Wolfram's father was a novelist and his mother a professor of philosophy. Often described as a child prodigy, he published an article on particle physics at age 15 and entered Oxford (St John's College) at age 17. He received his Ph.D in particle physics from Caltech at age 20 and joined the faculty there. At age 21, Wolfram won the MacArthur "Genius" award.
He developed a computer algebra system at Caltech, but the school's patent rules denied him ownership of the invention. He left for the physics department of Princeton University, where he studied cellular automata, mainly with computer simulations.
Wolfram left for the University of Illinois at Urbana-Champaign and started to develop the computer algebra system Mathematica in 1986, to be released in 1988. He founded a company, Wolfram Research, which continues to extend the program and market it with considerable success. Wolfram Research also pays Eric Weisstein to work on his math encyclopedia MathWorld, which is hosted at the company's web site.
From 1992 to 2002, Wolfram worked on his book A New Kind of Science, which introduced and justified the study of simple, abstract systems of the type easily embodied as simple computer programs. Additionally, it argued that for fundamental reasons these types of systems, rather than traditional mathematics, are needed to model and understand complexity in nature. Some have interpreted the idea of having underlying regularity and simplicity in nature as proof of the existence of God.
The book was widely anticipated by the community. His book was published by his own company and subsequently was criticized for lack of peer review. His work also disputed the importance of Theory of Evolution and other established theories, leading to some mathematicians and scientists critized his book and his writing style which some see as being somewhat arrogant (however Wolfram says he does this for clarity). The impact of the book is, however, yet to be seen.