This essay relates Thomas Kuhn’s Paradigm Theory with Genrich Altshuller’s Theory of Inventive Problem Solving (TRIZ for short). Despite their clearly divergent cultural roots, both understand paradigm shifts as the result of problem-solving processes—Kuhn in science and Altshuller in technology. In contrast to Kuhn, Altshuller used paradigm shifts to study creative problem solving in technology in order to make invention on purpose possible. He summarized his finding in the Algorithm of Inventive Problems Solving (ARIZ), which, as we will show, can be made explicit in a more general system theoretical framework. This allows for its application outside of the technological domain without relying on crutches such as metaphorical analogies. In order to demonstrate the application of this generalized version of ARIZ, we reconstruct one of the most famous paradigm shifts in the history of science—the shift from the Ptolemaic geo-centric system to Copernicus’ helio-centric one.