pith. machine review for the scientific record. sign in

arxiv: 2604.17484 · v1 · submitted 2026-04-19 · 💻 cs.IR · cs.LG

Recognition: unknown

Matlas: A Semantic Search Engine for Mathematics

Haocheng Ju , Leheng Chen , Peihao Wu , Bryan Dai , Bin Dong
Authors on Pith no claims yet

Pith reviewed 2026-05-10 05:29 UTC · model grok-4.3

classification 💻 cs.IR cs.LG
keywords semantic searchmathematical statementstheorem retrievaldependency extractionnatural language queriesmathematical corpusknowledge retrieval
0
0 comments X

The pith

Matlas builds a semantic search engine over 8 million extracted mathematical statements using natural language queries.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces Matlas as a system that extracts mathematical statements along with their dependencies from hundreds of thousands of papers and textbooks. It then uses document-level dependency graphs to unfold those statements in topological order, creating versions that stand more independently. On this corpus the authors layer a semantic retrieval method so that ordinary language questions can surface relevant mathematical results. A reader would care if this works because it directly tackles the scattered and context-dependent nature of mathematical literature, potentially speeding up checks for prior work and supplying references for AI math tools.

Core claim

Matlas is a semantic search engine for mathematical statements built on a corpus of 8.07 million statements extracted from 435K peer-reviewed papers and 1.9K textbooks, where statements and dependencies are assembled into document-level graphs and then recursively unfolded in topological order to yield more self-contained representations that support efficient natural language retrieval.

What carries the argument

Automated extraction of statements together with their dependencies, followed by topological unfolding via document-level graphs to produce self-contained forms for semantic retrieval.

If this is right

  • Mathematicians can check whether a given result already exists by entering a plain-language description rather than formal notation.
  • Related results and historical origins become locatable through semantic similarity instead of exact keyword matches.
  • AI systems for mathematics receive a large structured corpus that can ground their outputs against existing literature.
  • Overall retrieval time for mathematical knowledge decreases because context is supplied automatically through unfolding.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Linking the search results to formal proof assistants could let users verify whether a retrieved statement applies in a new setting.
  • Patterns in query logs over time might highlight which mathematical areas are most actively explored or overlooked.
  • Extending the corpus to include extracted proofs alongside statements could support queries about derivation methods rather than just final claims.

Load-bearing premise

That the automated extraction and unfolding process yields statements whose meaning is sufficiently accurate and complete for reliable matching against natural language queries.

What would settle it

Measure precision at rank 5 or 10 when mathematicians pose natural language descriptions of known theorems and check how often the exact matching statement appears in the top results.

read the original abstract

Retrieving mathematical knowledge is a central task in both human-driven research, such as determining whether a result already exists, finding related results, and identifying historical origins, and in emerging AI systems for mathematics, where reliable grounding is essential. However, the scale and structure of the mathematical literature pose significant challenges: results are distributed across millions of documents, and individual statements are often difficult to interpret in isolation due to their dependence on prior definitions and theorems. In this paper, we introduce Matlas, a semantic search engine for mathematical statements. Matlas is built on a large-scale corpus of 8.07 million statements extracted from 435K peer-reviewed papers spanning 1826 to 2025, drawn from a curated set of 180 journals selected using an ICM citation-based criterion, together with 1.9K textbooks. From these sources, we extract mathematical statements together with their dependencies, construct document-level dependency graphs, and recursively unfold statements in topological order to produce more self-contained representations. On top of this corpus, we develop a semantic retrieval system that enables efficient search for mathematical results using natural language queries. We hope that Matlas can improve the efficiency of theorem retrieval for mathematicians and provide a structured source of grounding for AI systems tackling research-level mathematical problems, and serve as part of the infrastructure for mathematical knowledge retrieval.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper introduces Matlas, a semantic search engine for mathematical statements. It extracts 8.07 million statements from 435K peer-reviewed papers (1826–2025) across 180 journals and 1.9K textbooks, builds document-level dependency graphs, recursively unfolds statements in topological order to produce self-contained representations, and implements a semantic retrieval system supporting natural-language queries over the resulting corpus.

