Vladyslav Prytula is an applied mathematician who has spent his career moving between dynamical systems, homogenization of PDEs and machine learning. His training began in Kharkiv under Igor Chueshov, whose attractor theory sits underneath much of this book, and continued through a PhD and postdoctoral years in partial differential equations and infinite-dimensional dynamical system: well-posedness, global attractors, homogenization , from a doctoral student in Spain to an Abel Fellow and associate professor in Norway.

These days he is Principal ML/AI research scientist / Director of ML/AI at a European e-commerce company, building search, recommendation, and agentic systems at production scale. The book came out of a stubborn conviction that the way actor-critic methods converge is best understood not as an optimization trick but as the long-time behaviour of a coupled flow — actor, critic, and state distribution moving together on one phase space — and that you can write those dynamics down precisely, prove things about them, and have a machine check the proofs.

He lives in Munich, where most of his thinking happens on long trail runs and in the mountains.