>> There is perhaps a way to endow people with these concepts when they couldn't otherwise arrive at them through rigorous proving. Indeed it would be great if

>> There is perhaps a way to endow people with these concepts when they couldn't otherwise arrive at them through rigorous proving. Indeed it would be great if there is such a way. But sadly, without proofs, these concepts are half baked and are thus harmful as they give a false sense of understanding and thence the more harmful overconfidence. I remember the great thought that applies to entire math education (and also to education in general) - "There is no royal road to geometry." [1] [1] https://en.wikipedia.org/wiki/Royal_Road#A_metaphorical_.E2.80.9CRoyal_Road.E2.80.9D_in_famous_quotations https://en.wikipedia.org/wiki/Royal_Road#A_metaphorical_.E2....