Doughnut theory of dating


"We've found a new form of moonshine, which in math refers to an idea so farfetched as to sound like lunacy," says Ken Ono, a number theorist at Emory University."And we've used this moonshine to show the mathematical usefulness of the O'Nan pariah group in a way that moves it from theory to reality.It turns out that the O'Nan group knows deep information about elliptic curves." published the representation theory for the O'Nan group developed by Ono, John Duncan (also a number theorist at Emory) and Michael Mertens (a former post-doctoral fellow at Emory who is now at the University of Cologne)."We've shown that the O'Nan group, a very large pariah group, actually organizes elliptic curves in a beautiful and systematic way," Duncan says."And not only does it organize them, it allows us to see some of their deepest properties.

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"You can think of it as a doughnut together with specific, delicate configurations of rational points that are very carefully placed," Duncan says."So, in the simplest of terms, it's like a doughnut that you eat, that may have sprinkles on it.The whole game in the math of elliptic curves is determining whether the doughnut has sprinkles and, if so, where exactly the sprinkles are placed." Unlike an edible doughnut, however, these mathematical doughnuts are not visible."Imagine you are holding a doughnut in the dark," Ono says.

"You wouldn't even be able to decide whether it has any sprinkles.

But the information in our O'Nan moonshine allows us to 'see' our mathematical doughnuts clearly by giving us a wealth of information about the points on elliptic curves." The findings are especially surprising since none of the pariahs, as six of math's sporadic simple groups are known, had previously appeared in moonshine theory, or anywhere else in science.


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