100 years of Zermelo's axiom of choice: what was the problem with it?

Abstract

In February 2005 the Third Annual University of London Kolmogorov Lecture was held at Royal Holloway. These annual lectures were established in 2003. The lecture was given by Professor Per Martin-Löf of Stockholm University—one of the world's foremost researchers in the field of constructive mathematics. Professor Martin-Löf was presented with the Kolmogorov Lecture medal in recognition of his contribution to mathematical logic. Professor Alex Gammerman, Director of Royal Holloway's Computer Learning Research Centre, said: ‘The annual lectures are devoted to Andrei Nikolaevich Kolmogorov (1903–1987) who was one of the foremost Soviet mathematicians of the Twentieth Century. He was active in many mathematical fields, with interests in both theory and application. The work of Kolmogorov is the basis of Complexity Science: he made one of the most beautiful discoveries of the 20th century—what is now known as Kolmogorov Complexity or Algorithmic Information Theory. This discovery is crucial to the great advances currently being made in machine learning, and particularly here at Royal Holloway's world-renowned Computer Learning Research Centre. We have established the annual Kolmogorov Lecture to acknowledge the profound importance of his research. For many years A. N. Kolmogorov was head of the mathematical logic department at Moscow State University, and Per Martin-Löf studied under his supervision in 1964–65’.