A significant breakthrough in large language models (LLMs) has been claimed by Subquadratic, a Miami-based AI startup, which asserts that it has overcome a mathematical bottleneck hindering LLM development for nearly a decade1. Subquadratic's innovation, dubbed SubQ, allegedly enables faster and more cost-effective LLMs. Although the company's initial announcement was met with skepticism due to a lack of details, Subquadratic has since provided independent evaluation results that lend credibility to its claims. The potential implications of this breakthrough are substantial, as improved LLMs could have far-reaching consequences for various sectors, including policy, security, and workforce dynamics. If Subquadratic's claims are verified, this could mark a major milestone in AI development, allowing for more efficient and effective LLMs. This matters to practitioners because a breakthrough in LLMs could significantly impact the development of AI systems, affecting their performance, security, and overall reliability.