"We identified a profound duality in our research: when the proof difficulty of a geometric proposition is far higher than its construction complexity, it possesses 'aesthetic value' as an ...

Discover the diverse forms of intelligence beyond traditional academics. This article explores five types including naturalistic, logical-mathematical, existential, linguistic, and kinaesthetic ...

Mathematical logic provides a rigorous framework for analysing the structure of mathematical reasoning, enabling a deep understanding of both formal systems and the nature of proofs. Central to this ...

Over the last decade, artificial intelligence (AI) has been largely built around large language models (LLMs). These systems are based on a language and guess words in a chain in the form of tokens.

Alibaba released a new artificial intelligence (AI) model on Thursday, which is said to rival OpenAI’s GPT-o1 series models in reasoning capability. Launched in preview, the QwQ-32B large language ...