Learn about the complex relationship between automatic differentiation (AD) and scientific simulations in this JuliaCon 2024 conference talk. Explore how AD tools interface with numerical analysis, implicit differentiation, and physical symmetries through examples from materials science, specifically focusing on density-functional theory in DFTK.jl. Discover the distinctions between obtained gradients through AD and desired gradients based on physical principles, gaining insights into the challenges and considerations when applying automatic differentiation to large-scale scientific computations.