  Partial differential equations are central objects in the mathematical
modeling of natural and social sciences (sound propagation, heat diffusion,
thermodynamics, electromagnetism, elasticity, fluid dynamics, quantum
mechanics, population growth, finance...etc). They were for a long time
restricted only to the study of natural phenomena or questions pertaining to
geometry, before becoming over the course of time, and especially in the last
century, a field in itself. The second half of the XXth century was the "golden
age" of the exploration of partial differential equations from a theoretical
perspective. The mathematical work of Louis Nirenberg since the early 1950s has
to a large extent contributed to the growth of this fundamental area of human
knowledge. The name Nirenberg is associated with many of the milestones in the
study of PDEs. The award of the Abel Prize to Louis Nirenberg marks a special
occasion for us to revisit the development of the field of PDEs and the work of
one of the main actors of its exploration.
