[NoMoreNicksLeft]

> It seems that "solving algebra problems and doing two-column geometry proofs" is a necessary step on the road to "generating your own questions about whatever interests you and trying to answer them".

Is this so, or is it true that we merely do not allow any other path?

At least in the United States, very few children attend anything other than public schools, and these public schools have a strict curriculum that introduces few concepts but in a rigid order, interspersed with months of monotonous busy-work that comprises little more than arithmetic and solving equations.

As a whole, society has never ran the experiment to see if it is a necessary step, so claiming that it is necessary is silly. It is perhaps true that if we did run the experiment, it would fail repeatedly, but only then could it be claimed to be necessary.