AI, this surprising new colleague

W hen August, sated with summer, begins its inexorable descent into September, some researchers like to be in the laboratory, where everything is quieter than usual, as if isolated in a suspended moment. This atmosphere is conducive to trying new things, to taking alternative paths that the concern for daily efficiency usually forces us to postpone indefinitely.

This is how one of our colleagues, Antoine Lefort (not his real name), came up with the idea of ​​testing Jarvis-5 (another not his real name), the new version of AI everyone's talking about. Antoine was interested in the following problem, a good job for a robot: take a tiling made of irregular polygonal tiles. For his physics research—and we'll see on this occasion that math and physics sometimes get mixed up—he had to study a certain quantity, depending on the design of the tiling, the "total isoperimetric quotient." This is the sum over all the polygons of the square of their perimeter divided by their area, a number that gets smaller the more "round" the tilings are.

He asked the robot the question in the form: "Do you think this quotient has such and such mathematical property (P)?" – the detail of (P) is unimportant here. It is not so much the robot's answer that astonished him as its reasoning, a progression that one can ask the site to display. For, in his analysis, Jarvis begins by judging a priori that the said property (P) is not verified and sets out to construct an example to show it. He then notes that the example does not confirm his intuition, but perseveres by constructing a different example. By testing it, he realizes that, here again, (P) is verified, and therefore concludes that his initial intuition is perhaps false. Finally, he sets about proving the proposition (P), which he manages to do in one case, all this in less than two minutes...

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