randomness, and the stability of these definitions under different models of computation, give evidence that Martin-Löf randomness is a fundamental property of mathematics and not an accident of Martin-Löf's particular model. The thesis that the definition of Martin-Löf randomness "correctly" captures the intuitive notion of randomness has been called the "Martin-Löf–Chaitin Thesis"; it is somewhat similar to the Church–Turing thesis. Following Martin-Löf's work, algorithmic information theory defines a random string as one that cannot be produced from any computer program that is shorter than the string (Chaitin–Kolmogorov randomness); i.e. a string whose Kolmogorov complexity is at least the length of the string. This is a different meaning from the usage of the term in statistics. Whereas statistical randomness refers to the process that produces the string (e.g. flipping a coin to produce each bit will randomly produce a string), algorithmic randomness refers to the string itself. Algorithmic information theory separates random from nonrandom strings in a way that is relatively invariant to the model of computation being used. An algorithmically random sequence is an infinite sequence of characters, all of whose prefixes (except possibly a finite number of exceptions) are strings that are "close to" algorithmically random (their length is within a constant of their Kolmogorov complexity). Mathematical statistics Per Martin-Löf has done important research in mathematical statistics, which (in the Swedish tradition) includes probability theory and statistics. Bird-watching and sex determination Per Martin-Löf began bird watching in his youth and remains an enthusiastic bird-watcher. As a teenager, he published an article on estimating the mortality rates of birds, using data from bird ringing, in a Swedish zoological journal: This paper was soon cited in leading international journals, and this paper continues to be cited. In the biology and statistics of birds, there are several problems of missing data. Martin-Löf's first paper discussed the problem of estimating the mortality rates of the Dunlin species, using capture-recapture methods. The problem of determining the biological sex of a bird, which is extremely difficult for humans, is one of the first examples in Martin-Löf's lectures on statistical models. Probability on algebraic structures Martin-Löf wrote a licenciate thesis on probability on algebraic structures, particularly semigroups, while a student of Ulf Grenander at Stockholm University. Statistical models Martin-Löf developed innovative approaches to statistical theory. In his paper "On Tables of Random Numbers", Kolmogorov observed that the frequency probability notion of the limiting properties of infinite