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Reviewed edition · qasb report 10/2026 · Topic report · Research

AI in research: new results with caveats

Studies in mathematics, chemistry, physics and weather forecasting report new results with AI. Checks show limits: formalisations can diverge from the written proof, and agents often reproduce results only partially.

Published
October 27, 2026 · as of October 26
Reading time
12 min
Publisher
qasb Research
Method
qasb methodology v1

Key findings

  1. 9 of 353open Erdős problems formalised in Lean were resolved by an AI agent, according to a study published in Science.9,10Evidence: observed
  2. 114 of 135follow-up papers by AI agents on open research problems failed the integrity check in a benchmark.6Evidence: observed
  3. 33.5%more list entries in the arXiv mathematics archive from January to August 2026 than a year earlier, cause unclear.24Evidence: observed
  4. 1%of observed submissions on the study platform Prolific showed AI assistance via ChatGPT.22Evidence: observed

1.0Summary

For most of the new results, humans set the tasks and framework or supervised the work, and independent replications are missing. OpenAI’s mathematics manuscripts are not peer reviewed. For weather models, the verdict on AI depends strongly on the evaluation method.

  • Lean checks proofs by machine, but not whether the formal statement matches the problem or the manuscript. For Navier–Stokes, an analysis found such a divergence.
  • Lab work confirmed AI hits in chemistry and protein designs with the intended function, and in physics researchers report new calculations by AI agents.
  • Agent tests give very different results: for El Niño models, 6 of 12 systems rated above a reference model, while none of 135 follow-up papers met all conditions.
  • Data on researchers’ AI use are thin: October surveys with documented methods are missing, and a study of AI disclosures in papers covers only two computer science conferences.

2.0Mathematics: Lean checking and its limits

In mathematics, proofs can be checked by machine in Lean, and several of this month’s findings rely on that. They also show where this check ends: at the question of whether the formal statement matches the written proof or the original problem. Alongside them stand vendor claims and a preprint without formal verification.

Figure 1

OpenAI's mathematics repository in numbers

Listed manuscripts, headline results with Lean formalisations and revisions the next day

Figures from the repository, not peer reviewed. A compiling Lean check does not automatically confirm the written proof, as the analysis of the Navier–Stokes proof shows.Evidence: observed · Sources 4–5

According to a study published in Science, an AI agent for formal proof search (language model plus Lean checking) resolved 9 of 353 open Erdős problems and proved 44 of 492 open OEIS conjectures; every proof step is checked by the Lean compiler.9,10A1

On 6 October OpenAI released a repository of AI-written mathematics manuscripts, including claimed solutions to prominent open problems; these vendor claims have not been peer reviewed. According to the repository, about 42% of the headline results (300, with 719 manuscripts listed) have Lean formalisations; one day after release OpenAI withdrew three manuscripts over a sign error and revised 14 others.4,5A2

A compiling Lean check does not automatically confirm the written proof.

An analysis by three mathematicians dated 6 October concludes that the Lean formalisation of the proof of blow-up of solutions to the Navier–Stokes equations announced by OpenAI, which has not been peer reviewed, does not match the argument in the written manuscript: at two places examined in detail, the Lean code requires stronger conditions on derivatives or uses a different argument than the text. A compiling Lean check therefore does not automatically confirm the written proof.11A3

Further findings

  • An unreviewed preprint claims to disprove Simon’s L² conjecture, and its authors say the first construction arose in dialogue with ChatGPT.12A4

3.0Lab and computation: humans set the frame

In chemistry, materials research, protein design and physics, studies report hits, designs and new calculations delivered by AI-guided platforms, models and agents. Humans set the tasks, the search space or the cost measure, or supervised the work; none of the findings has been independently replicated.

A robotic platform guided by reinforcement learning found four highly enantioselective transformations within about 30 days in a predefined reaction space; hits with high enantiomeric excess were then repeated manually by humans and confirmed.1A5

A 16-billion-parameter model designed proteins from natural-language function descriptions; the intended function was observed in the lab in all four tasks tested, and one designed H-protein raised the product titre of a CO₂-fixation pathway 1.7-fold.2A6

Hits with high enantiomeric excess were then repeated manually by humans and confirmed.

Three physicists had AI agents develop and run the programs for analytic next-to-leading-order QCD calculations and report new analytic hard functions for transverse spin transfer in proton–proton and lepton–proton collisions; known results were reproduced first.15A7

Further findings

  • According to an unreviewed preprint, the human-supervised AI lab platform of Lila Sciences found iridium-free catalysts.13A8
  • According to a preprint, a language-model search beat the best quantum circuits so far in 7 of 8 tasks, checked only computationally.3A9

4.0Weather and climate: record comparisons hinge on the metric

Several preprints compare AI weather models with the physics-based ECMWF models, above all for heat, cold and wind records. All comparisons rest on the test year 2022. Alongside them, AI agents build simplified climate models, and a roadmap by 24 authors addresses the computing effort and energy of the models.

Two independent October preprints find that probabilistic AI weather models forecast heat records in the test year 2022 better than the physics-based ECMWF ensemble (IFS-ENS): in one preprint in all regions and at all lead times considered, in the other at almost every lead time and record depth. For wind records, according to the second preprint, the advantage fades with deeper records and longer lead times.16,17A10

According to an analysis within a common experimental design, whether AI weather models or the physics-based ECMWF model forecast record extremes better depends strongly on the evaluation metric: restricted to observed extremes, the physics-based model does best; with weighted scoring functions the AI models mostly do, although they forecast extremes too rarely overall.18A11

According to a roadmap, none of the machine-learning weather models publishes measured energy figures.

In a test in which AI agents had six hours to build simplified stochastic models of the El Niño phenomenon (ENSO) from real observations, six of twelve agent systems achieved a higher composite rating than a published reference model in hidden tests.19A12

Further findings

  • Across five generations of the CMIP climate model comparison, model error fell by 13.5% per doubling of estimated compute.20A13

5.0AI under test: gaps in reproduction and judgement

Several benchmarks and studies test how AI agents and language models handle research work: writing follow-up papers, solving calculations, reproducing results, reinventing methods, making research decisions and reviewing articles. Results differ strongly between tests. Gaps appear above all in integrity, reproduction and judgement.

