**Vladimir Igorevich Arnold** born in 1937 has been professor at the Moscow University since 1961.**Louis Nirenberg** born in Canada 1925 became an American citizen in 1954. Since 1957 he has been a professor at Courant Institute, New York University.

The subject for this year´s Crafoord Prize is non-linear differential equations. Modern analysis is entirely based on the ideas which Newton introduced to describe the movements of planets around the sun. he related the position, the velocity and the acting forces of a body to each other and had then introduced the first differential equations. These natural equations are non linear and can therefore not well be analyzed by explicit mathematical computations and many natural questions are still open. With modern computers we can make detailed predictions but questions such as stability of the planetary movements are still unsolved. Arnold has given very important contributions to questions of this type and taken a big step to the understanding of the celestial movements. In later papers, he has treated general questions of singularities of mappings. These relate to the new efforts to understand mathematically complicated developments which are known under the concept of catastrophe theory.

Newton´s ideas were used to describe many different systems in physics and in geometry, which may depend on several variables simultaneously. The equations are then called partial differential equations and again the most interesting ones are non-linear. Nirenberg has treated a great number of problems of this nature. As an example from geometry one can mention the problem to find a surface with given curvature and from physics studies of the equations for viscose fluids and concerning existence of free streamlines. Nirenberg´s work ranges over a variety of problems and has been of basic importance for the development of the field.

Besides the Crafoord Prize a sum of 300 000 Swedish crowns will be awarded as grants within the same3 field in mathematics. Crafoordlectures will be held on the 29th of September at 3 P.M. and on the 30th from 10 A.M. throughout the day.

The Crafoord fund was constituted in 1980 when Mr. And Mrs. Crafoord donated a large sum to the Academy. The fund will support scientific research work within the fields of mathematics, astronomy, geosciences, biosciences (especially ecology) and polyartritis.

Unfortunately Professor V. I. Arnold is unable to attend the Ceremony on Wednesday September 29th 1982.