OEIS Open: How many conjectures can language models turn into theorems?

We construct OEIS Open, a benchmark based on 492 open mathematical conjectures from the OEIS, formalized in Lean by Tsoukalas et al. Whereas these conjectures had previously been attempted only with a bespoke agent, our open-source evaluation code runs any generic language model (LM) against them, and is secure against LM cheating attempts. We find that LMs equipped with a minimal set of tools resolve 147 of these conjectures with a budget of \$50 per attempt, scoring 30% on OEIS Open. OEIS Open Lite is a random subset of 100 conjectures for cheaper evaluation. When evaluated with a budget of \$200 per attempt, the best current LM scores 44% on OEIS Open Lite. Giving LMs access to the mathematics literature via 476,000 papers from arXiv did not increase performance on OEIS Open Lite, and nor did using more sophisticated agent loops. The conjectures covered in this work are of uncertain mathematical significance, and most have likely received little previous attention. Nevertheless, our results show that LMs can resolve open research conjectures autonomously and at modest cost.

MirrorCode: AI can rebuild entire programs from behavior alone

AI models are rapidly improving at autonomous coding, as shown by benchmark progress and one-off demonstrations such as AI implementing a C compiler. However, existing coding benchmarks tend to focus on shorter tasks, and one-off demonstrations are hard to compare systematically because they often have some human guidance, and are not standardized or repeated across models. To address these challenges, we introduce MirrorCode, a long-horizon coding benchmark based on reimplementing entire software projects. In MirrorCode, AI agents must replicate the functionalities of an existing program, without access to its source code. AI solutions must match the original program's output exactly on end-to-end tests, including held-out tests. MirrorCode's 25 target programs span different areas of computing: Unix utilities, data serialization and query tools, bioinformatics, interpreters, static analysis, cryptography, and compression. Existing AI models can already reimplement complex software, with the strongest model scoring 56% across the benchmark. For example, AI can reimplement gotree, a 16,000-line bioinformatics toolkit - a task that we believe would take weeks for a human engineer. However, studying the frontier of performance requires a larger inference budget than typical benchmarks, for example, \$2,600 over 19 days for a single attempt on a large task. We show that AI agents can already complete long-horizon software engineering tasks, especially when requirements are precisely specified. More broadly, our work suggests AI will have transformative effects on software engineering, as autonomous agents continue to improve.