---
title: "History of randomness"
chunk: 3/4
source: "https://en.wikipedia.org/wiki/History_of_randomness"
category: "reference"
tags: "science, encyclopedia"
date_saved: "2026-05-05T03:40:15.668742+00:00"
instance: "kb-cron"
---

The words of Goethe proved prophetic, when in the 20th century randomized algorithms were discovered as powerful tools. By the end of the 19th century, Newton's model of a mechanical universe was fading away as the statistical view of the collision of molecules in gases was studied by Maxwell and Boltzmann. Boltzmann's equation S = k loge W (inscribed on his tombstone) first related entropy with logarithms.

== 20th century ==

During the 20th century, the five main interpretations of probability theory (e.g., classical, logical, frequency, propensity and subjective) became better understood, were discussed, compared and contrasted. A significant number of application areas were developed in this century, from finance to physics. In 1900 Louis Bachelier applied Brownian motion to evaluate stock options, effectively launching the fields of financial mathematics and stochastic processes.
Émile Borel was one of the first mathematicians to formally address randomness in 1909, and introduced normal numbers. In 1919 Richard von Mises gave the first definition of algorithmic randomness via the impossibility of a gambling system. He advanced the frequency theory of randomness in terms of what he called the collective, i.e. a random sequence. Von Mises regarded the randomness of a collective as an empirical law, established by experience. He related the "disorder" or randomness of a collective to the lack of success of attempted gambling systems. This approach led him to suggest a definition of randomness that was later refined and made mathematically rigorous by Alonzo Church by using computable functions in 1940. Von Mises likened the principle of the impossibility of a gambling system to the principle of the conservation of energy, a law that cannot be proven, but has held true in repeated experiments.
Von Mises never totally formalized his rules for sub-sequence selection, but in his 1940 paper "On the concept of random sequence", Alonzo Church suggested that the functions used for place settings in the formalism of von Mises be computable functions rather than arbitrary functions of the initial segments of the sequence, appealing to the Church–Turing thesis on effectiveness.
The advent of quantum mechanics in the early 20th century and the formulation of the Heisenberg uncertainty principle in 1927 saw the end to the Newtonian mindset among physicists regarding the determinacy of nature. In quantum mechanics, there is not even a way to consider all observable elements in a system as random variables at once, since many observables do not commute.