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Sunday, July 30, 2006

Gambling on the Riemann Hypothesis

I discussed the idea of Bayesianism and gambling in mathematics back on 3 November. Now, from sigpe, I see that you can trade in futures for mathematical results such as the Riemann Hypothesis. Of course, to put a finite time limit on a mathematical gamble, it has to be of the form, 'By 20XX, the Y conjecture will have been proved.' In the case of the Riemann hypothesis, it's 2020.

But, clearly your degree of belief in RH's being proved by 2020 is upper bounded by your degree of belief in it's truth. Put the other way around, if you happened to believe that it is 70% likely that RH is false, you would be very happy to sell options at its current price. This price has fluctuated significantly over the decade of the future's existence. Presumably most of the fluctuation comes from evidence that someone is closing in on a proof. It would be interesting to see how, say, analogical evidence for or against its truth, such as Deninger provides, played out.


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