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The Kolmogorov Answer to Probability
Kolmogorov developed an axiomatic framework which enabled us to move probability on in a mathematically consistent and logical way. It gives you the ability to actually talk about probability in a sort of axiomatic way, which is what mathematics somehow has always been built on. The ancient Greeks did geometry by writing down properties of how lines join points and things like this. From that they could then develop a systematic logical mathematics, which couldn't be questioned.