NumAStAI (Numerical Analysis for Stable AI) is an ERC Advanced Grant project based at the University of Edinburgh. We aim to identify, quantify and reduce weaknesses in artificial intelligence algorithms through numerical analysis, combining matrix analysis, optimization, backward error analysis, condition number theory and stochastic computation. Our research spans six interconnected themes — Inevitability, Editability, Targetability, Universality, Roundability and Legislatability — studying adversarial attacks, model editing, data representation bias, low-cost universal attacks, the effects of low-precision computation, and how these findings can inform AI policy and regulation, in pursuit of more ethical, secure and reliable AI systems.