Bradley Efron introduced the bootstrap in this 1979 paper in The Annals of Statistics. The problem he addressed is fundamental: given a sample of data, how confident should you be in a statistic computed from it, such as a median or a regression coefficient? Classical answers required deriving the sampling distribution of the statistic by hand, which is often impossible for anything but the simplest cases.
The bootstrap sidesteps the mathematics by treating the observed sample as a stand-in for the population. You draw many new datasets by sampling, with replacement, from your original data, recompute the statistic on each, and look at how much it varies. That spread is a direct estimate of the statistic’s uncertainty, obtained without formulas. Efron worked through examples including the variance of the sample median, error rates in discriminant analysis, ratio estimation, and regression.
A second contribution of the paper was to clarify the older jackknife technique by showing it is essentially a linear approximation to the bootstrap, which unified two strands of resampling under one idea.
The bootstrap matters because it democratized statistical inference. With cheap computation, anyone can attach honest error bars to almost any estimate, no matter how complicated the underlying procedure. That made it a staple of modern data analysis and machine learning, where it is used to gauge the reliability of predictions and to build ensemble methods that combine many resampled models.