You're assuming there is a meaningful notion of maths ability that's independent of effort. I don't believe this. How could you possibly define, let alone measure, such a thing?
But this idea applies to literally everything (you can't measure ability to learn a language until you measure what a student can learn after a certain amount of effort). Yet we still have ways of estimating ability. IQ is one of them.
Actually, now that I thInk about it, brain scans may be starting to reveal some of this kind of information.
Right. The fact that some people are intrinsically more able that other people at certain things is just part of the way the world is. Just because a "thing" like ability may be hard to pin down, doesn't mean it's not a "thing".
As to be not clearly stating assumptions, okay,
mea culpa. ColinsMum's and JonLaw's objections are legitimate, but it's just an internet forum, so I like to say things succinctly, and let people fill in the gaps.
As to Dude's objection to my statistics:
Each year, the IMO will have a few dozen contestants at at least +5SD, and will occasionally have a +6SD contestant. (This is talking about math ability, not IQ per se.)
Consider what the "I" in IMO stands for.