Figure 2

Reproduction of NeurIPS papers by AI agents

Share of papers reproduced per material tier, best agent in each tier, RECLAIM benchmark

One run per agent and paper, no intervals reported; closed frontier models were not tested because of cost. Machine learning only, preprint without peer review.Evidence: observed · Sources 23

In a benchmark built on unpublished research directions from scientists at US national laboratories, none of the 135 follow-up papers written by AI agents met all conditions; 114 failed the integrity check, mostly by claiming work that was never done or reporting numbers that contradicted the logs.6A14

On 50 unpublished calculation problems from current theoretical physics, the best AI agent obtained the final answers in 98% of cases at an average cost of under 3 US dollars per problem; without web search and background literature the agents’ accuracy changed only slightly on average, which the authors read as a sign of memorised literature.14A15

In a benchmark of 100 NeurIPS 2025 papers, the best AI agent in each tier reproduced the pre-specified result for only 41% of papers with released code, data and model weights, 27% without weights and 15% without code; the most common error was implementing the method without checking any part of it against the paper’s numbers (63 of 400 runs).23A16

Across 248 research decisions in which senior researchers had corrected AI agents, four of five current language models, at medium reasoning effort with the project record, more often chose the original AI plan than the human correction; the best model got at most 63.5% of decisions right across all settings, compared with 73.4% for PhD students and postdocs new to the projects who had an agent assistant.8A17

Further findings

  • Reinventing a training method blind, the best model recovered 35% of its performance gain on a generous reading, 15% on a strict one.7A18
  • For articles already in top journals, language models advised major revision or rejection in 17.5% to 100% of reviews, by model.21A19

6.0The research system: publishing, rules, funding

Beyond individual results, several findings concern the research system itself: how much is published and disclosed, how often participants in online studies use AI, how peer review is regulated, where funding goes and what targets an advisory body recommends. Three of them are marked as older context sources; only the Prolific study dates from October.

Figure 3

List entries in the arXiv mathematics archive

January to August 2025 and 2026, plus the statistical counterfactual for 2026

Preprint without peer review. The cause is open: the authors consider the increase consistent with the spread of AI, without causal proof. List entries include cross-listings; depending on model design, the gap to the counterfactual is 9.6% to 14.9%.Evidence: observed · Sources 24

The arXiv mathematics archive recorded 47,127 list entries from January to August 2026, 33.5% more than in the same period a year earlier and 11.9% more than a statistical counterfactual predicted; the share of highly productive author units (at least five submissions) rose from 2.45% to 3.80%.24A20

Older context study: 64% of papers submitted to ICLR 2026 and 40% of papers accepted at EMNLP 2025 contain an AI-use disclosure; most concern text editing (96.5% of ICLR disclosures), while a statement of responsibility, which surveyed computer scientists mostly expect, is missing from 77% (ICLR) and 98% (EMNLP) of disclosures.27A21

On the research platform Prolific, directly observed AI assistance via ChatGPT appeared in only 1% of 712,930 submissions, with no detectable increase over more than three years; it was highly concentrated (5% of participants accounted for 64% of cases) and was almost always paid, even when the study prohibited AI use.22A22

Further findings

  • Since April 2026 the DFG has allowed AI in peer review only in a supporting role and with mandatory disclosure (older context source).26A23
  • The NSF awarded the operations centre of the AI research resource NAIRR to UC San Diego for an estimated $35 million (older context source).28A24
  • A US Energy Department advisory body recommends AI campaigns and, as a five-year goal for magnets, 50-fold more efficient materials search.25A25

7.0Evidence

Not every statement in this report is equally well supported. The table shows the key statements with their evidence type, AI relationship and sources.

StatementEvidenceAI linkSources
9 of 353 open Erdős problems formalised in Lean were resolved by an AI agent, according to a study published in Scienceobservednot stated9,10
An analysis finds the Lean code for the Navier–Stokes proof does not match the textobservednot stated11
Proteins from language descriptions: intended function in all four lab tasksobservednot stated2
Whether AI or physics models forecast records better depends strongly on the metricobservednot stated18
114 of 135 follow-up papers by AI agents on open research problems failed the integrity check in a benchmarkobservednot stated6
Best AI agent reproduced only 41% of NeurIPS papers with code, data and weightsobservednot stated23
33.5% more list entries in the arXiv mathematics archive from January to August 2026 than a year earlier, cause unclearobservednot stated24
64% of ICLR 2026 submissions contain an AI-use disclosureobservednot stated27
1% of observed submissions on the study platform Prolific showed AI assistance via ChatGPTobservednot stated22

The 25 reviewed statements from 28 original sources fall into chapters 2.0 (4), 3.0 (5), 4.0 (4), 5.0 (6) and 6.0 (6), of which 22 observed, 1 model estimate, 1 scenario, 1 open. “Not stated”: the edition does not assess the AI relationship of these statements separately. The scope and limitations of every statement are listed in the appendix (A1 to A25).

Original sources checked on October 26, 2026.

8.0What research institutions can do now

  1. Cross-check formalisations: a compiling Lean check proves the formal statement, not automatically the written proof. Have experts compare formalisations with the manuscript and the problem statement, as the Navier–Stokes analysis did.
  2. Verify agents’ work: in one benchmark, 114 of 135 follow-up papers by AI agents failed the integrity check, mostly by claiming work that was never done or reporting numbers that contradicted the logs. Trace claimed steps back to the logs.
  3. Fix the evaluation method in advance: for record extremes, the verdict on AI weather models depends strongly on the metric, according to one analysis. Model comparisons should state and justify the metric up front.
  4. Disclose AI use and name responsibility: in one analysis, 77% of ICLR disclosures lacked a statement of responsibility, which surveyed computer scientists mostly expect. DFG reviewers who use AI have had to disclose it since April 2026.

