To be honest I suspect the next scientific revolution would be a refutation of Church-Turing, or maybe something more like an extension of it to phenomena we are not closely studying yet, a bit like my understanding of the relation between Newtonian mechanics, and General Relativity and Quantum mechanics. Unfortunately that won't be me bringing that revolution about, so you won't get to say you exchanged views with a scientific legend :P
For the time being of course we can agree that our brains probably do some kind of maths, as far as we understand it. I'm guessing the way we understand maths has everything to do with the way our brains understand maths because, well, that's my position in our disagreement. But, see, I can do maths by counting on my fingers, so the question is really what kind of maths we're talking about and how complex can they realistically be. My argument is that if it's not the kind of maths a standard human being can calculate very quickly without pen or paper, then that's a no-go, because that leaves plenty of time to be eaten by a sabretooth, or what have you.
For the time being of course we can agree that our brains probably do some kind of maths, as far as we understand it. I'm guessing the way we understand maths has everything to do with the way our brains understand maths because, well, that's my position in our disagreement. But, see, I can do maths by counting on my fingers, so the question is really what kind of maths we're talking about and how complex can they realistically be. My argument is that if it's not the kind of maths a standard human being can calculate very quickly without pen or paper, then that's a no-go, because that leaves plenty of time to be eaten by a sabretooth, or what have you.