Large language models (LLMs) are increasingly trusted with mathematical, scientific and engineering work, yet their mistakes are often confidently written and hard to spot. A single wrong step tends to propagate, making the model waste inference tokens following a false premise. Existing safeguards either check only the final answer and restart from scratch, or rely on a verifier LLM that competes for GPU capacity and slows down response time. We propose online, deterministic verification: many kinds of reasoning steps can be validated by code, so a step can be verified in real time, as it is written, without any model call or GPU use. Whenever a check fails, we point out the mistake and let the model continue from the same spot. We demonstrate this approach on symbolic mathematics, where derivations already contain explicit expressions that a computer algebra system can check in milliseconds. Tested on the ASyMoB benchmark with three open-weights models, our online validation improves accuracy by 1.4-5.6 percentage points, corresponding to a 1.8-14.9% net reduction in incorrect answers, while increasing token usage by only 6-7%. Because the verifier is independent of the model, the approach complements progress in LLMs rather than competing with it: every new model can benefit immediately, and the benefit grows as deterministic checkers extend to more kinds of reasoning steps.
As AI's mathematical capabilities rapidly improve, meaningful benchmarks are shifting from university-level problems and math olympiads to research-level mathematics. The Ramanujan Challenge is a benchmark comprised of research-level problems in number theory, including unpublished results and open conjectures. It presented concrete formulas for mathematical constants whose correctness can be checked numerically, while their proofs may require non-obvious mathematics. Here, we analyze the Challenge submissions, measuring the relative success of different AI models, Computer Algebra Systems (CAS), and formal tools. We find correct submissions that are conceptually distinct from the official solutions, and a proof of one of the published open conjectures. Evaluating the submissions exposed a second challenge: judging complex proofs reliably at scale. We introduce an AI-assisted evaluation pipeline for natural language proofs, CAS code, and Lean formalizations that assesses semantic and logical correctness. Compared with the conventional one-shot LLM judgment, our pipeline reduces false-positive verdicts on natural language proofs from 23% to 6% and improves judgment accuracy on supporting code from 46% to 58%. This approach provides a methodology for evaluating research-level mathematics at scale, with potential applications across mathematics and AI for science.