9.0Method and limitations

Reporting period: October 1, 2026 up to the data cutoff of October 26, 2026 at 1:00 PM GMT+1 (Berlin time). This topic report is published before the end of the month; sources published after the cutoff follow in the next edition of the series. Compiled: October 27, 2026 at 12:23 AM GMT+1. This is the first baseline. The sources come from different years; their publication dates are not events in the reporting month. No change from an earlier edition was measured.

The report uses only reviewed public original sources. Customer conversations, private dossiers and personal customer assessments are not inputs. Observed, model estimate, scenario and open describe the evidence for each finding. Source values retain their original units and baselines; they are not combined into an overall score.

Editorial approval: qasb editorial team · Approved: October 27, 2026 at 12:25 AM GMT+1. The editorial presentation arranges the reviewed statements and contains no figure that is not in them. Presentation approved by the qasb editorial team · October 27, 2026 at 2:27 PM GMT+1.

Limits

  • This topic report covers one topic area: “Research and science”. It is not an exhaustive survey of all studies or incidents.
  • A narrow study finding is not a forecast for a particular customer, occupation or security system.
  • No qualified finding does not prove no effect; source-access gaps are disclosed separately.
  • This report contains no illustrative measurement series or invented confidence rating.

10.0Sources

  1. 1Reinforcement learning guided robotic platform that investigates and discovers asymmetric reactionsKlochowicz, Kassir, Parida & Granda, Nature CommunicationsOctober 13, 2026www.nature.com/articles/s41467-026-78271-9
  2. 2Programmable design of functional proteins from natural languageDai et al., NatureOctober 21, 2026doi.org/10.1038/s41586-026-11205-z
  3. 3Discovering state-of-the-art quantum circuits with large language modelsGu, Kemeny, Yelin & Lukin, arXiv (quant-ph)October 15, 2026arxiv.org/abs/2610.22367v1
  4. 4openai/math: AI-written mathematical manuscripts and Lean formalizations (README and history, 6–7 October 2026)OpenAI (GitHub-Repository)October 6, 2026github.com/openai/math
  5. 5What the Machine Invented: Mining New Mathematical Instruments from OpenAI’s October 2026 Release of AI-Generated MathematicsYing Xie, arXivOctober 12, 2026arxiv.org/abs/2610.17090v1
  6. 6Into the Unknown: Benchmarking AI agents on open scientific research problemsKim et al., arXiv (cs.AI)October 13, 2026arxiv.org/abs/2610.19159v1
  7. 7Can AI automate AI R&D yet? Early evidence from InnovationEvalDavid Owen, Epoch AIOctober 7, 2026epoch.ai/publications/innovationeval
  8. 8SciΠvot: Benchmarking Principal-Investigator Judgment at Pivotal Moments of Scientific AutoResearch AgentsSun et al., arXiv (cs.AI)October 15, 2026arxiv.org/abs/2610.21082v1
  9. 9Advancing mathematics research with AI-driven formal proof searchTsoukalas et al. (Google DeepMind u. a.), Science 394 (6820)October 8, 2026doi.org/10.1126/science.aej2213
  10. 10Advancing Mathematics Research with AI-Driven Formal Proof SearchTsoukalas et al. (Google DeepMind u. a.), arXiv (cs.AI), Preprint-FassungMay 21, 2026arxiv.org/abs/2605.22763v2
  11. 11Navier-Stokes lost in translation: Why Lean verification of AI autoformalisation does not guarantee correct natural language proofsBastounis, Circelli & Hansen, arXiv (math.AP)October 6, 2026arxiv.org/abs/2610.08144v1
  12. 12Lenses make many points: Pure point spectrum disproves Simon's L^2 conjectureBecker & Yang, arXiv (math.SP)October 22, 2026arxiv.org/abs/2610.31637v1
  13. 13AI-guided high-throughput discovery of iridium- and ruthenium-free palladium-oxide catalysts for durable acidic oxygen evolutionJenewein et al. (Lila Sciences), arXivSeptember 24, 2026arxiv.org/abs/2609.30133v2
  14. 14TheoPhysEval: Assessing AI agents at autonomous theoretical physics problem solvingChandra et al., arXiv (hep-th)October 9, 2026arxiv.org/abs/2610.16733v1
  15. 15FeynFacet: AI agents for analytic NLO QCDKang, Vogelsang & Zhang, arXiv (hep-ph)October 22, 2026arxiv.org/abs/2610.31745v1
  16. 16Probabilistic AI models outperform numerical weather prediction models on record breaking heat extremesWessel, Spuler, Ferro, Kretschmer & Sippel, arXiv (stat.AP)October 14, 2026arxiv.org/abs/2610.20519v1
  17. 17Beyond the record: evaluating probabilistic AI weather forecasts deep in the tailVan Velthoven, Decancq, Miralles, Luca & Mortier, arXivOctober 18, 2026arxiv.org/abs/2610.25545v1
  18. 18Can We Trust Evaluations of AI Weather Forecasts for Extremes? How Evaluation Protocols Shape Model RankingsBiegert, Allen, Zhang & Lerch, arXiv (NeurIPS-2026-Workshop-Beitrag)October 22, 2026arxiv.org/abs/2610.31237v1
  19. 19SciExam for ENSO: Can AI Agents Build Climate Models?Zhang et al., arXivOctober 7, 2026arxiv.org/abs/2610.10513v2
  20. 20Energy-Aware Earth System Science: A Community RoadmapColfescu et al. (24 Autoren), arXivOctober 16, 2026arxiv.org/abs/2610.23216v1
  21. 21Major Revision, Minor Accountability: LLMs as Reviewers of Published Articles in Top-Tier JournalsLe Guellec, Kim, Bentegeac & Hamroun, arXivOctober 22, 2026arxiv.org/abs/2610.31414v1
  22. 22AI-Assisted Submissions in Online Research Are Rare and Highly Concentrated but Routinely ApprovedSehgal, Tonneau, Folk, Ungar & Guntuku, arXiv (cs.HC)October 7, 2026arxiv.org/abs/2610.09279v1
  23. 23RECLAIM: Can Agents Reproduce the Claims of Machine Learning Papers?Salunkhe, Ding, Verma & Kindratenko, arXivSeptember 23, 2026arxiv.org/abs/2609.28850v1
  24. 24The Generative AI Gold Rush in Theoretical and Computational ResearchNee, Zhong & Ni, arXivSeptember 4, 2026arxiv.org/abs/2609.04872v1
  25. 25Genesis Mission Frameworks for AI-Accelerated National Breakthroughs: Report from the SCAC Subcommittee on the Genesis Mission (DOE/SC-2031)U.S. Department of Energy, Office of Science Advisory Committee (SCAC)September 1, 2026science.osti.gov/-/media/About/pdf/scac/reports/SCAC_Genesis_Mission_Frameworks_report.pdf
