In science, complexity theory is an ill-defined field generally consisting of attempted classifications of complex systems according to difficulty of algorithms, computational methods, and computer simulations. [1] In 1984, Belgian chemist Ilya Prigogine gave the following date as to the start of complexity science: [2]

“As for the birth of the ‘science of complexity’, we propose to date it in 1811, the year Joseph Fourier won the prize of the French Academy of Science for his mathematical description of the propagation of heat in solids.”

It is difficult to say, however, as of 2010, if complexity is a legitimate branch of science; moreover, the branch of science Fourier won his prize in his call the science of heat transfer. In any event, complexity theory, in biology and sociology, is often used as an umbrella term for a mixture of chaos theory, cybernetics, information theory, general systems theory, and thermodynamics, among others. An example of a theorist in this field is French sociologist Edgar Morin, known as the sociologist of complexity theory.

References
1. Bothamley, Jennifer. (2002). Dictionary of Theories: One Stop to more than 5,000 Theories. Visible Ink.
2. Prigogine, Ilya. (1984). Order Out of Chaos – Man’s New Dialogue with Nature (pg. 104). New York: Bantam Books.

Further reading
● Gregoire, Nicolis and Prigogine, Illya. (1989). Exploring Complexity - an Introduction. New York: Freeman and Co.