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Around 1960 digitalisation and computers started to spread through American society and in their wake came a reappraisal of machines: from a production method to a means of innovation. This art historical case study aims to show that mathematical machines were used in early computer, serial and conceptual art not only to explore their aesthetic potential and the media involved. Machines in art of the period also conjured the interplay of the human and machine in creative processes and thus examined creativity itself within human-machine networks. Comparison of these art forms delivers a surprising insight: although one can assume for all three art movements affinity for the idea and thinking, one encounters ambivalence and criticism concerning logical machines and their creative potential. Paradoxically put, with mathematical machines and critical algorithmic practices, some artists turned against a kind of "machine thinking".