In the 17th century, also known as the illumination period, astronomers like Johannes Kepler, Galileo Galilei, and Isaac Newton brought important truths to understanding planetary movements. Newton's laws were so powerful for predicting information about an object's potential movements using the initial conditions of an object. Newton's discoveries allowed dynamic systems to be determined.1
Another term for Chaos Theory is deterministic chaos. The term suggests a paradox since something chaotic cannot necessarily be determined. This paradox contained two notions, the first being randomness and unpredictability. This idea follows that the world is unpredictable due to its complexity. The second being that of deterministic motion. This idea follows Isaac Newton's predictions of planets and shows a system can be complex, yet predictable.2
"Determinism is predictability based on scientific casualty.3" A French philosopher by the name of d'Holbach discussed how the universe is not a deterministic system. In 1778, the mathematician and astronomer Pierre-Simon Laplace discussed how determinism would cause nothing to be uncertain. Laplace used differential equations to explain Isaac Newton's laws.3
In 1885, the king of Sweden and Norway offered a reward to a person who could prove the stability of the solar system. Many well-known mathematicians of the nineteenth century addressed this problem and presented their findings. Many proofs and models showed the short-term stability to the solar system, but none could prove a long-term model. A French Mathematician by the name of Henri Poincaré analyzed a two-body system of orbiting planets. He concluded that the calculations still "blew up" to an uncertain final prediction. However, Poincaré won the contest resulting in the discovery of dynamic instability, even though it would not be discovered until 70 years later.1
In 1961, a meteorologist by the name of Edward Lorenz was using a mathematical model to predict the weather. At the time, Lorenz was one of the few scientists who owned a new, powerful, room-sized computer that could crunch numbers and predict weather patterns. Lorenz input initial conditions, and the computer generated the predicted weather. One day, Lorenz tried re-running a mathematical model with the same numbers. Lorenz took a break and returned to the resulting weather being exponentially different from the original, predicted model. The only difference was his input was rounded to 3 decimal places, rather than the original 6.3 This infinitesimal difference caused a massive change in results.
After Lorenz's discovery, more scientists began to apply Chaos Theory. Thus, Chaos Theory became a branch of mathematics.
Chaos Theory uses everything from calculus, to nonlinear systems of equations, to geometry, and system of dynamics. Almost any scientist can apply Chaos Theory to their field of work including biologists, chemists, physicists, engineers, ecologists, astronomers, and meteorologists. Chaos Theory also can be used by economists and business people. Chaos Theory is significant since it applies to a wide range of subjects; however, Chaos Theory is based upon predictions. Chaos Theory applies to predicting the weather, the orbit of the planets, the stock market, population growth over time, and even spread of diseases.
Defnitions provided by Oxford Languages, Merriam Webster, and Google.
