · Finding a Holy Grail · 0.98

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