AI-assisted research in mathematics and the sciences
An archive of attempts to solve research problems with AI.
AI-assisted research is accelerating, but its prompts, methods, and outcomes are scattered. Prompts for Progress collects them in context so researchers can study how the work is being done, learn from prior attempts, and plan better-informed work of their own.
Use the complete archive
Clone the repository and work with every prompt at once.
git clone https://github.com/wintercarver/prompts-for-progress.gitProblems, not just announcements
Follow one question across every attempt.
Use the problems index to see which approaches have been tried on a question and how their outcomes differ.
Open problems index →Documented activity
The public record is accelerating.
The timeline shows documented activity using the known run date when available, otherwise the first dated public event. Counts reflect this archive rather than all AI-assisted research.
Complete resultPartial progressMixed campaignDocumented attempt
Seed corpus
Study the prompts, methods, and outcomes together.
Browse 23 of 23 records. Each full record keeps the prompt close to its context and evidence.
Domain
Outcome
01
ACRA converts literature procedures into robotic syntheses
ACRA generated executable procedures from published chemistry, completed several physical syntheses, and preserved a failed reaction that a chemist also could not reproduce without substantial changes.
- System
- Autonomous Chemputer Reaction Agents, Chemputer, Opentrons, OpenAI API-based models, exact production version undisclosed
- Prompt
- full
- Evidence
- Experimental
- First dated event
- Apr 3, 2026
Keep in view: This is primarily a literature-reproduction workflow rather than discovery of a new reaction. The system makes explicit best-guess substitutions for ambiguous prose, and some Chemputer-specific packages are not openly downloadable.
02
AILA benchmarks agents on physical microscopy tasks
AILA performed real atomic-force-microscopy workflows and evaluated four language models over 300 task instances, exposing code failures, routing errors, and safety-relevant instruction drift.
- System
- AILA, GPT-4o, GPT-3.5-turbo-0125, Llama-3.3-70B-versatile, Claude-3.5-sonnet-20241022
- Prompt
- full
- Evidence
- Experimental
- First dated event
- Oct 14, 2025
Keep in view: The campaign automates established microscopy workflows rather than establishing a new physical finding. A correct final measurement did not guarantee that the agent followed safe or authorized instructions.
03
A-Lab GPSS runs 352 spinel-electrolyte experiments
A GPT-5 agent proposed and executed 263 samples in a 352-experiment lithium-halide campaign, raising the joint phase-purity and conductivity hit rate while preserving the full low-yield denominator.
- System
- A-Lab GPSS, GPT-5 with high reasoning effort, Bayesian optimization
- Prompt
- full
- Evidence
- Experimental
- First dated event
- Nov 3, 2025
Keep in view: Humans constrained the search space and handled several physical and analytical steps. The final joint hit rate was 5.33%, so the result is an optimization campaign with many unsuccessful experiments rather than one autonomous breakthrough.
04
Aletheia scans 700 open-labeled Erdős problems
A batch campaign narrowed 700 problems to 200 graded candidate outputs; 63 were technically correct but only 13 were judged meaningfully correct, while 137 were fundamentally flawed.
- System
- Aletheia, Gemini Deep Think
- Prompt
- partial
- Evidence
- Expert-reviewed
- First dated event
- Dec 2, 2025
Keep in view: Many technically correct outputs exploited unintended readings or rediscovered literature; the system configuration and raw outputs were not fully reproducible from the paper alone.
05
AlphaProof Nexus searches open Erdős and OEIS problems
A Lean-guided campaign reported nine Erdős results and 44 OEIS conjecture proofs, while also documenting failure modes such as restating the hard step behind a new unproved lemma.
- System
- AlphaProof Nexus, Gemini prover and rater agents, Lean
- Prompt
- representative
- Evidence
- Formal
- First dated event
- May 21, 2026
Keep in view: Results for stronger or related variants must not be counted as literal resolutions of the canonical problems; full per-run transcripts are unavailable.
06
AstroAgents generates hypotheses from meteorite spectra
Eight collaborating agents generated more than 100 hypotheses from meteorite and soil mass-spectrometry data; one astrobiology expert judged 36% plausible and 66% of that subset novel.
- System
- AstroAgents, Gemini 2.0 Flash, Claude 3.5 Sonnet, Semantic Scholar
- Prompt
- full
- Evidence
- Expert-reviewed
- First dated event
- Mar 29, 2025
Keep in view: Novelty and plausibility ratings from one domain expert are proposal triage, not confirmation. The public artifacts still need enumeration to determine whether every generated hypothesis and iteration is preserved.