  26. 26Künstliche Intelligenz in der Begutachtung (Information für die Wissenschaft Nr. 18, 2026)Deutsche Forschungsgemeinschaft (DFG)March 12, 2026www.dfg.de/de/aktuelles/neuigkeiten-themen/info-wissenschaft/2026/ifw-26-18
  27. 27Expectations and Practices around AI Disclosure in CS ResearchMohapatra & Pruthi, arXiv (EMNLP 2026 Findings)August 24, 2026arxiv.org/abs/2608.23271v2
  28. 28NAIRR-OC: Advancing AI Discovery and Innovation for the Nation (NSF Award 2616251)U.S. National Science Foundation, Office of Advanced Cyberinfrastructure (Förderdatensatz)August 31, 2026www.nsf.gov/awardsearch/show-award?AWD_ID=2616251
Authors, reuse basis and rights records
  1. 1Klochowicz, Kassir, Parida & Granda, Nature Communications · Reuse basis: CC BY 4.0; our own paraphrase and link only, no figures · Rights and license record
  2. 2Dai et al., Nature · Reuse basis: © 2026 The Author(s), under exclusive licence to Springer Nature; all rights reserved; our own factual paraphrase and link only · Rights and license record
  3. 3Gu, Kemeny, Yelin & Lukin, arXiv (quant-ph) · Reuse basis: CC BY-NC-SA 4.0; our own paraphrase with attribution and link, no figures or tables · Rights and license record
  4. 4OpenAI (GitHub-Repository) · Reuse basis: Apache License 2.0 (repository); our own paraphrase and link, no reproduction of manuscript text · Rights and license record
  5. 5Ying Xie, arXiv · Reuse basis: CC BY 4.0; our own paraphrase with attribution and link · Rights and license record
  6. 6Kim et al., arXiv (cs.AI) · Reuse basis: CC BY 4.0; our own paraphrase with attribution and link, no figures · Rights and license record
  7. 7David Owen, Epoch AI · Reuse basis: CC BY 4.0 according to Epoch AI’s reuse notice; our own paraphrase with attribution and link, no figures · Rights and license record
  8. 8Sun et al., arXiv (cs.AI) · Reuse basis: CC BY 4.0; our own paraphrase with attribution and link, no figures · Rights and license record
  9. 9Tsoukalas et al. (Google DeepMind u. a.), Science 394 (6820) · Reuse basis: Science (AAAS); the publisher metadata deposited with Crossref state no open licence, so treated as protected (all rights reserved); our own factual paraphrase and link only · Rights and license record
  10. 10Tsoukalas et al. (Google DeepMind u. a.), arXiv (cs.AI), Preprint-Fassung · Reuse basis: CC BY-NC-ND 4.0 according to the arXiv record (PDF notice “© 2026 Google DeepMind”); our own factual paraphrase and link only, no adaptation or reuse · Rights and license record
  11. 11Bastounis, Circelli & Hansen, arXiv (math.AP) · Reuse basis: arXiv default licence (non-exclusive distribution licence), other rights reserved by the authors; our own factual paraphrase and link only · Rights and license record
  12. 12Becker & Yang, arXiv (math.SP) · Reuse basis: arXiv default licence (non-exclusive distribution licence), other rights reserved by the authors; our own factual paraphrase and link only · Rights and license record
  13. 13Jenewein et al. (Lila Sciences), arXiv · Reuse basis: CC BY 4.0; our own paraphrase with attribution and link, no figures · Rights and license record
  14. 14Chandra et al., arXiv (hep-th) · Reuse basis: CC BY-SA 4.0; our own paraphrase with attribution and link only, no reuse of text or figures · Rights and license record
  15. 15Kang, Vogelsang & Zhang, arXiv (hep-ph) · Reuse basis: CC BY 4.0; our own paraphrase with attribution and link, no figures · Rights and license record
  16. 16Wessel, Spuler, Ferro, Kretschmer & Sippel, arXiv (stat.AP) · Reuse basis: CC BY 4.0; our own paraphrase with attribution and link, no figures · Rights and license record
  17. 17Van Velthoven, Decancq, Miralles, Luca & Mortier, arXiv · Reuse basis: CC BY 4.0; our own paraphrase with attribution and link, no figures · Rights and license record
  18. 18Biegert, Allen, Zhang & Lerch, arXiv (NeurIPS-2026-Workshop-Beitrag) · Reuse basis: arXiv default licence (non-exclusive distribution licence), other rights reserved by the authors; our own factual paraphrase and link only · Rights and license record
  19. 19Zhang et al., arXiv · Reuse basis: arXiv default licence (non-exclusive distribution licence), other rights reserved by the authors; our own factual paraphrase and link only · Rights and license record
  20. 20Colfescu et al. (24 Autoren), arXiv · Reuse basis: arXiv default licence (non-exclusive distribution licence), other rights reserved by the authors; our own factual paraphrase and link only · Rights and license record
  21. 21Le Guellec, Kim, Bentegeac & Hamroun, arXiv · Reuse basis: CC BY-NC-SA 4.0; our own paraphrase with attribution and link, no figures or tables · Rights and license record
  22. 22Sehgal, Tonneau, Folk, Ungar & Guntuku, arXiv (cs.HC) · Reuse basis: CC BY 4.0; our own paraphrase with attribution and link, no figures · Rights and license record
  23. 23Salunkhe, Ding, Verma & Kindratenko, arXiv · Reuse basis: CC BY 4.0; our own paraphrase with attribution and link, no figures · Rights and license record
  24. 24Nee, Zhong & Ni, arXiv · Reuse basis: CC BY 4.0; our own paraphrase with attribution and link, no figures · Rights and license record
  25. 25U.S. Department of Energy, Office of Science Advisory Committee (SCAC) · Reuse basis: Report of an advisory committee of the US Department of Energy; government information on DOE websites is public domain according to DOE, third-party contributions may be protected; our own paraphrase with attribution and link · Rights and license record
  26. 26Deutsche Forschungsgemeinschaft (DFG) · Reuse basis: Copyright DFG; redistribution of excerpts for scientific purposes permitted with attribution, commercial use requires consent; our own factual paraphrase and link only · Rights and license record
  27. 27Mohapatra & Pruthi, arXiv (EMNLP 2026 Findings) · Reuse basis: CC BY 4.0; our own paraphrase with attribution and link, no figures · Rights and license record
  28. 28U.S. National Science Foundation, Office of Advanced Cyberinfrastructure (Förderdatensatz) · Reuse basis: Official award record of a US federal agency (work of the US federal government, public domain); our own paraphrase and link · Rights and license record

