From toy math to open problems in 3 years

What just changed in math

OpenAI says a new internal model, trained for only 24 days, “has already resolved more than 100 long-standing open problems across most areas of mathematics,” with the pace surprising even their own mathematicians and an external advisory group (including Edward Witten, Timothy Gowers, and Martin Hairer) now helping assess and release results [[1]](https://x.com/choblin29/status/2102095044543160555).

That’s all we concretely know about the system:

• It is “new” and “internal.”
• Training started 24 days before the announcement.
• OpenAI claims >100 “long-standing open problems” across “most areas of mathematics” have been resolved.
• An independent group of mathematicians is advising OpenAI on assessment, communication, and standards around new mathematical results [[1]](https://x.com/choblin29/status/2102095044543160555).

No model name, no architecture, no benchmarks, no specific problems.

But we *do* have more detailed, adjacent evidence for how frontier models are being used to actually do novel work in:

• Historical research with GPT-6 variants and Opus 5.5 [[2]](https://resobscura.substack.com/p/ai-labs-need-to-start-funding-historical)
• Biological discovery with Claude [[3]](https://x.com/DarioAmodei/status/2102831170299834652)

If you’re building agentic systems, you can treat the OpenAI math claim as one more data point in a trend whose mechanisms are much clearer elsewhere.

The emerging pattern: “tractable” problems + agent swarms

Benjamin Breen’s account of using GPT-6 Sol, GPT-6 Astra, and Opus 5.5 is unusually explicit about where these systems actually work and why [[2]](https://resobscura.substack.com/p/ai-labs-need-to-start-funding-historical).

He observes that models perform best on problems that are:

• Pre-scoped by experts: a known list of problems that “need solving.”
• Fully digitized: relevant data is already online and accessible.
• Aligned with “spiky” strengths: multilingual reasoning, advanced math, large-scale data trawling, and writing bespoke code [[2]](https://resobscura.substack.com/p/ai-labs-need-to-start-funding-historical).
• Decidable: candidate solutions can be clearly proven or disproven [[2]](https://resobscura.substack.com/p/ai-labs-need-to-start-funding-historical).

He explicitly connects this to why models have “run rampant in mathematics but not in humanistic fields,” because math offers clear correctness criteria while much of history does not [[2]](https://resobscura.substack.com/p/ai-labs-need-to-start-funding-historical).

This framing maps directly onto:

• OpenAI’s math-claim environment: lots of existing problem lists, clear notions of proof, and (presumably) large digitized literature.
• Anthropic’s biology workflow: a broad but well-defined search space (genome data and literature) plus lab experiments to validate discrete hypotheses [[3]](https://x.com/DarioAmodei/status/2102831170299834652).

As a builder, that’s your design constraint: you get extreme leverage when you can turn your domain into a well-scoped, decidable search/inference problem over large digital corpora or data.

How these systems are actually being run

1. Historical research: multi-agent archives and code

Breen describes several concrete workflows with GPT-6 Astra, GPT-6 Sol, and Opus 5.5 [[2]](https://resobscura.substack.com/p/ai-labs-need-to-start-funding-historical):

Cryptography and codebreaking

• Astra decrypted a 1941 German army communication and a WWI German radio cipher in work documented by others [[2]](https://resobscura.substack.com/p/ai-labs-need-to-start-funding-historical).
• In one case, the key step was not raw cryptanalysis but noticing a note about additional radio message collections at the German Bundesarchiv, then using that cross-corpus information to complete the break [[2]](https://resobscura.substack.com/p/ai-labs-need-to-start-funding-historical).
• Researchers analyzing Astra’s logs found it referenced specific archive file codes correctly, despite those files not being hosted on the crypto researcher’s site; it’s unclear how the model accessed or inferred them [[2]](https://resobscura.substack.com/p/ai-labs-need-to-start-funding-historical).

Mechanism pattern:

• Model is given a specific cryptographic open problem (message to decrypt).
• It autonomously searches relevant web sources, including obscure notes and metadata.
• It uses cross-document linkage (e.g., matching message numbers and units) to constrain keys and settings.
• Human experts later try to reconstruct what it did from logs.

