I think it would be remiss to not include Markov in any conversations about influential statisticians, and when discussing mathematics and physics the definitive answer Gauss. As for another remarkable mathematician, perhaps the man who produced the most conceptually advanced theories is John Nash, not just with his work in game theory, but for developing the Nash Embedding Theorem.
If your looking for something to twist your mind make sure you read into that!
I would argue that Bayes, Fermat and Gauss should be considered among the 3 greatest mathematicians in probability/statistics. Fermat is seen along with Blaise Pascal as one of the fathers of using probability as a science. Gauss’ discovery of the normal distribution is groundbreaking and still in wide use today. Bayes’ work laid a foundation for later work on conditional probability.
My top choice is Carl Friedrich Gauss! Computer operations came from his number theory. Inventing the use of 1s and 0s which eventually led to computers being able to solve problems using his number theory. Second choice is Alan Turing his work as a Cryptanalyst was simply brilliant! Finally I’d say Greek Mathematician Pythagoras, trigonometry just isn’t trigonometry without Pythagorean Theorem!!