Significance. If the extraction and unfolding steps produce sufficiently accurate and complete statements, the resulting corpus and retrieval system could serve as valuable infrastructure for theorem retrieval by mathematicians and as grounding data for AI systems performing research-level mathematics. The reported scale is substantial and the dependency-unfolding approach directly targets a known difficulty with isolated mathematical statements.

major comments (2)
  1. [Abstract] Abstract: the central claim that Matlas 'enables efficient search for mathematical results using natural language queries' is unsupported by any quantitative evidence. The manuscript describes the pipeline and corpus size but reports no retrieval metrics (precision, recall, nDCG), no baseline comparisons, no error analysis of the extraction or unfolding stages, and no user studies, leaving the effectiveness claim without direct substantiation.
  2. [Pipeline description] Pipeline description: the recursive unfolding step that produces 'more self-contained representations' is load-bearing for the utility of the corpus, yet the text supplies no measured accuracy for statement extraction, dependency-graph construction, or topological unfolding fidelity. Without such validation, it is impossible to determine whether retrieval operates on reliable content or on propagated parsing artifacts.
minor comments (2)
  1. [Abstract] The date range '1826 to 2025' includes a future year; clarify the actual cutoff date of the corpus.
  2. The manuscript would benefit from an explicit related-work section comparing Matlas to prior mathematical search engines, theorem databases, and semantic retrieval systems in IR.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback and positive assessment of Matlas's potential value as infrastructure for mathematical knowledge retrieval. We address each major comment below and commit to revisions that directly incorporate the requested evidence.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that Matlas 'enables efficient search for mathematical results using natural language queries' is unsupported by any quantitative evidence. The manuscript describes the pipeline and corpus size but reports no retrieval metrics (precision, recall, nDCG), no baseline comparisons, no error analysis of the extraction or unfolding stages, and no user studies, leaving the effectiveness claim without direct substantiation.

    Authors: We agree that the abstract's effectiveness claim requires quantitative support, which is absent from the current version. The manuscript prioritizes describing the corpus construction at scale (8.07M statements, dependency graphs, and topological unfolding). In the revised manuscript we will add a dedicated evaluation section reporting retrieval metrics (precision@K, recall@K, nDCG) on a held-out query set, baseline comparisons (e.g., BM25 and standard embedding retrieval without unfolding), and error analysis of extraction/unfolding stages via manual annotation of random samples. We will also outline plans for future user studies with mathematicians. These additions will directly substantiate the claims. revision: yes

  2. Referee: [Pipeline description] Pipeline description: the recursive unfolding step that produces 'more self-contained representations' is load-bearing for the utility of the corpus, yet the text supplies no measured accuracy for statement extraction, dependency-graph construction, or topological unfolding fidelity. Without such validation, it is impossible to determine whether retrieval operates on reliable content or on propagated parsing artifacts.

    Authors: We concur that validation of the pipeline components is essential given the load-bearing role of unfolding. The current text describes the methods but omits accuracy measurements. In revision we will add quantitative validation: precision/recall for statement extraction on annotated samples, accuracy of dependency identification in the graphs, and fidelity of unfolding (manual verification of completeness and absence of artifacts on a stratified sample of statements). These metrics will be reported with methodology details so readers can assess corpus reliability. revision: yes

Circularity Check

0 steps flagged

No circularity: systems paper with no derivation chain or predictions

full rationale

The paper describes a pipeline for extracting 8.07M statements from papers and textbooks, building document-level dependency graphs, recursively unfolding statements, and enabling natural-language semantic retrieval. No equations, fitted parameters, predictions, or first-principles derivations are claimed. The contribution is the construction and indexing of the corpus itself; nothing reduces by construction to its own inputs. Self-citations are absent from the provided text, and the work is self-contained as an engineering description without load-bearing self-referential steps.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that mathematical statements and dependencies can be reliably extracted at scale from text; no free parameters or invented entities are introduced.

axioms (1)
  • domain assumption Mathematical statements and their dependencies can be accurately extracted from peer-reviewed papers and textbooks at scale.
    Invoked in the corpus construction step to produce self-contained representations.

pith-pipeline@v0.9.0 · 5538 in / 1120 out tokens · 35072 ms · 2026-05-10T05:29:06.336830+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

13 extracted references · 12 canonical work pages · 3 internal anchors

  1. [1]

    Semantic search over 9 million mathematical theorems.arXiv preprint arXiv:2602.05216, 2026

    Luke Alexander, Eric Leonen, Sophie Szeto, Artemii Remizov, Ignacio Tejeda, Jarod Alper, Giovanni Inchiostro, and Vasily Ilin. Semantic search over 9 million mathematical theorems.arXiv preprint arXiv:2602.05216, 2026

    work page arXiv 2026

  2. [2]

    Leanexplore: A search engine for lean 4 declarations.arXiv preprint arXiv:2506.11085,

    Justin Asher. LeanExplore: A Search Engine for Lean 4 Declarations.arXiv preprint arXiv:2506.11085, 2025

    work page arXiv 2025

  3. [3]

