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Poincaré credited his sudden mathematical insight to "unconscious work," an ability to mull over the mathematics while he was preoccupied with unrelated activities, like talking to a friend on the bus.
He felt at any moment he could have the next mathematical insight.
But in 1988, using a combination of mathematical insight and computer muscle, the American Noam Elkies discovered that 2,682,4404 + 15,365,6394 + 18,796,7604 = 20,615,6734 a stupendous counterexample that destroyed Euler's conjecture.
It derives from a mathematical insight known as geometrical progression and is most commonly used to help predict the speed at which epidemics of contagious disease are likely to spread.
GEMC theory posits that dynamic gestures mediate the generation of correct mathematical insight during proof production.
More mathematical insight on the subject can also be found in [31].
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While performing mathematically relevant directed actions facilitated key mathematical insights and intuitions for two tasks (Triangle and Gear), directed actions on their own did not lead to superior informal proofs compared to irrelevant actions.
Performing mathematically relevant directed actions (without pedagogical language) will predict student performance on mathematical insights.
Nash's two embedding theorems are considered classics, providing some of the deepest mathematical insights of the last century.
The challenge has been to combine its mathematical insights with the kinds of adjustments that are needed to make its models fit the economy's irreducibly human element.
On its own terms, though, the movie succeeds in dramatizing Mr. Nash's mental illness and, to a lesser extent, his mathematical insights.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com