It may be true that in the Seventies more activities were going on. It was then that multiuser information theory was developed and that lead to large activities. Those came to an end when one solved those problems which were not too difficult to solve and then one had to look for something else. Now, it is definitely true that in the last ten years there were many very interesting propositions, many in- teresting new ideas. Perhaps they were not followed through in such detail as they would have been in the Seventies, because there were not enough people working on the field. But, the problems were there, and there is still time to continue and work on them.

Let me just mention a few such problems which are known to me, which are close to me. I do not want to claim in any manner that those are the most important prob- lems. There may be others that are similar or even more impor- tant. There was, for example, the idea of hypothesis testing and statistical estimation using communication over channels of finite capacity. This is the problem of multiterminal detec- tion, multiterminal estimation. Then there was the advance of Shannon theory methods in secrecy problems. The wiretap channel, the idea of generating a secret key using a public channel, and privacy amplification are certainly very in- teresting. Then there was the identification capacity prob- lem, a completely new field which nobody ever thought would come into existence and it lead to very nice developments. And the most recent one, the so-called resolvability prob- lem, which involves the com- plexity of generating randomness, a completely new kind of ap- proximation problem which Sergio Verd' u and Te Sun Han are doing with great success. These are just a few new directions which in my opinion are very important.

Now, I think it is even more important that information theory has very useful applications within Mathematics itself. I have considered in my life a very important task to convince mathematicians that information theory is interesting and it is hardcore mathematics. I think it is demonstrated now beyond any doubts. Let me mention a few examples.

At one time it was declared that ergodic theory was dead. And now ergodic theory is flourishing, thanks to a great extent to information theory. It was Kolmogorov's idea that entropy can be used to study isomor- phism of transformations that led to to the present very big developments in ergodic theory. As another example, take the statistical applications of information theory. The very word information is a basic word for Statistics. Statisticians always want to get information from the data. Still, until recently this was considered a completely dif- ferent kind of in- formation than we had in mind. So the techniques or methods of information theory were not particularly relevant for statisti- cal inquiry. Even though the works of Kullback were there. But that was somehow isolated. But now we have the Maximum Entropy and Minimum Description Length methods which certainly appear very powerful. I think they give a very substantial contribution to statistics. Another field which is important in communications, but even more in computer science, is combinatorics.

You may know that my friend Janos Korner was supposed to sit here, unfor- tunately he could not come. I wish he could talk about the subject himself, he developed a very powerful method of dealing with certain combinatorial problems using quite deep techniques of information theory. Using those techniques he and his colleagues were able to solve famous unsolved prob- lems posed maybe twenty years ago and in combinatorics this is quite a substantial new development.

I just wanted to mention those things to emphasize that as a scientific theory, information theory is very much alive. Of course its future will depend on the young people. If enough talented young people will come to the area then they will continue this work and the field with contiunie to flourish. I am not qualified to talk about the communication theory applications which were the original applications of infor- mation theory. I understand they are still the most impor- tant ones to other people. Dave Forney has explained how important developments have appeared re- cently in that direc- tion. I just wanted to emphasize that also in the theoreti- cal field there were some very important developments and that there is substantial hope for much more. Thank you.