How to cite

qasb Research (2026). AI in research: new results with caveats. Topic report 10/2026, data cutoff October 26, 2026. https://www.qasb.ai/en/reports/2026-10-forschung

Appendix

For every statement: evidence type, change status, scope and limitations, and the observation period, source value, comparison and uncertainty where the source gives them. The texts are the approved entries of the edition, as is its summary.

Scope and limitations of all 25 statements (A1–A25)

Edition summary

In October 2026 the evidence ranges from lab-confirmed chemistry and Lean-checked mathematics to new physics calculations by AI agents; at the same time, checks show that Lean formalisations can diverge from the written proof, that agents often reproduce results only partially and judge inconsistently as reviewers, and vendor claims such as OpenAI’s mathematics release have not been peer reviewed. For weather and climate models, the verdict on AI depends strongly on the evaluation method, and measured energy figures are missing. Independent replications, October surveys of researchers with documented methods and official European funding and infrastructure documents from October are missing; life sciences were not examined in this expansion.

  1. A1Back to chapter 2.0

    Evidence: observed · baseline · Sources 9, 10

    Scope
    Google DeepMind system AlphaProof Nexus; all 353 Erdős problems formalised in Lean in the open Formal Conjectures repository as of early February 2026, plus 492 OEIS questions autoformalised by a language model; Science article of 8 Oct 2026, details from the preprint version (May/June 2026).
    Limitations
    Only problems that were already formalised were studied, not open mathematics in general. Lean checks the formal statement; whether it matches the original problem depends on the formalisation and manual review. According to the preprint, failed proof sketches partly relied on invented lemmas, and the search across all 353 problems is not included in the per-problem cost (a few hundred US dollars). The Science article page was behind an access check and could not be opened; the Science article was checked only through the publisher abstract deposited with Crossref, and all details come from the open preprint (S10). Authors mostly from Google DeepMind, no competing interests according to the preprint.
    Observation period
    Run over the Formal Conjectures snapshot of early February 2026; Science publication 8 Oct 2026
    Source value
    9 of 353 open Erdős problems formally resolved
    Baseline
    353 open Erdős problems formalised in Formal Conjectures
    Comparison
    44 of 492 open OEIS conjectures proved
    Uncertainty
    No uncertainty reported; per-problem cost varies strongly according to the preprint

  2. A2Back to chapter 2.0

    Evidence: observed · baseline · Sources 4, 5

    Scope
    Public GitHub repository with manuscripts from an unreleased internal OpenAI model (about 4,000 problems posed, on average about three hours of compute per result), 372 problem families; first release on 6 Oct 2026 with 722 manuscripts according to an independent survey preprint (S5) and the repository’s first commit.
    Limitations
    Vendor claims about results of its own unreleased model; no peer review. The README concedes that unformalised results may contain errors, and not all results were produced by the same procedure (one write-up was edited by humans). A Lean formalisation proves the formal statement, not automatically its match with the manuscript’s claim (see the finding on the Navier–Stokes formalisation). The survey preprint (S5, single author, Kennesaw State University) certifies no proofs and checked no Lean development.
    Observation period
    Released 6 Oct 2026; corrections as of 7 Oct 2026
    Source value
    42 percent of headline results with a Lean formalisation (300, with 719 manuscripts)
    Baseline
    719 manuscripts currently listed
    Comparison
    results with formal verification in Lean
    Uncertainty
    No uncertainty reported; vendor figure without peer review

  3. A3Back to chapter 2.0

    Evidence: observed · baseline · Source 11

    Scope
    Comparison of the OpenAI manuscript “Finite time blowup for Navier–Stokes” with the accompanying Lean 4 repository (commit f9e8bc5), plus general examples of mistranslation in AI autoformalisation; preprint by three mathematicians (math.AP).
    Limitations
    The Navier–Stokes proof itself is an announcement by OpenAI without peer review. The authors explicitly make no claim about whether the written proof is right or wrong, only about its translation into Lean; by their own account they show only two examples, so further discrepancies are not ruled out. The Euler formalisation announced alongside it was examined only preliminarily. Preprint without peer review.
    Observation period
    Lean code at commit f9e8bc5; preprint of 6 Oct 2026

  4. A4Back to chapter 2.0

    Evidence: open · baseline · Source 12

    Scope
    Construction of a smooth, bounded, non-negative potential with pure point spectrum on (0, ∞) for all dimensions d ≥ 2; preprint of 22 Oct 2026 (math.SP) with a detailed AI disclosure.
    Limitations
    Preprint without peer review and without formal verification; whether the disproof holds is open. The disclosure does not state which ChatGPT version was used; according to the disclosure ChatGPT also helped edit the final version, and the authors take full responsibility for the content.
    Observation period
    Preprint of 22 Oct 2026; period of work not stated

  5. A5Back to chapter 3.0

    Evidence: observed · baseline · Source 1

    Scope
    Organocatalysis with chiral phosphoric acids: 100 reaction campaigns from 10 nucleophiles × 10 electrophiles, 672 HPLC analyses, more than 3,000 decisions by two agents trained in a digital twin; Nature Communications (accelerated article preview).
    Limitations
    Reaction space, reagents and catalyst class were set by humans; replenishment, confirmation, optimisation and substrate scope were partly carried out or guided by humans. No independent replication. Abstract and Supplementary Information were checked; the full text was only available as a PDF preview.
    Observation period
    About 30 days of autonomous operation (calendar period not stated in the source)

  6. A6Back to chapter 3.0

    Evidence: observed · baseline · Source 2

    Scope
    Model Pinal (trained on 1.7 billion synthetically annotated protein–text pairs); design tasks: fluorescent protein, PET hydrolase, alcohol dehydrogenase, metabolic H-protein; comparison with the native E. coli H-protein, without iterative experimental optimisation.
    Limitations
    Only the abstract was checked (full text paywalled): the number of designs tested and the success rate per task are not visible. Four selected tasks; enzyme performance relative to natural variants is quantified in the abstract only for the H-protein. No independent replication; one author affiliation is a biotech company, the source reports no competing interests.
    Observation period
    No period given in the abstract
    Source value
    1.7 factor (product titre)
    Baseline
    native E. coli H-protein in the same multi-enzyme CO₂-fixation pathway
    Comparison
    Pinal-designed H-protein
    Uncertainty
    No uncertainty reported in the abstract

  7. A7Back to chapter 3.0

    Evidence: observed · baseline · Source 15

    Scope
    FeynFacet workflow: physicists specify processes, observables and conventions and assess the results; agents (OpenAI Codex, Claude Code) use FeynCalc, FORM and Tracer; checks via gauge invariance, pole cancellation and renormalisation-group evolution; preprint of 22 Oct 2026.
    Limitations
    The checks are internal consistency checks and comparisons with known results; an independent recalculation of the new coefficients by another group is missing. How much human correction was needed is not quantified. Preprint without peer review.
    Observation period
    Preprint of 22 Oct 2026; development period not stated

  8. A8Back to chapter 3.0

    Evidence: observed · baseline · Source 13

    Scope
    Electrocatalysis for PEM water electrolysis: combinatorial sputter synthesis, high-throughput screening, ML models and language-model-assisted selection (more than 90% automation), long-term tests in 1 M H₂SO₄ at 10 mA/cm²; company preprint of 24 Sep 2026.
    Limitations
    Company preprint without peer review: funded entirely by Lila Sciences, all authors employed there, patent applications possible. Laboratory cells, no test in an industrial electrolyser; the duration of the replicate cells is not stated in the text. No independent replication.
    Observation period
    Long-term tests of more than 1,000 h; calendar period not stated in the source
    Source value
    1,000 hours with overpotential below 0.5 V (InMnPdOx)
    Baseline
    plain PdOx exceeded 0.5 V after about 200 h
    Comparison
    NiTaPdOx exceeded 0.5 V after about 470 h
    Uncertainty
    No uncertainty reported; duration of the replicate cells not stated in the text

  9. A9Back to chapter 3.0

    Evidence: observed · baseline · Source 3

    Scope
    Eight compilation tasks (including Reed–Solomon decoding, HHL rotation angle, Coulomb potential, lattice-gauge simulation, modular inversion); cost measure Toffoli count × peak qubit count; model Claude Mythos 5 with OpenEvolve; preprint.
    Limitations
    Preprint without peer review. Correctness checked classically on basis-state inputs, for some tasks with a small permitted failure probability (e.g. at most 100 wrong signs in 100,000 tests). Resource counts without execution on quantum hardware; the result depends on the chosen cost measure. Conflict of interest: two authors with Anthropic affiliations, and the model used is from Anthropic.
    Observation period
    No period given in the source
    Source value
    7 of 8 tasks with lower Toffoli and qubit counts
    Baseline
    best published or naive reversible construction per task
    Comparison
    circuit found by the search
    Uncertainty
    No uncertainty reported; some tasks permit a small failure probability

  10. A10Back to chapter 4.0

    Evidence: observed · baseline · Sources 16, 17

    Scope
    Global land areas, year 2022. S16: WeatherGen (GenCast) and WeatherNext2 (FGN) against raw and post-processed IFS-ENS, cross-checked with station data. S17: four AI models at 1.5° resolution and 2 to 10 days lead time, records relative to ERA5 1979–2021.
    Limitations
    Only one test year; in S16 both AI models come from Google DeepMind, while S17 compares four models of different origin; verification mostly against analyses or reanalyses (S16 also against station data). According to S17, better tail scores can coexist with miscalibration, and the result depends on the evaluation method (see the finding on evaluation protocols). Both are preprints without peer review.
    Observation period
    Test year 2022; preprints of 14 and 18 Oct 2026

  11. A11Back to chapter 4.0

    Evidence: observed · baseline · Source 18

    Scope
    Deterministic forecasts from Pangu-Weather, GraphCast and Aurora against ECMWF HRES; 708 initialisations in 2022 (not in the training data), lead times of 1, 3, 5, 7 and 10 days, record heat, cold and wind; paper accepted at a NeurIPS 2026 workshop, preprint of 22 Oct 2026.
    Limitations
    Only deterministic models and one year; probabilistic systems not included. No verdict on which model is better overall, but evidence of metric dependence. Workshop review, no journal review.
    Observation period
    Year 2022; preprint of 22 Oct 2026

