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With a three-part series of articles (in issues 428, 431 and 433), Futuribles journal devoted a large amount of space to understanding the human brain in 2019. Underlying many of the pieces was the question whether machines will one day outstrip human beings in their capacity to reason. But this is far from being a new question and revisiting the thinking of two pioneers in the field of human brain/machine comparison—Alan Turing and John von Neumann—offers a different view on the first machines to be inspired by, or to resemble, the functioning of the brain.Pierre Papon demonstrates the contribution made by the two mathematicians in this area. And if the human-intelligence-versus-AI debate continues to rage, as increasingly rapid and scary technological developments come on the scene, current studies—like older ones—seem to indicate that the human brain still maintains a substantial lead over the capabilities of machines. Any number of analogies are invoked, but for the moment the complexity of the human brain seems unparalleled and unrivalled.