Peter D. Lax, an American mathematician, has been awarded the 2005 Abel Prize, the most prestigious award that mathematicians can receive, and has sometimes been considered the substitute for the Nobel Prize for not existing Nobel Prize in Mathematics. Lax receives the award for his work in the field of differential equations.
In the 1950s and 1960s, he laid the foundation for the theory of nonlinear differential equations and developed numerous numerical methods to solve them. The importance of this work is not merely theoretical; many differential equations presented in real problems are non-linear. Hence Lax's fame in relating theory and applications. Hence he has received other awards, such as the Steele of the American Mathematical Association.