"No more than these machines need the mathematician know what he does"
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A mathematician, Poincare implies, can be as mindless as a machine - and that is both a warning and a flex. Writing at the dawn of modern science, when calculation was becoming routinized and mechanical metaphors for thought were in vogue, he draws a sharp line between producing results and understanding them. The sting is in the comparison: machines grind out outputs without self-knowledge; a mathematician who only manipulates symbols can do the same. The line reads like praise for mathematical power, but it’s really a critique of mathematical complacency.
Poincare’s deeper target is the fantasy that formal procedure equals insight. If math is reduced to a set of moves you can execute blindly, then it’s portable: a clerk, a crank, or a device could replace the “genius.” That’s not a triumph of democratization; it’s an impoverishment of the discipline. He’s defending a view of mathematics as creative judgment - choosing fruitful definitions, sensing analogies, deciding what matters - not just running an algorithm.
The subtext also anticipates a future argument about computation: if a system can generate correct statements without “knowing,” where does meaning live? In the human act of selection and interpretation. Poincare isn’t denying technique; he’s insisting that technique without reflection is just motion. The mathematician’s job, in his telling, begins where the machine’s ends: with the why behind the proof, not the proof-shaped product.
Poincare’s deeper target is the fantasy that formal procedure equals insight. If math is reduced to a set of moves you can execute blindly, then it’s portable: a clerk, a crank, or a device could replace the “genius.” That’s not a triumph of democratization; it’s an impoverishment of the discipline. He’s defending a view of mathematics as creative judgment - choosing fruitful definitions, sensing analogies, deciding what matters - not just running an algorithm.
The subtext also anticipates a future argument about computation: if a system can generate correct statements without “knowing,” where does meaning live? In the human act of selection and interpretation. Poincare isn’t denying technique; he’s insisting that technique without reflection is just motion. The mathematician’s job, in his telling, begins where the machine’s ends: with the why behind the proof, not the proof-shaped product.
Quote Details
| Topic | Reason & Logic |
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