Tracing textual transmission

• GPT-6 Astra identified the source of a passage that Isaac Newton had translated into Latin from a French alchemical text, apparently a previously unknown connection [[2]](https://resobscura.substack.com/p/ai-labs-need-to-start-funding-historical).
• Opus 5.5 downloaded >5,000 files from Samuel Hartlib’s archive, spawned sub-agents to search Google Books and other archives, and tried to identify anonymous sources Hartlib relied on, especially around alchemical knowledge [[2]](https://resobscura.substack.com/p/ai-labs-need-to-start-funding-historical).
• It inferred that both Newton and Hartlib encoded “Hungarian vitriol” using different letter manipulations, and used exact letter-level analysis and marginal annotations to argue they were referencing the same ingredient and likely the same underlying manuscript [[2]](https://resobscura.substack.com/p/ai-labs-need-to-start-funding-historical).

Mechanism pattern:

• One orchestrator prompts the model to:
• Crawl a fixed archive (Hartlib papers).
• Create sub-agents to search external sources (Google Books, other archives).
• Cross-compare phrases, quantities, and encodings across languages.
• The model uses its math-like capabilities (anagram detection, character frequency analysis) as building blocks inside a historical inference pipeline.
• It then synthesizes findings into a structured “report” the human can evaluate.

Deciphering early modern codes

• Opus 5.5 partially deciphered two 16th-century Spanish letters in Emperor Charles V’s code, only to later discover both had already been decrypted (one in the 1530s, one in 1916) [[2]](https://resobscura.substack.com/p/ai-labs-need-to-start-funding-historical).
• This served as a validation that the model’s decryptions matched known plaintext once it found the historical decodings, but also an example of wasted effort without prior literature checking [[2]](https://resobscura.substack.com/p/ai-labs-need-to-start-funding-historical).

Mechanism pattern:

• Model first attacks cipher directly (pattern analysis).
• Only afterwards is it steered to check for existing scholarship, where it finds the “gold standard” plaintext and can compare its guesses [[2]](https://resobscura.substack.com/p/ai-labs-need-to-start-funding-historical).

For you, the transferable bit is not “use GPT-6” but how the tasks are shaped:

• Explicit problem instances (this cipher, this archive, this manuscript).
• Strong constraints (finite data, verifiable correctness).
• Orchestration that allows:
• Recursive search (sub-agents).
• Tool-like use of math inside non-math domains.
• Post-hoc trace analysis by humans.

2. Biology: model-driven hypothesis → human-run experiments

Anthropic’s described workflow with Claude shows the same pattern in a different domain [[3]](https://x.com/DarioAmodei/status/2102831170299834652):

• Humans define a broad research area in biology.
• Claude:
• Reads the literature and “a bunch of genome data.”
• Identifies “something interesting” — here, a molecular machine in bacteriophage DNA that might be a new gene editing mechanism [[3]](https://x.com/DarioAmodei/status/2102831170299834652).
• Proposes experiments to verify the discovery.
• Human scientists execute experiments in a BSL1/BSL2 lab (no dangerous materials), validate results over a few weeks, and iterate with Claude when needed [[3]](https://x.com/DarioAmodei/status/2102831170299834652).
• Anthropic reports that only a “handful of known” systems resemble the enzyme system Claude found and notes that similar reverse-transcriptase-based systems have recently been described independently by others, though they are distinct and independently evolved [[3]](https://x.com/DarioAmodei/status/2102831170299834652).

Mechanism pattern:

• AI is a literature and data engine that proposes structured hypotheses (“this looks like a novel system”).
• It also generates *experiment plans* that are then executed by humans.
• Feedback from wet-lab results closes the loop with the model, but the model is not directly controlling lab hardware today [[3]](https://x.com/DarioAmodei/status/2102831170299834652).

Dario Amodei explicitly places this in a general pattern where AI performance in new intellectual domains goes from weak → competition-grade → minor open problems → significant open problems → “top few open problems” over roughly a few-year window, with math as the worked example from 2023–2026 [[3]](https://x.com/DarioAmodei/status/2102831170299834652).

