This video is about one of my absolute favorite mathematical notions which is now regarded as one of the most fundamental scientific concepts, conmogorov complexity. In the middle of the 1960s something extraordinary happened. Three scientists came upon the same idea independently. It looks as if that idea was just waiting to be discovered at that time and that scientific community was ready to pick it like a ripe fruit. These three scientists were Ray Solomonov, Andrey Kolmogorov, and Gregory Chitin. All three defined the very same notion now known as Kolmogorov complexity. The most surprisingly element in this story is that the three of them were working on seemingly different unrelated topics. Let's start with Ray Solomonov. In 1964 he was 38 years old. His focus was on machine learning and particularly the problem of induction. Among the infinite number of hypotheses that fit observed data, which one should be preferred? His answer was to the less complex one. In 1965 Andrey Kolmogorov, aged 62, was a renowned mathematician and theoretical physicist. 32 years before he had already established fundamental axioms to define probability theory. Later he worked on a mathematical definition of the quantity of information and in 1965 he was hunting for correct definition of randomness. Ray Kolmogorov Chitin was only 19 in 1966. He had the intuition that information had to be grounding on computation rather than on probability. His purpose was to show that the power of mathematical theories is limited by their informational content. Despite being immersed in different quests, these three scientists came upon defining the same concept, which is named after the most famous among them Kolmogorov complexity. The notion of Kolmogorov complexity is or could be involved in many aspects of artificial intelligence that otherwise would seem disconnected. Technically, the Kolmogorov complexity C of X, of an object X, is the size of the shorter than the shortest program that outputs X. Here, you represent a unisoltering machine, which means an idealized computer with unlimited memory. We consider the set of all programs P that produce X when run on that machine and we measure the length in bits as a short set's one. Since P is a minimal set of instructions sufficient to retrieve X, it captures the information contained in X. Kolmogorov complexity is a foundation for algorithmic information theory or AIT. Since the early 1970s, many scientists have studied the implications of Kolmogorov complexity in the domain of artificial intelligence. However, recent developments suggest that much remains to be discovered. Artificial intelligence is sometimes considered as a mere collection of ingenious methods. AIT could put it on the path of being perceived as a real science, grounded on fundamental mathematical principles. In conclusion, a purely algorithmic definition of information was discovered in the 1960s. Known as Kolmogorov complexity, it measures information by the size of the shortest binary description.