I would like to thank our Swiss hosts very warmly for organizing so flawlessly and for giving us such a beautiful locale for the 1994 ICM.
I am here as the chairman of the Fields Medal Committee for this Congress, whose other members are:
I should add that we consulted many others in making our decisions.
As the committee compiled lists of names of candidates and their accomplishments, we found ourselves both pleased and awed by the great fecundity of recent mathematics, and by the great number of possible candidates representing a great number of areas of mathematical research. What to me it the most miraculous aspect of our field is that it is growing in so many directions: limbs sprout new growth and new shoots go off in unexpected dimensions. There is growth by deep and subtle proofs of old problems, and by the discovery and exploration of wholly new phenomena with new models. Our response to this is to try to reward excellence in as many areas as possible. Fields himself realized that at least two medals were needed "because of the multiplicity of the branches of mathematics" and, as you know, this has grown to three or four medals. With at most four, we have to make quite a few very painful choices.
Fields also said in his 1932 memorandum on the Medals:
"It is understood that in making the awards, while it was in recognition of work already done, it was at the same time intended to be an encouragement for further achievements on the part of the recipients and a stimulus to renewed effort on the part of others... with a view to encouraging furter development along these lines".
We have followed previous committees interpreting his intend by restricting ourselves to considering candidates who are at most 40 (forty), in the year of the award ceremony. His words also bring up an issue which is central to the future of our field: in many countries, governments have been attempting in the last few years to channel mathematical research along lines that bureaucrats deem to be productive and useful. Note that Fields' recommendation is instead to let mathematics develop by its internal forces, to let its success encourage further success. I agree with him that, in the long run, this will produce more results for both mathematics and for society.
Finally, we must bear in mind how clearly hindsight shows that past recipients of the Fields' Medal were only a selection from a much larger group of mathematicans whose impact on mathematics was at least as great as that of the chosen.
So now, with great pleasure, let me announce the recipients whose work, in the view of the whole committee, embodies the best in mathematicas today. In alphabetical order, they are: