History of probability

Probability is a way to understand how likely something is to happen. It helps us make sense of events that seem random, like flipping a coin or rolling dice. People have been thinking about probability for a long time, especially in areas like the law of evidence.

In the 16th and 17th centuries, famous thinkers such as Cardano, Pascal, Fermat, and Christiaan Huygens started to study probability using math. They looked at games of chance, like throwing dice or flipping coins, to understand patterns in random events.

Today, probability is very important in many areas, from games and science to making decisions when we don’t have all the information. It helps us predict what might happen and understand the world around us better.

Etymology

The words "probable" and "probability" come from an old word in Latin called probabilis. Long ago, people used this word to describe ideas that seemed plausible or generally accepted. The word "probability" itself came from Old French and directly from Latin.

In the 1700s, people also used the word "chance" to talk about probability, calling it the "Doctrine of Chances." The word "chance" originally meant "a fall" or "a case" in Latin. The word "likely" has roots in old Germanic languages and originally meant something that seemed strong or similar in appearance. By the 1500s, "likely" also began to mean "probably."

Origins

See also: Timeline of probability and statistics

In old times, courts used different levels of proof to handle unsure evidence. During the Renaissance, people talked about betting using terms like "ten to one," and they estimated insurance costs based on risk, but they didn’t know how to calculate these properly.

The math of probability started with Gerolamo Cardano in the 1560s, though his work wasn’t published until much later. Then, in 1654, Pierre de Fermat and Blaise Pascal wrote letters to each other about fair ways to split money in games that got interrupted. Later, Christiaan Huygens wrote the first book on probability in 1657, explaining ways to solve gambling problems.

People have always played games of chance, like rolling dice, but they didn’t have a system to understand the chances involved. Games like snakes and ladders have ancient roots, and dice were used in ancient Greece and Egypt. It wasn’t until Cardano that someone tried to put these ideas into math, looking at things like the chances of rolling certain numbers with dice. His work, and the letters between Pascal and Fermat, helped start modern probability theory.

Seventeenth century

Between 1613 and 1623, Galileo studied dice throws and noticed that some numbers appear more often because there are more ways to get them.

In 1654, Pascal and Fermat started writing letters about games of chance. They looked at how to fairly split the money if a game stops early. Their work laid the groundwork for modern probability.

Christiaan Huygens wrote the first book only about probability in 1657. He showed how to solve gambling problems with math. In 1665, Pascal shared his work on Pascal's triangle, a key idea in counting.

In 1662, a book called La Logique ou l'Art de Penser linked probability to smart decisions when you’re not sure what will happen. The same year, John Graunt wrote about the population of London and made one of the first life tables, showing chances of living to different ages.

Later, Johan de Witt used these ideas in 1671 to help decide how long people might live, showing how useful probability could be for real problems.

Eighteenth century

In the 1700s, probability became a serious math subject with many uses. Jacob Bernoulli’s book Ars Conjectandi (published after his death in 1713) showed the law of large numbers. This means that if you flip a fair coin many times, like 1000 times, the number of heads will be close to half of them.

Abraham De Moivre’s book The Doctrine of Chances (1718) used probability for harder problems, like games, how long people live, and money matters. This helped make probability useful in real life and in theory.

Nineteenth century

During the 1800s, probability became more connected to real-world data and science. Gauss used probability to figure out the path of a small planet called Ceres using only a few observations. This helped create a way called the method of least squares to fix mistakes in measurements. Laplace wrote about these ideas in his book and talked about new ways to think about probability and testing ideas.

Later in that century, probability helped big scientific discoveries. Ludwig Boltzmann and J. Willard Gibbs used probability to explain how gases behave by looking at how tiny particles move randomly. This led to statistical mechanics, an important use of probability in physics.

The history of probability as a field began with a book by Isaac Todhunter in 1865. His book talked about the work of early thinkers like Pascal and Fermat up to Laplace, showing how probability grew into a clear math subject.

Twentieth century

Probability and statistics grew closer through the work of R. A. Fisher and Jerzy Neyman. They created tools like significance testing and confidence intervals that scientists still use today. These tools help check if a hypothesis, such as a drug being effective, matches what we observe.

The study of random processes expanded to areas like Markov processes and Brownian motion, which describe how tiny particles move randomly in liquids. These ideas influenced fields like physics and economics, even helping create ways to understand stock markets, such as the Black–Scholes formula.

The twentieth century also saw debates about what probability really means. Some, called Frequentism, saw probability as how often events happen over many tries. Others, using Bayesian methods, saw it as a measure of belief or evidence. These debates shaped how we use probability in science and decisions.

In 1933, Kolmogorov's axioms gave probability a strong mathematical foundation. These rules made it possible to work with probabilities even when there are endless possible outcomes. This system became the standard for modern probability and opened up new uses in areas like physics, genetics, and computer science.