Explore quantum mechanical computations and their dimensional challenges in this 26-minute talk by Codina Cotar from the Department of Statistical Science at UCL. Delve into the complexities of Schroedinger's equation for many-electron problems and understand why solving it accurately and efficiently remains a significant challenge. Learn about density functional theory (DFT) as an approximation method for simulating chemical behavior in large systems. Discover recent approaches to tackle existing issues in the field, including insights from probability theory and optimal transport. Gain an introduction to quantum computing, data science applications in quantum mechanics, and the historical context of these developments. Examine the interaction between electrons and key quantum mechanics quantities while uncovering interesting facts about this cutting-edge area of research.