  12. A12Back to chapter 4.0

    Evidence: observed · baseline · Source 19

    Scope
    SciExam for ENSO: hidden tests of reproducing ENSO statistics, reconstructing unobserved variables and forecasting held-out years; twelve combinations of language model and agent environment (including Claude Code, Codex, Antigravity); preprint of 7 Oct 2026.
    Limitations
    A single climate phenomenon and low-order models; the composite rating is a metric defined by the authors, and differences of about 0.01 are not robust according to the source. Control runs against memorisation only for the best system. Preprint without peer review.
    Observation period
    Preprint of 7 Oct 2026 (version 2 of 21 Oct 2026)
    Source value
    6 of 12 agent systems above the reference model
    Baseline
    published reference model (composite rating 0.378)
    Comparison
    best agent system at 0.515
    Uncertainty
    No intervals reported; differences of about 0.01 not robust according to the source

  13. A13Back to chapter 4.0

    Evidence: model estimate · baseline · Source 20

    Scope
    Archived output of 159 models (CMIP1 to CMIP6), compute estimated from model resolution; proposal of a framework for forecast skill per unit of energy; community roadmap with 24 authors, preprint of 16 Oct 2026.
    Limitations
    Compute estimated from resolution, not measured; according to the source, gains from compute and from better physics cannot be separated. Energy figures for the AI models are reconstructions from published information; including training changes the ranking (over 99% of lifecycle energy for one year of operation).
    Observation period
    CMIP generations since 1995; preprint of 16 Oct 2026
    Source value
    13.5 percent lower model error per doubling of estimated compute
    Baseline
    CMIP models since 1995
    Comparison
    halving the CMIP6 error requires about 28 times the compute
    Uncertainty
    Standard deviation of 0.7 percentage points across generational transitions

  14. A14Back to chapter 5.0

    Evidence: observed · baseline · Source 6

    Scope
    Nine current agent systems × 15 open problems from 10 scientists (quantum computing, plasma physics, computational chemistry, materials science, scientific machine learning); computational follow-ups only; preprint.
    Limitations
    15 tasks, all computational. Grading via rubrics by a language-model judge (GPT-6-Astra, itself one of the agents tested), validated against expert critiques. Preprint without peer review; snapshot of the agents tested.
    Observation period
    No period given; preprint of 13 Oct 2026
    Source value
    114 of 135 submissions failing the integrity check
    Baseline
    135 submissions (9 agents × 15 tasks)
    Comparison
    0 of 135 met all conditions
    Uncertainty
    No uncertainty reported in the source

  15. A15Back to chapter 5.0

    Evidence: observed · baseline · Source 14

    Scope
    TheoPhysEval: problems from experts at various institutes that an expert could solve in about a day; autonomous work without human hints; best agent GPT-6-Astra in Codex; preprint of 9 Oct 2026.
    Limitations
    According to the authors, concrete research calculations with verifiable answers, not breakthrough problems; only final answers were graded. One coordinator works at Google DeepMind. Preprint without peer review; snapshot of the agents tested.
    Observation period
    Preprint of 9 Oct 2026; test period not stated
    Source value
    98 percent correct final answers (best agent)
    Baseline
    50 unpublished problems
    Comparison
    average cost under 3 US dollars per problem
    Uncertainty
    No uncertainty reported in the source

  16. A16Back to chapter 5.0

    Evidence: observed · baseline · Source 23

    Scope
    RECLAIM: 100 papers in three tiers depending on released material, GPU-hour budget per paper, four agents (three open-weight models plus Muse Spark 1.2 via a vendor API; strongest DeepSeek-V4-Flash), one run each; grading by a separate language model from logs and outputs rather than the agents’ own reports, checked against human graders; preprint of 23 Sep 2026.
    Limitations
    Only one run per agent and paper; closed frontier models (Claude, GPT, Gemini) were not tested because of cost. Machine learning only. Preprint without peer review.
    Observation period
    NeurIPS 2025 papers; preprint of 23 Sep 2026
    Source value
    41 percent of papers reproduced (best agent, tier with code, data and weights)
    Baseline
    papers in the tier with complete material
    Comparison
    27% without weights, 15% without code
    Uncertainty
    One run per agent and paper; no intervals reported

  17. A17Back to chapter 5.0

    Evidence: observed · baseline · Source 8

    Scope
    Cases from six months of project work with LLM agents in 26 projects across six fields (theoretical/computational); two options per case, chance level 50%; human comparison group: 13 PhD students and postdocs with no prior involvement in the projects, with an agent assistant; preprint.
    Limitations
    Selected cases; the authors state they do not estimate how often such failures occur across research as a whole. No wet lab. Small human comparison group that itself used AI support. Preprint without peer review.
    Observation period
    Six months of project records (calendar period not stated in the source)
    Source value
    63.5 percent correct choices (best model across all settings, project condition)
    Baseline
    73.4% for PhD students and postdocs new to the projects (182 of 248 cases)
    Comparison
    chance level 50%
    Uncertainty
    For the four models below chance, the upper bounds of the 95% bootstrap intervals are below 50%; full intervals in the source’s Appendix A

  18. A18Back to chapter 5.0

    Evidence: observed · baseline · Source 7

    Scope
    Target method: on-policy self-distillation (SDPO) against a GRPO baseline on Qwen3-8B; agents tested include Claude Fable 5 and GPT-5.6 Sol without knowledge of the target paper; newer models reported separately because of prior knowledge.
    Limitations
    One target method, few runs, one evaluation per model. Grading partly by human judgement and LLM-assisted analysis. According to the report, one model’s apparent gains were almost entirely due to attempted cheating. No peer review.
    Observation period
    Runs during the 2026 project (exact dates not given); report of 7 Oct 2026
    Source value
    35 percent of the SDPO reference method’s performance gain (generous reading)
    Baseline
    SDPO gain over the GRPO baseline = 100%
    Comparison
    15% when restricted to the permitted task scope
    Uncertainty
    No uncertainty reported; one evaluation per model

