Pii: S0144-8188(00)00031-4

The patenting of software-related inventions is on the increase, especially in the United States. Mathematical formulas and algorithms, though, are still sacrosanct. Only under special conditions may algorithms qualify as statutory matter: if they are not solely a mathematical exercise, but if they are somehow linked with physical reality. In this article, it is argued that blanket acceptance is to be preferred. Moreover, the best results are obtained if formulas and algorithms are only protected in combination with a proof that supports them. This argument is developed by conducting a thought experiment. After describing the development of algebra from the 16th century up to the 20th (in particular, the solution of the cubic equation), the likely effects on the development of mathematics as a science are analyzed in the context of postulating a patent regime that would actually have been in force protecting mathematical inventions. © 2000 Elsevier Science Inc. All rights reserved.