But past mathematicians already just taught what they thought was true then.
But we don’t know that we are living in the optimal timeline. Maybe relativity would have arrived sooner with fewer people in the past insisting that space is necessarily Euclidean.
I’m asking what relevance you think it has for current math education.
The topic is philosophy education. Science can test its theories empirically. Philosophy can’t. Mathematics can take its axioms for granted. Philosophy can’t.
As it is said, keep an open mind, but not so open your brain falls out. Teaching a specific thing impedes progress when that thing is wrong or useless, but it aids progress when that thing is a foundation for later good things.
The difficulty is that we don’t have certain knowledge of what is in fact right or wrong: we have to use something like popularity or consensus as a substitute for “right”.
It may well be the case that one can go too far in teaching unpopular ideas, but it doesn’t follow that the optimal approach is to teach only “right” ideas, because that means teaching only the current consensus, and the consensus sometimes needs to be overthrown.
The optimal point is usually not an extreme, or otherwise easy to find.
But we don’t know that we are living in the optimal timeline. Maybe relativity would have arrived sooner with fewer people in the past insisting that space is necessarily Euclidean.
The topic is philosophy education. Science can test its theories empirically. Philosophy can’t. Mathematics can take its axioms for granted. Philosophy can’t.
The difficulty is that we don’t have certain knowledge of what is in fact right or wrong: we have to use something like popularity or consensus as a substitute for “right”.
It may well be the case that one can go too far in teaching unpopular ideas, but it doesn’t follow that the optimal approach is to teach only “right” ideas, because that means teaching only the current consensus, and the consensus sometimes needs to be overthrown.
The optimal point is usually not an extreme, or otherwise easy to find.