This is the comment Nominull was referring to:

Ha ha -- this is a Bayesian problem drawn from a Bayesian perspective!

Surely a frequentist would have a different perspective and propose a different kind of solution. Instead of designing an experiment to determine which is better, how about extrapolating from the evidence we already have. Humans have made a certain amount of progress in mathematics -- has this mathematics been mainly developed by frequentists or Bayesians?

(Case closed, I think.)

I roughly consider Bayesians the experimental scientists and frequentists the theoretical scientists. Mathematics is theoretical, which is why the frequentists cluster there. Do you disagree with this?

(Nevertheless, the challenge sounds fun.)

My response to Nominull: the cases aren't really parallel, but I do need to emphasize that I don't think the Bayesian perspective is wrong; it just hasn't been the perspective, historically, of most mathematicians.

... but, finally, when I think of Baysian mathematics being a new or under-utilised thing, I see an analogy with computers. Perhaps Bayesian theory could be a power-horse for new mathematics. I guess my perspective was that mathematicians will use whichever tools available to them, and they used frequentist theory instead. But perhaps they didn't understand Bayesian tools or it wasn't the time for them yet.