Lars Hörmander explained his reaction to being asked to contribute an article to the book on Fields Medallists Lectures in his article L Hörmander, Looking forward from ICM 1962, in M Atiyah and D Iagolnitzer (eds.), Fields Medallists Lectures (Singapore, 1997). Hörmander writes:-

When I received the invitation to contribute to a volume entitled Fields Medallists' lectures, intended to be similar to Nobel lectures in physics, my first reaction was quite negative. The Nobel prizes and the Fields medals are so very different in character; while Nobel prizes are supposed to be given for work of already recognized importance, often the work of a lifetime, the Fields medals are given 'in recognition of work already done, and as an encouragement for further achievement on the part of the recipients'. However, since this may imply an obligation to account for the expected further achievements, I have decided to contribute to this volume a brief survey of the later development of the work for which I assume that I received a Fields medal in 1962. It will not be a complete survey even of the development of these topics in the theory of linear partial differential equations since 1962, for I concentrate on my own work and only mention work by others interacting with it.

JOC/EFR March 2006

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