The speaker at the Third Annual Kolmogorov Lecture, held at Royal Holloway on 10th February 2005, was given by Professor Per Martin-Löf of Stockholm University. Professor Martin-Löf presented a lecture entitled "Zermelo's axiom of choice: What was the problem with it?"
"An analysis of Zermelo's axiom of choice in constructive type theory reveals that the problem with it is not the existence of the choice function but the extensionality of it, which is not visible in an extensional framework where all functions are by definition extensional."