    Eigenweights for arithmetic hirzebruch proportionality.arXiv preprint arXiv:2601.23245, 2026

    Tony Feng. Eigenweights for arithmetic Hirzebruch Proportionality.arXiv preprint arXiv:2601.23245, 2026

    work page arXiv 2026

  4. [4]

    Aletheia tackles FirstProof autonomously.arXiv preprint arXiv:2602.21201, 2026

    Tony Feng, Junehyuk Jung, Sang-hyun Kim, Carlo Pagano, Sergei Gukov, Chiang-Chiang Tsai, David Woodruff, Adel Javanmard, Aryan Mokhtari, Dawsen Hwang, et al. Aletheia tackles FirstProof autonomously.arXiv preprint arXiv:2602.21201, 2026

    work page arXiv 2026

  5. [5]

    Towards Autonomous Mathematics Research.arXiv preprint arXiv:2602.10177, 2026

    Tony Feng, Trieu H Trinh, Garrett Bingham, Dawsen Hwang, Yuri Chervonyi, Junehyuk Jung, Joonkyung Lee, Carlo Pagano, Sang-hyun Kim, Federico Pasqualotto, et al. Towards Autonomous Mathematics Research.arXiv preprint arXiv:2602.10177, 2026

    work page arXiv 2026

  6. [6]

    A Semantic Search Engine for Mathlib4

    Guoxiong Gao, Haocheng Ju, Jiedong Jiang, Zihan Qin, and Bin Dong. A Semantic Search Engine for Mathlib4. In Yaser Al-Onaizan, Mohit Bansal, and Yun-Nung Chen, editors,Findings of the Association for Computational Linguistics: EMNLP 2024, pages 8001–8013, Miami, Florida, USA, November 2024. Association for Computational Linguistics. doi: 10.18653/v1/2024....

    work page doi:10.18653/v1/2024.findings-emnlp.470 2024

  7. [7]

    Automated Conjecture Resolution with Formal Verification

    Haocheng Ju, Guoxiong Gao, Jiedong Jiang, Bin Wu, Zeming Sun, Leheng Chen, Yutong Wang, Yuefeng Wang, Zichen Wang, Wanyi He, et al. Automated Conjecture Resolution with Formal Verification.arXiv preprint arXiv:2604.03789, 2026

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  8. [8]

    Lower bounds for multivariate independence polynomials and their generalisa- tions

    Joonkyung Lee and Jaehyeon Seo. Lower bounds for multivariate independence polynomials and their generalisa- tions. arXiv preprint arXiv:2602.02450, 2026

    work page arXiv 2026

  9. [9]

    DeepSeek-V3.2: Pushing the Frontier of Open Large Language Models

    Aixin Liu, Aoxue Mei, Bangcai Lin, Bing Xue, Bingxuan Wang, Bingzheng Xu, Bochao Wu, Bowei Zhang, Chaofan Lin, Chen Dong, et al. DeepSeek-V3.2: Pushing the Frontier of Open Large Language Models.arXiv preprint arXiv:2512.02556, 2025

    work page internal anchor Pith review arXiv 2025

  10. [10]

    Lean Finder: Semantic Search for Mathlib That Understands User Intents

    Jialin Lu, Kye Emond, Weiran Sun, and Wuyang Chen. Lean Finder: Semantic Search for Mathlib That Understands User Intents. In2nd AI for Math Workshop @ ICML 2025, 2025. URLhttps://openreview.net/ forum?id=5SF4fFRw7u

    2025

  11. [11]

    The simplicity of the hodge bundle.arXiv preprint arXiv:2603.19052, 2026

    Anand Patel. The Simplicity of the Hodge Bundle.arXiv preprint arXiv:2603.19052, 2026

    work page arXiv 2026

  12. [12]

    Lemmabench: A live, research-level benchmark to evaluate LLM capabilities in mathematics.CoRR, abs/2602.24173, 2026

    Antoine Peyronnet, Fabian Gloeckle, and Amaury Hayat. LemmaBench: A Live, Research-Level Benchmark to Evaluate LLM Capabilities in Mathematics.arXiv preprint arXiv:2602.24173, 2026

    work page arXiv 2026

  13. [13]

    Qwen3 Embedding: Advancing Text Embedding and Reranking Through Foundation Models

    Yanzhao Zhang, Mingxin Li, Dingkun Long, Xin Zhang, Huan Lin, Baosong Yang, Pengjun Xie, An Yang, Dayiheng Liu, Junyang Lin, et al. Qwen3 embedding: Advancing text embedding and reranking through foundation models. arXiv preprint arXiv:2506.05176, 2025

    work page internal anchor Pith review arXiv 2025