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I seem to remember that as late as in the XIX century there was a prominent mathematician who denied that the theory of probability was part of mathematics, since it does not deal with certainty. Do you know who was that mathematician?

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It was Hardy and Littlewood. They said in a footnote to an article in the early 1920s (this was notably before Kolmogorov's measure-theoretic foundations were developed) that "Probability is not a notion of pure mathematics, but of philosophy or physics." See p. 37 of their paper Some Problems of Partitio Numerorum III.

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    $\begingroup$ so it was in the XX century, even later than I remembered! It's true that before Kolmogorov the foundation of probability were shaky, but the same happened with calculus before Cauchy, and mathematicians were not worried. $\endgroup$
    – mau
    Commented Jun 18, 2017 at 11:03

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