That time-series is important context for OpenAI’s claim: it’s not an isolated boast, but consistent with an observed trend from another lab.

How this fits into your stack

Even without internal details from OpenAI, the three cases (math, history, biology) are structurally similar:

1. Problem scoping layer

• Humans define:
• The problem family (e.g., “Enigma messages from 1941” [[2]](https://resobscura.substack.com/p/ai-labs-need-to-start-funding-historical), “gene editing-like systems in phage genomes” [[3]](https://x.com/DarioAmodei/status/2102831170299834652), “long-standing math conjectures” [[1]](https://x.com/choblin29/status/2102095044543160555)).
• The datasets or corpora.
• The accept/reject criteria for candidate solutions.

1. Agentic search / reasoning layer

• You run a frontier model (or many copies) with:
• Access to the scoped data (archives, genome databases, problem lists).
• Tools: web access, code execution, data download—these are all implied in Astra and Opus spawning sub-agents and crawling archives [[2]](https://resobscura.substack.com/p/ai-labs-need-to-start-funding-historical).
• Orchestration patterns include:
• Recursive delegation (Opus 5.5 creating sub-agents) [[2]](https://resobscura.substack.com/p/ai-labs-need-to-start-funding-historical).
• Multi-step strategies (first break cipher, then search if it was already broken) [[2]](https://resobscura.substack.com/p/ai-labs-need-to-start-funding-historical).
• Intensive document cross-linking and letter-level analysis in text-heavy domains [[2]](https://resobscura.substack.com/p/ai-labs-need-to-start-funding-historical).

1. Verification and adjudication layer

• Math:
• For OpenAI, independent mathematicians are explicitly in the loop to “assess and communicate new mathematical results” and “uphold academic and professional standards” [[1]](https://x.com/choblin29/status/2102095044543160555).
• History:
• Breen repeatedly validates AI findings against primary sources, existing scholarship, and sanity checks (e.g., confirming anagrams with editorial notes; realizing an “apparently new” cipher break was already done in 1916) [[2]](https://resobscura.substack.com/p/ai-labs-need-to-start-funding-historical).
• Biology:
• Claude’s hypotheses are tested via lab experiments and only then communicated publicly, with Anthropic emphasizing they don’t yet know the system’s function or significance [[3]](https://x.com/DarioAmodei/status/2102831170299834652).

1. Release and governance layer

• OpenAI: sets up an advisory group to guide how they “responsibly share advances in AI and mathematics,” covering assessment, communication, standards, and tooling [[1]](https://x.com/choblin29/status/2102095044543160555).
• Anthropic: positions the discovery as one step in a long pipeline, not a finished biotech product, and ties it to broader goals like accelerating disease research with appropriate safety constraints [[3]](https://x.com/DarioAmodei/status/2102831170299834652).
• Breen: calls for AI labs to fund digitization, open access, and systematic collaboration with historians and archivists to make this kind of work less ad hoc [[2]](https://resobscura.substack.com/p/ai-labs-need-to-start-funding-historical).

As a builder, that suggests a stack design:

• Inputs: a curated, digitized, permission-cleared corpus + explicit open problem list.
• Core: an agent framework that:
• Spawns sub-agents to search, cross-link, and code.
• Logs reasoning in enough detail that humans can later audit it (as with the Astra logs and archive file references) [[2]](https://resobscura.substack.com/p/ai-labs-need-to-start-funding-historical).
• Outputs: candidate solutions and supporting evidence, optimized not just for correctness but *checkability*.
• Guardrails: human experts and/or external committees with authority to accept, reject, or withhold results.

Why this matters now for builders

From the sources we have, three things are already clearly in play:

1. Frontier models can now do publishable-grade work under the right conditions.

• Math: claims of resolving >100 long-standing open problems in under a month of model training [[1]](https://x.com/choblin29/status/2102095044543160555).
• History: at least one plausible new finding about Newton’s sources, plus non-trivial cryptographic and textual identifications [[2]](https://resobscura.substack.com/p/ai-labs-need-to-start-funding-historical).
• Biology: discovery of a previously unknown enzyme system that might represent a new gene-editing mechanism, confirmed by lab experiments and compared to a small set of known analogous systems [[3]](https://x.com/DarioAmodei/status/2102831170299834652).

