Quantamagazine.org By KEVIN HARTNETT October 31, 2018 A new statistical model appears to undermine long-held assumptions in number theory. How much should it be trusted when all that really matters is proof? 4 What points on the elliptic curve y 2 = x 3 – 4 x + 1 are rational (meaning their values can be expressed as fractions)? To find them, draw lines through pairs of rational points. All the additional points that the lines intersect will also be rational. David Song/Quanta Magazine Four researchers have recently come out with a model that upends the conventional wisdom in their field. They have used intensive computational data to suggest that for decades, if not longer, prevailing opinion about a fundamental concept has been wrong. These are not biologists, climatologists or physicists. They don’t come from a field in which empirical models get a say in determining what counts as true. Instead they are mathematicians, representatives of a discipline whose standard c
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