Chaos is said to have been discovered in 1963 by Edward Lorenz who was working on a model for long term weather prediction. Although his Lorenz system did not turn out to aid in forecasting weather, it peaked interest and paved the way for research in the area of chaos theory. Ordinary people tend to think of chaos as random and undeterminable. Mathematicians have yet to agree on a succinct definition for chaos but there are several key aspects that are agreed upon. Chaos is largely unpredictable long-term evolution occurring in a determinist, nonlinear dynamical system because of sensitivity to initial conditions.
Chaos deals with how a system evolves and changes over time.
Chaos only happens in deterministic, nonlinear, dynamical systems that exhibit sensitivity to initial conditions . Lorenz described sensitivity to initial conditions, in terms of weather prediction, as the Butterfly Effect. The idea is that a butterfly flapping its wings in China could produce a tornado in Kansas. Nonlinear means that it is not directly proportional to input, i.e. an equation is nonlinear if it does not plot as a straight line in the normal Cartesian plane graph. Deterministic means that based on a current state and any set of inputs, there exists only one unique output which is always produced.