The Abel Prize for 2005 is awarded to Peter D. Lax, Courant Institute of Mathematical Sciences, New York University. The Abel Prize is a mathematics prize of the Norwegian Academy of Science and Letters, dedicated to the memory of Niels Herik Abel (1802-1929) on the occasion of the bicentenary of his birth. It is modeled after the Nobel Prize. The Abel Prize has been awarded annually beginning in the year 2003. Prof. Lax receives the Abel Prize "for his groundbreaking contributions to the theory and application of partial differential equations and to the computation of their solutions" to quote the Abel committee.

Professor Lax is considered one of the most versatile mathematicians of his generation. He is able to join together pure and applied mathematics, combining a deep understanding of analysis with an extraordinary capacity to find unifying concepts. Prof Lax laid the foundation for the modern theory of nonlinear hyperbolic systems in the 1950s and 1960s. His contribution to entropy, solitons and shock waves are considered groundbreaking. His name is associated to many major mathematical results and numerical methods. To name a few, these include Lax pairs, Lax-Milgram theorem, Lax equivalence theorem, etc.

Sitting on the editorial board of the Journal of Hyperbolic Differential Equations, Professor Lax lends his expertise in nonlinear hyperbolic systems to refereeing papers on the theory and numerical analysis of hyperbolic conservation laws and of hyperbolic partial differential equations arising in mathematical physics. Having won the prestigious Wolf Prize in Mathematics in 1987, his life and works are also featured in Volume 2 of  Wolf Prize in Mathematics published by World Scientific.