07
CDC-style attempt on the Bartnik admissible-extension conjecture
A CDC-style multi-agent prompt ran in Codex for 2 hours 47 minutes and ended without a proof after several candidate routes failed adversarial audit.
- System
- Codex multiagent v2 (underlying model not recorded in the task export)
- Prompt
- full
- Evidence
- Reported
- First dated event
- Jul 15, 2026
Keep in view: This is one documented attempt under a deliberately strict success criterion, not evidence against the conjecture. The run ended before the prompt's requested four-hour minimum, and the underlying model identifier was not exposed in the accessible task export.
08
BixBench publishes 2,120 bioinformatics trajectories
BixBench releases 2,120 raw agent trajectories across research-like bioinformatics questions, with generated notebooks, repeated runs, configurations, and evaluation data.
- System
- BixBench, GPT-4o configurations, Claude configurations
- Prompt
- full
- Evidence
- Reported
- First dated event
- Feb 28, 2025
Keep in view: These are benchmark attempts derived from published notebooks, not 2,120 new biological findings. Open-ended scores rely on automated grading, and embedded source materials may retain third-party terms.
09
GPT-5.6 produces a proof of the Cycle Double Cover Conjecture
A long-running 64-agent search produced a claimed complete proof, followed by a public Lean formalization and a separate model-assisted write-up.
- System
- GPT-5.6 Sol Ultra, GPT-5.6 Sol, Codex, Lean
- Prompt
- full
- Evidence
- Formal
- First dated event
- Jul 9, 2026
Keep in view: No complete run transcript was located, and the result was extremely recent at the research cutoff.
10
EarthLink attempts an eight-month Atlantic Niño forecast
EarthLink proposed an Atlantic wind-thermocline precursor and improved on persistence and ENSO-only comparators, but its hindcasts missed the requested temporal-correlation target above 0.5.
- System
- EarthLink, Exact production backbone undisclosed
- Prompt
- full
- Evidence
- Expert-reviewed
- First dated event
- Jul 23, 2025
Keep in view: The numerical target was not met, the mechanism remains an author-proposed hypothesis, and the exact model used for this production run is not sufficiently clear from the public materials.
11
EinsteinArena agents improve twelve mathematical bounds
A live distributed arena reported twelve verifier-backed state-of-the-art scores, including a dimension-11 kissing-number construction improving the known lower bound from 593 to 604.
- System
- EinsteinArena, Heterogeneous user-supplied agents with generally undisclosed model configurations
- Prompt
- representative
- Evidence
- Certified
- First dated event
- Mar 19, 2026
Keep in view: The twelve results are construction or bound improvements, not twelve theorem proofs. Agent model settings and result-specific prompts are not generally public, and current leaderboard scores can differ from the dated paper snapshot.
12
GPT-5 contributes the key idea for Erdős problem 848
GPT-5 proposed a stability or density idea that Mehtaab Sawhney and Mark Sellke corrected, tightened, and developed into a full solution.
- System
- GPT-5 Pro
- Prompt
- partial
- Evidence
- Expert-reviewed
- First dated event
- Oct 2025
Keep in view: Substantial human correction and proof development were required; this was not an autonomous resolution. The public shared page preserves all textual user messages but not the bodies of two uploaded attachments.
13
FunSearch improves cap-set constructions
An evolutionary LLM-and-evaluator loop found larger cap sets in several dimensions and new online bin-packing heuristics.
- System
- FunSearch, PaLM 2
- Prompt
- partial
- Evidence
- Peer-reviewed
- First dated event
- Dec 14, 2023
Keep in view: The prompt is an evolving program scaffold plus exemplars, not a single natural-language research prompt.
14
Robin proposes a dry-AMD drug-repurposing direction
FutureHouse's Robin connected ROCK inhibition to improved retinal pigment epithelium phagocytosis and guided two experimental rounds; Y-27632 and ripasudil improved phagocytosis in vitro.
- System
- Robin
- Prompt
- full
- Evidence
- Experimental
- First dated event
- May 2025
Keep in view: ROCK inhibition and phagocytosis were individually known; the novel contribution is chiefly the proposed dry-AMD connection, and evidence remains in vitro.
15
GPT-4 proposes breast-cancer drug combinations
GPT-4 proposed drug pairs for breast-cancer cell lines; several showed positive synergy, while most first-round pairs did not clear the stated bar and one explanation was biologically wrong.
- System
- GPT-4
- Prompt
- full
- Evidence
- Experimental
- First dated event
- May 2024
Keep in view: Cell-line synergy is not equivalent to therapeutic efficacy or safety; the same campaign contains explicit model errors and failed combinations.
