What are the most important statisticians, and what is it that made them famous?
(Reply just one scientist per answer please.)
Reverend Thomas Bayes for discovering Bayes' theorem
Ronald Fisher for his fundamental contributions to the way we analyze data, whether it be the analysis of variance framework, maximum likelihood, permutation tests, or any number of other ground-breaking discoveries.
John Tukey for Fast Fourier Transforms, exploratory data analysis (EDA), box plots, projection pursuit, jackknife (along with Quenouille). Coined the words "software" and "bit".
Karl Pearson for his work on mathematical statistics. Pearson correlation, Chi-square test, and principal components analysis are just a few of the incredibly important ideas that stem from his works.
Carl Gauss for least squares estimation.
William Sealy Gosset for Student's t-distribution and the statistically-driven improvement of beer.
Andrey Nikolayevich Kolmogorov, for putting probability theory on a rigorous mathematical footing. While he was a mathematician, not a statistician, undoubtedly his work is important in many branches of statistics.
Pierre-Simon Laplace for work on fundamentals of (Bayesian) probability.
Francis Galton for discovering statistical correlation and promoting regression.
George Box for his work on time series, designed experiments and elucidating the iterative nature of scientific discovery (proposing and testing models).
Andrey Markov for stochastic processes and markov chains.
How has Sir David Roxbee Cox not been mentioned yet?
Some feats: Cox proportional hazards models, experimental design, he did a lot of work on stochastic processes and binary data. He also advised many students who went on to do great work (Hinkley, McCullagh, Little, Atkinson, etc.)
And the man was knighted!
Leo Breiman for CART, bagging, and random forests.
Harold Jeffreys for revival of Bayesian interpretation of probability.
Edwin Thompson Jaynes for work on objective Bayesian methods, particularly MaxEnt and transformation groups.
C.R. Rao for the Rao–Blackwell theorem and the Cramer-Rao bound.
Florence Nightingale for being "a true pioneer in the graphical representation of statistics" and developing the polar area diagram. Yes, that Florence Nightingale!
Blaise Pascal and Pierre de Fermat for creating the theory of probability and inventing the idea of expected value (1654) in order to solve a problem grounded in statistical observations (from gambling).
W. Edwards Deming for promoting statistical process control
George Dantzig for the Simplex Method, and for being the student who mistook two open statistics problems that Neyman had written on the board for homework problems, and in his "ignorance" solving them. I'd vote for him just for the story.
Samuel S. Wilks was a leader in the development of mathematical statistics. He developed the theorem on the distribution of the likelihood ratio, a fundamental result that is used in a wide variety of situations.
He also helped found the Princeton statistics department, where he was Fred Mosteller's advisor, among others, and has a prestigious ASA award named after him.
John Nelder, for providing us the now omnipresent generalized linear model framework. By his approach of unifying various standard statistical models and its estimation method, the iteratively reweighted least squares method for ML, he gave us tools that we are using now in almost all applied and theoretical concepts that are related to exponential family models. Not to mention his contributions to optimization as the superb Nelder-Mead-Algorithm.
Lucien Le Cam for his contribution to mathematical statistics. (maybe Local asymptotic normality and contiguity made him famous)
Leland Wilkinson for his contribution to statistical graphics.
David Donoho development of multiscale ideas in statistics, and a lot of theoretically justified while practically very efficient ideas in very high dimensional statistics, CHA: computational harmonic analysis,...
Adolphe Quetelet for his work on the "average man", and for pioneering the use of statistics in the social sciences. Before him, statistics were largely confined to the physical sciences (astronomy, in particular).