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 true or accepted.

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" comes from old Germanic languages and meant something that seemed strong or similar. 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 for unsure evidence. During the Renaissance, people talked about betting and estimated insurance costs, but they didn’t know how to calculate these properly.

The math of probability began with Gerolamo Cardano in the 1560s, though his work wasn’t published until later. In 1654, Pierre de Fermat and Blaise Pascal wrote letters about fair ways to split money in games that were interrupted. Later, Christiaan Huygens wrote the first book on probability in 1657, showing 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. 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 chances like 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 saw that some numbers come up more often because there are more ways to roll them.

In 1654, Pascal and Fermat wrote letters about games of chance. They thought about how to fairly split the money if a game stops early. Their work helped create modern probability.

Christiaan Huygens wrote the first book just about probability in 1657. He showed how to use math to solve gambling problems. In 1665, Pascal shared his work on Pascal's triangle, an important idea for counting.

In 1662, a book called La Logique ou l'Art de Penser linked probability to making good choices 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 figure out how long people might live, showing how useful probability could be for real problems.

Eighteenth century

In the 1700s, probability became an important part of math with many uses. Jacob Bernoulli’s book Ars Conjectandi showed the law of large numbers. This means that if you flip a fair coin many times, the number of heads will be close to half of the flips.

Abraham De Moivre’s book The Doctrine of Chances used probability for difficult problems, like games and money matters. This helped make probability useful in real life.

Nineteenth century

In the 1800s, probability became more useful for real data and science. Gauss used it to find the path of a small planet called Ceres with just 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.

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

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

Twentieth century

Probability and statistics became more connected through the work of R. A. Fisher and Jerzy Neyman. They created tools that scientists still use today. These tools help check if ideas, like a drug working, match what we see.

The study of random processes grew to include things like Markov processes and Brownian motion. These ideas describe how tiny particles move randomly and influenced fields like physics and economics. They even helped create ways to understand stock markets, such as the Black–Scholes formula.

The twentieth century also had debates about what probability 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. These debates shaped how we use probability in science and decisions.

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