16
Lossfunk preserves one completed and three failed research attempts
A six-agent research pipeline completed one workshop paper while three other ideas failed during implementation or evaluation, with workflow prompts and per-attempt failure analyses published together.
- System
- Lossfunk AI Scientist pipeline, Six specialized LLM agents
- Prompt
- full
- Evidence
- Reported
- First dated event
- 2025
Keep in view: Workshop acceptance is not independent confirmation of the completed paper's claims. The artifact repository had no visible license file at the research cutoff, so the archive links rather than mirrors its prompt text.
17
Point convergence of Nesterov accelerated gradient
GPT-5 suggested a useful restructuring during a multi-session collaboration; Ernest Ryu recognized the key structure, corrected errors, and developed the complete proof with Uijeong Jang.
- System
- GPT-5
- Prompt
- unavailable
- Evidence
- Expert-reviewed
- First dated event
- Jul 22, 2025
Keep in view: No complete transcript was located; the model made many incorrect suggestions and did not assemble the final proof autonomously.
18
OpenAI attempts all ten First Proof problems
An internal model produced attempts for ten research-level problems; expert assessments varied, and one attempt initially thought likely correct was later acknowledged as incorrect.
- System
- Undisclosed OpenAI internal model, ChatGPT
- Prompt
- representative
- Evidence
- Expert-reviewed
- First dated event
- Feb 14, 2026
Keep in view: The prompt appendix simulates the interaction pattern but is not a complete raw transcript; validation status remains problem-specific and mutable.
19
SciExplorer investigates initially unknown physics models
A general-purpose agent used experiments and code to recover equations of motion and Hamiltonians across simulated physical systems, while full logs also preserve premature and incorrect model commitments.
- System
- SciExplorer, Gemini 2.5 Pro, GPT-5 mini, GPT-5 nano
- Prompt
- full
- Evidence
- Peer-reviewed
- First dated event
- Sep 29, 2025
Keep in view: The agent rediscovered models in controlled simulations rather than previously unknown laws of nature. The environments and scoring rules were designed by the researchers.
20
ChatGPT suggests a differential-equation counterexample
ChatGPT-5.5 Pro supplied the key oscillatory construction for a smooth non-uniqueness counterexample after five comparison models failed or returned incorrect proofs.
- System
- ChatGPT-5.5 Pro, ChatGPT-5.2 Pro, ChatGPT-5.4 Pro, Gemini 3 DeepThink, Claude Opus 4.6 Extended
- Prompt
- full
- Evidence
- Reported
- First dated event
- Mar 27, 2026
Keep in view: The work is a recent preprint without formal verification or identified peer review. The printed prompt uses a closely related weighted-Laplace formulation rather than the final theorem verbatim.
21
AI model disproves the planar unit-distance conjecture
An internal OpenAI model produced an infinite family contradicting Erdős's conjectured upper-bound behavior, followed by human simplification, context, and extensions.
- System
- Undisclosed OpenAI internal model
- Prompt
- full
- Evidence
- Expert-reviewed
- First dated event
- May 20, 2026
Keep in view: The internal model identity, hidden system prompt, attempt count, and compute budget were not disclosed; the public trace is abridged.
22
Virtual Lab designs SARS-CoV-2 nanobody variants
A GPT-4o PI agent and specialist agents designed 92 nanobody mutants; more than 90% expressed solubly and two improved binding against newer variants in wet-lab tests.
- System
- Virtual Lab, GPT-4o
- Prompt
- full
- Evidence
- Experimental
- First dated event
- 2025
Keep in view: The work mutated known scaffolds and measured binding, not viral neutralization; humans supplied high-level feedback and ran the experiments.
23
GPT-5.6 closes a zeroth-order convex-optimization gap
A 148-minute run using a CDC-style prompt produced the main quadratic lower-bound argument; Phillip Kerger checked and formally verified it, then obtained a stronger refinement in a later chat.
- System
- GPT-5.6 Sol Pro, Lean
- Prompt
- full
- Evidence
- Formal
- First dated event
- Jul 15, 2026
Keep in view: The result was new and not peer reviewed at the research cutoff; the human researcher selected the problem, authored the elaborate prompt, checked the proof, and formalized it.
About the archive
A reference set of research problems, prompts, attempts, and outcomes.
Each record brings together the problem targeted, the prompt or workflow, the reported outcome, contributors, dates, source material, and available validation. Together, they make it easier to compare how researchers frame problems, direct AI systems, judge outputs, and report unsuccessful attempts.
The collection includes successes, partial progress, disputed claims, rediscoveries, and documented attempts that produced no result.
The metadata remains provisional while the corpus grows. Primary sources stay linked, and prompt text is mirrored only when permission or licensing allows it.
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