Reasoning capability is being distilled into models that run on cheaper hardware and inside private environments.
Small Reasoning Models: Parallax Index score. Score: W1 38, W2 41, W3 44, W4 47, W5 51, W6 54, W7 57, W8 60, W9 63, W10 66, W11 69, W12 72.
OpenAI announced on 26 October 2026 that its internal models produced a disproof of the Exponential Time Hypothesis, a proof of the local smoothing conjecture in every dimension, and an existence proof for quantum chromodynamics. It is handing verification to unpaid external groups rather than to journals.
The Simons Foundation announced on 15 October 2026 that it, Anthropic and OpenAI will commit $15 million in combined funding and resources to help mathematicians evaluate AI-assisted results and set standards for using the tools. The foundation will award the money through an open call for proposals.
Google released Gemini 4 Argon to developers, enterprises and consumers on 13 October 2026, thirteen days after a restricted launch to cyber defenders. It ranks first on the Vals Index and joint fourth on Artificial Analysis's Intelligence Index.
OpenAI posted 722 mathematical manuscripts in 372 result families to a GitHub repository on 6 October 2026, produced by an unreleased internal model. Measured against recommendations published on 29 September by the Advisory Group on Mathematics and Artificial Intelligence, the release delivers the requested formalisation artefacts and version protocols but withholds the model's name, the prompts, and all but ten reasoning summaries.
The declaration argues that AI companies announcing solutions in a rush strips out attribution, method and the human transmission of ideas. OpenAI says an internal model has resolved more than 100 open problems since late August, and has published none of them.
A calculation that nobody in the scattering amplitudes field had finished was completed by a model running largely unsupervised, for roughly one to two thousand dollars. The physicist who set the challenge says the lesson is not that machines are superhuman but that the limit was lower than experts believed.
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