ChatGPT 5.5 Pro can produce PhD-level research in approximately one hour with minimal mathematical input. Large language models are increasingly capable of solving complex research-level problems, including those related to the Erdős conjectures.

Diffusion language models (DLMs) enable parallel token generation, potentially overcoming the sequential limitations of autoregressive (AR) decoding. However, DLMs currently underperform AR models in quality due to a lack of introspective consistency, where AR models align with their generated outputs.

In July 2025, AI models successfully solved five out of six problems at the International Mathematical Olympiad, surprising mathematicians with their rapid advancement. Despite these impressive results, the impact of AI on research mathematics remains uncertain.

Claude found an odd-m construction for the open Hamiltonian decomposition problem, impressing Prof. Donald Knuth, who titled the resulting paper "Claude’s Cycles." The updated research reveals that for the base case m=3, there are 11,502 Hamiltonian cycles, with 996 generalizing to all odd-m, and 760 valid "Claude-like" decompositions identified.

Anthropic's Trust Center focuses on AI safety and research, emphasizing transparency and secure practices in AI development. The initiative aims to support the safe transition to transformative AI technologies.

A Ramsey-style problem on hypergraphs has been solved by Kevin Barreto and Liam Price using GPT-5.4 Pro. The solution has been confirmed by Will Brian and will be published, along with a transcript of the original conversation.

Attention Residuals (AttnRes) serves as a drop-in replacement for standard residual connections in Transformers, allowing each layer to selectively aggregate earlier representations. It includes two variants: Full AttnRes, where each layer attends over all previous outputs, and Block AttnRes, which groups layers into blocks to reduce memory usage from O(Ld) to O(Nd).

Artificial General Intelligence (AGI) can accelerate scientific discovery and address significant global challenges. Evaluating progress toward AGI requires diverse methods and approaches, with cognitive science offering valuable tools for assessment.

The LLM Architecture Gallery compiles architecture figures and fact sheets from significant LLM comparisons. Users can enlarge figures and navigate to corresponding sections using model titles.

Billion-parameter theories aim to explain complex phenomena in the universe using concise mathematical formulations. Historical explanations of natural events transitioned from mystical interpretations to scientific inquiry with succinct equations like F=ma and E=mc².