Some recent progress in statistical mechanics

It is the tradition of our Society that the last official act of the retiring president should be an exposition in general terms of the field of physics in which he is especially interested and in which, supposedly, he has done some original work. Although I have had to do such a task a few times before in my life, I must say that I have always approached it with trepidation. It is so unnatural to talk especially about theoretical problems without formulas and without a blackboard that it is like doing a juggling act with your hands tied! So I hope you will forgive me for many statements without proof. I can only try to discuss with you some of the problems which have occupied me and I hope that I can convince you that perhaps they have some real interest.