Day 283 · Oct 9

The Birthday of Andrei Kolmogorov (1903)

Kolmogorov founded modern probability theory with his 1933 book ‘Foundations of the Theory of Probability’, basing it on measure theory. He introduced the axioms of probability (non‑negativity, total probability 1, countable additivity). He also worked on turbulence (Kolmogorov’s 5/3 law), algorithmic information theory (Kolmogorov complexity), and the theory of Markov processes. He was a prolific mathematician and an educator who reformed Soviet mathematics. His work on complexity says that a random string has no short description – a profound insight into the nature of randomness.

What is Kolmogorov complexity? The length of the shortest program that outputs a given string. Random strings have high complexity; regular patterns have low complexity.

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