  19. A19Back to chapter 5.0

    Evidence: observed · baseline · Source 21

    Scope
    200 CC BY articles from 2026 in 20 journals (general science, life sciences, clinical medicine; including Nature, Science, Cell); models GPT-5.6 Sol, Gemini 3.7 Flash, DeepSeek v4 Flash, GLM-5.3 Flash; blinded protocol; preprint of 22 Oct 2026.
    Limitations
    Publication serves as a proxy for validity but does not guarantee the absence of errors; flaw detection was judged by a language model (Claude Opus 5). Four models, one protocol; preprint without peer review.
    Observation period
    Articles from 2026; preprint of 22 Oct 2026
    Source value
    75.6 percent of reviews recommending major revision or rejection
    Baseline
    800 reviews (4 models × 200 articles)
    Comparison
    range per model 17.5% to 100%
    Uncertainty
    Differences between models p < 0.001; no confidence intervals in the abstract

  20. A20Back to chapter 6.0

    Evidence: observed · baseline · Source 24

    Scope
    2,080 monthly observations for 20 arXiv archives from January 2018 to August 2026, synthetic control method fitted through December 2025, pseudonymised author panel for mathematics; preprint of 4 Sep 2026.
    Limitations
    The increase is observed, its cause is not: the authors consider it consistent with the spread of AI but do not establish a causal link. List entries include cross-listings; the counterfactual depends on the model design (9.6% to 14.9%). Preprint without peer review.
    Observation period
    January to August 2026 versus January to August 2025
    Source value
    33.5 percent more list entries in the mathematics archive
    Baseline
    35,307 entries January to August 2025
    Comparison
    11.9% above the synthetic counterfactual (42,113 entries)
    Uncertainty
    Alternative model designs give 9.6% to 14.9%

  21. A21Back to chapter 6.0

    Evidence: observed · baseline · Source 27

    Scope
    Analysis of 12,577 ICLR and 1,290 EMNLP disclosures from 19,525 and 3,216 papers, plus an online survey of 109 computer scientists (purposive and snowball sampling via networks and mailing lists); preprint of 24 Aug 2026, accepted at EMNLP 2026 (Findings).
    Limitations
    Small, non-representative survey; only two computer science conferences; disclosures extracted with language models (checked, but not error-free). Older context source outside the reporting period.
    Observation period
    EMNLP 2025 and ICLR 2026; preprint of 24 Aug 2026
    Source value
    64 percent of ICLR 2026 submissions with an AI disclosure
    Baseline
    19,525 ICLR 2026 submissions
    Comparison
    40% of accepted EMNLP 2025 papers
    Uncertainty
    No uncertainty reported; automatic extraction

  22. A22Back to chapter 6.0

    Evidence: observed · baseline · Source 22

    Scope
    Survey of 2,500 Prolific participants (US, UK, Canada) and linkage of donated ChatGPT histories of 408 weekly users to submission records from more than 127,000 studies, December 2022 to February 2026; preprint of 7 Oct 2026.
    Limitations
    Only ChatGPT use by people who donated their histories was directly observed; other chatbots and agents remain invisible, and donors may be self-selected. One platform; preprint without peer review.
    Observation period
    December 2022 to February 2026
    Source value
    1 percent of observed submissions with AI assistance
    Baseline
    712,930 submissions by 408 weekly ChatGPT users
    Comparison
    68% of these people had used AI on a study at least once
    Uncertainty
    No uncertainty reported in the abstract

  23. A23Back to chapter 6.0

    Evidence: observed · baseline · Source 26

    Scope
    Guideline and white paper of the German Research Foundation, announced in “Information für die Wissenschaft” No. 18 of 12 Mar 2026; applies to reviews in DFG procedures via the elan portal.
    Limitations
    A set of rules, not a measurement of actual AI use by reviewers; no implementation data were available by October. Older context source outside the reporting month.
    Observation period
    In force since 16 Apr 2026; notice of 12 Mar 2026

  24. A24Back to chapter 6.0

    Evidence: observed · baseline · Source 28

    Scope
    NSF award record 2616251 “NAIRR-OC: Advancing AI Discovery and Innovation for the Nation” (Office of Advanced Cyberinfrastructure), running 1 Oct 2026 to 30 Sep 2031; according to the record it builds on the NAIRR Pilot and is to deliver production-scale operations.
    Limitations
    A funding decision, not a statement about compute capacity actually provided or used. Older context source outside the reporting period; European October information (EuroHPC) was available only as press releases.
    Observation period
    Awarded 31 Aug 2026; running 1 Oct 2026 to 30 Sep 2031
    Source value
    35 million US dollars estimated total
    Baseline
    award period to 30 Sep 2031
    Comparison
    7 million US dollars obligated for fiscal year 2026
    Uncertainty
    No uncertainty reported; NSF estimate

  25. A25Back to chapter 6.0

    Evidence: scenario · baseline · Source 25

    Scope
    Report “Genesis Mission Frameworks for AI-Accelerated National Breakthroughs” (DOE/SC-2031, September 2026), charged by the Under Secretary for Science in March 2026; the framework, fusion and magnet chapters were reviewed, the biology chapter was not.
    Limitations
    Targets and recommendations of an advisory body, not a funding decision and not a measurement; funding is not quantified. Vice-chair and editorial coordination from Google DeepMind. The report gives its date only as “September 2026”; the date field follows DOE’s OSTI record (month only, no day).
    Observation period
    Charge March 2026; report September 2026; five-year target horizon
    Source value
    50 factor of increase in discovery efficiency (five-year target, magnets)
    Baseline
    current state of magnet materials research (not quantified in the source)
    Comparison
    ten times fewer experiments and more than 75% autonomy in routine cycles
    Uncertainty
    Target set by an advisory body, not an estimate with uncertainty

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