Published posthumously in 1713, Ars Conjectandi contains the first proof of the law of large numbers: as the number of independent trials increases, the observed frequency of an event converges to its true probability. Bernoulli spent twenty years refining this proof, recognising it as the mathematical justification for empirical reasoning.
Before Bernoulli, probability was about individual events. His law shifted the frame to sequences of events, showing that randomness at the micro level produces regularity at the macro level. This insight is the bridge between probability theory and statistics — between what we assume and what we can measure.
The concept of repeated independent experiments with two outcomes (success or failure) is named after Jacob Bernoulli. These trials are the building blocks of binomial distributions, hypothesis testing, and the entire apparatus of frequentist statistics.
Our systems process hundreds of thousands of filings. The law of large numbers guarantees that patterns extracted from this corpus converge on real statistical properties — not noise. Scale is not just an advantage; it is a mathematical necessity.