1. **The bottleneck is often *infrastructure and access*, not just model quality.**

• Historical work repeatedly hits access walls: many relevant archives are digitized but not freely accessible; many more remain undigitized [[2]](https://resobscura.substack.com/p/ai-labs-need-to-start-funding-historical).
• Breen argues that digitization, open access, and free API/compute for historians could unlock many more results, analogous to mathematics where problems and data are already online [[2]](https://resobscura.substack.com/p/ai-labs-need-to-start-funding-historical).
• Anthropic’s biology program invests in lab capacity and a life sciences team, not just models, to close the loop from hypothesis to verification [[3]](https://x.com/DarioAmodei/status/2102831170299834652).

For your systems, that means the right data and tooling may be more important than another small increment in model quality.

1. Verification and governance are becoming first-class system components.

• OpenAI is embedding external mathematicians directly into the pipeline for evaluating and publishing results [[1]](https://x.com/choblin29/status/2102095044543160555).
• Anthropic is explicit that Claude’s new system has unknown function and significance and that the lab deliberately operates under biosafety constraints [[3]](https://x.com/DarioAmodei/status/2102831170299834652).
• Breen’s work shows how easy it is to “rediscover” known results without strong literature-in-the-loop tooling [[2]](https://resobscura.substack.com/p/ai-labs-need-to-start-funding-historical).

For production agents, “who verifies this, how, and with what logs?” needs to be a design-time question, not an afterthought.

What to watch next

Within the constraints of what’s documented, some concrete near-term questions for builders and observers:

• Math:
• Which specific “long-standing open problems” has OpenAI’s model purportedly solved, and how are proofs being vetted by the advisory group [[1]](https://x.com/choblin29/status/2102095044543160555)?
• Do we see replication in independent proof assistants or other labs?

• History:
• What happens when “hundreds or thousands of agents” are systematically applied to curated historical “millennium problems,” as Breen suggests, instead of one-off experiments [[2]](https://resobscura.substack.com/p/ai-labs-need-to-start-funding-historical)?
• Which digitization and access projects become chokepoints—or accelerators—for AI-augmented research [[2]](https://resobscura.substack.com/p/ai-labs-need-to-start-funding-historical)?

• Biology:
• Does Claude’s enzyme system mature into a useful gene-editing or measurement tool, or does it remain a curiosity [[3]](https://x.com/DarioAmodei/status/2102831170299834652)?
• How far can the “AI proposes, humans execute” model scale before pressure mounts to let models control lab hardware directly [[3]](https://x.com/DarioAmodei/status/2102831170299834652)?

Each of these is less about raw model IQ and more about the orchestration patterns you’re already using: data acquisition, agent design, logging, verification, and governance.

What is not documented

From these sources, we *do not* know:

• Any technical details of OpenAI’s new math model: architecture, size, training data, methods, or the exact list of problems it allegedly solved [[1]](https://x.com/choblin29/status/2102095044543160555).
• Exact tools, libraries, or infrastructure used to orchestrate GPT-6 Sol, GPT-6 Astra, or Opus 5.5 (only that they spawned sub-agents, crawled archives, and wrote reports) [[2]](https://resobscura.substack.com/p/ai-labs-need-to-start-funding-historical).
• Quantitative performance metrics (success rates, time-to-solution, compute budgets) for the historical case studies or Claude’s biological discovery [[2]](https://resobscura.substack.com/p/ai-labs-need-to-start-funding-historical) [[3]](https://x.com/DarioAmodei/status/2102831170299834652).
• Any formal proof that the historical findings (e.g., Newton–Hartlib linkage) are correct; they are argued to be compelling and potentially publishable but not yet presented as peer-reviewed results [[2]](https://resobscura.substack.com/p/ai-labs-need-to-start-funding-historical).
• Detailed experimental protocols, datasets, or validation pipelines for Claude’s discovery beyond the high-level description that the team proposed and ran experiments in a BSL1/BSL2 facility [[3]](https://x.com/DarioAmodei/status/2102831170299834652).