I believe that we should start mathematics education with programming, then go to generator systems for numbers and operators over them, then how to form lattices and operators on patterns in the lattice, and do approximately continuous math and physics only at the very end.
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Do we know that it isn't ? Could you elaborate ?
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You can construct every observable and mathematics itself using computational principles (i.e. via a trivially simple automaton), but if you introduce real infinities (including continuity), you have to already presuppose hypercomputation, and your axiomatic systems become filthy
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My maths edu was pretty good (& teacher who loved pushing our calculus knowledge beyond syllabus) but I realise I was lucky. To those who say things aren't dumbed down these days: wrong. Compare my exam papers at age X with similar today. Humanities are taught better today tho.
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