A survey of published research, from the Essentia Memoria newsroom. It lists real papers, each looked up at its DOI registry; the game has not repeated their results.

Research survey

What AI research has found: mathematics and proof

Happened: October 28, 2026 at 8:34 PM UTC · Published: October 28, 2026 at 8:34 PM UTC

9 published works on mathematics and proof, each looked up at its DOI registry before it was listed here, with what each one reports in plain words.

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News from the Essentia Memoria game universe. What AI research has found: mathematics and proof. 9 published works on mathematics and proof, each looked up at its DOI registry before it was listed here, with what each one reports in plain words. This survey lists what each paper reports. The game has not repeated these results. A search finds papers that match its words, so a listed paper may use AI only in part. Citation counts reward older work, so the newest results may be missing until they are cited. This report was written from the world record by a fixed template. The full story and its source records are on essentiamemoria.com.

The question

Can a model make a discovery in mathematics, or prove a theorem an olympiad would set?

Claims, and where each one comes from

Where this research lives in the game (a place the world grammar builds)university → school
Game simulation · Set in code src/lib/world-grammar/place-grammar.ts · resolvePurpose('university')
Published works in this survey, each resolved at its DOI registry9
Real-world knowledge · Source [1] [2] [3] [4] [5] [6] [7] [8] [9]
A language model paired with an automatic checker found new constructions in combinatorics that beat the best known ones.Romera-Paredes 2024
Real-world knowledge · Source [1]
AlphaGeometry solves olympiad geometry problems with proofs a person can read, trained without human-written proofs.Trinh 2024
Real-world knowledge · Source [2]
An Introduction to Matrix Concentration InequalitiesTropp 2015
Real-world knowledge · Source [3]
${k}$ -Space Deep Learning for Accelerated MRIHan 2019
Real-world knowledge · Source [4]
Portable Food‐Freshness Prediction Platform Based on Colorimetric Barcode Combinatorics and Deep Convolutional Neural NetworksGuo 2020
Real-world knowledge · Source [5]
Computing a nonnegative matrix factorization -- provablyArora 2012
Real-world knowledge · Source [6]
The Determinant of the Adjacency Matrix of a GraphHarary 1962
Real-world knowledge · Source [7]
Recognising textual entailment with logical inferenceBos 2005
Real-world knowledge · Source [8]
The Role of the Mizar Mathematical Library for Interactive Proof Development in MizarBancerek 2017
Real-world knowledge · Source [9]

References, checked at their registry

[1] Romera-Paredes (2024). Mathematical discoveries from program search with large language models. Nature. doi:10.1038/s41586-023-06924-6
Verified: the work exists and matches · checked at Crossref on Oct 28, 2026, 8:34 PM UTC · the registry holds “Mathematical discoveries from program search with large language models” (2024)
[2] Trinh (2024). Solving olympiad geometry without human demonstrations. Nature. doi:10.1038/s41586-023-06747-5
Verified: the work exists and matches · checked at Crossref on Oct 28, 2026, 8:34 PM UTC · the registry holds “Solving olympiad geometry without human demonstrations” (2024)
[3] Tropp (2015). An Introduction to Matrix Concentration Inequalities. Foundations and Trends® in Machine Learning. doi:10.1561/2200000048
Verified: the work exists and matches · checked at Crossref on Oct 28, 2026, 8:34 PM UTC · the registry holds “An Introduction to Matrix Concentration Inequalities” (2015)
[4] Han (2019). ${k}$ -Space Deep Learning for Accelerated MRI. IEEE Transactions on Medical Imaging. doi:10.1109/tmi.2019.2927101
Verified: the work exists and matches · checked at Crossref on Oct 28, 2026, 8:34 PM UTC · the registry holds “${k}$ -Space Deep Learning for Accelerated MRI” (2020)
[5] Guo (2020). Portable Food‐Freshness Prediction Platform Based on Colorimetric Barcode Combinatorics and Deep Convolutional Neural Networks. Advanced Materials. doi:10.1002/adma.202004805
Verified: the work exists and matches · checked at Crossref on Oct 28, 2026, 8:34 PM UTC · the registry holds “Portable Food‐Freshness Prediction Platform Based on Colorimetric Barcode Combinatorics and Deep Convolutional Neural Networks” (2020)
[6] Arora (2012). Computing a nonnegative matrix factorization -- provably. ACM Symposium on Theory of Computing (STOC). doi:10.1145/2213977.2213994
Verified: the work exists and matches · checked at Crossref on Oct 28, 2026, 8:34 PM UTC · the registry holds “Computing a nonnegative matrix factorization -- provably” (2012)
[7] Harary (1962). The Determinant of the Adjacency Matrix of a Graph. SIAM Review. doi:10.1137/1004057
Verified: the work exists and matches · checked at Crossref on Oct 28, 2026, 8:34 PM UTC · the registry holds “The Determinant of the Adjacency Matrix of a Graph” (1962)
[8] Bos (2005). Recognising textual entailment with logical inference. . doi:10.3115/1220575.1220654
Verified: the work exists and matches · checked at Crossref on Oct 28, 2026, 8:34 PM UTC · the registry holds “Recognising textual entailment with logical inference” (2005)
[9] Bancerek (2017). The Role of the Mizar Mathematical Library for Interactive Proof Development in Mizar. Journal of Automated Reasoning. doi:10.1007/s10817-017-9440-6
Verified: the work exists and matches · checked at Crossref on Oct 28, 2026, 8:34 PM UTC · the registry holds “The Role of the Mizar Mathematical Library for Interactive Proof Development in Mizar” (2018)

Review

Not peer reviewed. No human scientist has reviewed this survey. Its template and landmark summaries were written with an AI assistant (Claude); the papers it lists are real and each was checked at its registry, so anyone can follow the links and read them.

Each listed DOI was resolved, and its title, year and first author matched the listing.
Each work the search found is held by Crossref, a registry independent of the search.
Each number in the headline and summary is accounted for by a listed claim.
Not shown: 3 candidate work(s) whose registry record did not confirm them (10.1609/aimag.v26i4.1848 verified (not in Crossref); 10.12694/scpe.v9i3.534 verified (not in Crossref); 10.48550/arxiv.1705.08439 verified (not in Crossref)).

Code version: a2a323eb5778

What the record does not say

This survey lists what each paper reports; the game has not repeated these results. A search finds papers that match its words, so a listed paper may use AI only in part. Citation counts reward older work, so the newest results may be missing until they are cited.

How this was written

Landmark works named by the desk, then the most-cited works with a DOI that OpenAlex returns when titles and abstracts are searched for ("theorem proving" OR "mathematical discovery" OR combinatorics OR olympiad) AND ("machine learning" OR "deep learning" OR "neural network" OR "neural networks" OR "artificial intelligence" OR convolutional OR "reinforcement learning" OR "language model" OR transformer); a hit is kept only if its own title or abstract names the field and an AI method as whole words. Each candidate was looked up at Crossref (OpenAlex as second resolver) and its title, year and first author compared; a work the search found is shown only when Crossref holds it. Landmark summaries were written by the desk; the other works are listed by their own titles.

Source records: code:src/lib/world-grammar/place-grammar.ts#resolvePurpose · doi:10.1038/s41586-023-06924-6 · doi:10.1038/s41586-023-06747-5 · doi:10.1561/2200000048 · doi:10.1109/tmi.2019.2927101 · doi:10.1002/adma.202004805 · doi:10.1145/2213977.2213994 · doi:10.1137/1004057 · doi:10.3115/1220575.1220654 · doi:10.1007/s10817-017-9440-6