The Gatsby Unit seeks to appoint a new principal investigator with an outstanding record of research achievement and an innovative research programme in theoretical neuroscience or machine learning at any academic rank. In theoretical neuroscience, we are particularly interested in candidates who focus on the mathematical underpinnings of adaptive intelligent behaviour in animals, or develop mathematical tools and models to understand how neural circuits and systems function. In machine learning, we seek candidates who focus on the mathematical foundations of learning from data and experience, addressing fundamental questions in probabilistic or statistical machine learning and understanding; areas of particular interest include generative or probabilistic modelling, causal discovery, reinforcement learning, theory of deep learning, and links between these areas and neuroscience or cognitive science.