Explore the innovative application of partial differential equations (PDEs) in digital image compression through this Rothschild Lecture delivered by Professor Joachim Weickert from Saarland University. Dive into the intriguing concept of using PDEs, typically employed to model natural phenomena, for compressing digital images. Discover the three key questions addressed in this lecture: selecting which data to retain, identifying the most effective PDEs, and efficiently encoding the selected data. Gain insights into how this approach combines various mathematical disciplines, including mathematical modeling, optimization, interpolation, approximation, and numerical methods for PDEs. Designed for a broad audience, this 1-hour 22-minute talk requires no specific knowledge of image processing, making it accessible to those interested in the intersection of mathematics and digital imaging.