Are we actually in disagreement? I could just as well describe math as "deciding where and at what level to allocate partial structure..." in the same way. Mathematical researchers also build intuition over time allowing them to see certain big picture ideas more easily.
If I really take a step back and re-think this whole thread, I'd say the main different between mathematical researchers and programmers is just incentives. Funding and output are just fundamentally measured differently and the work is done very differently with respect to cooperation with others.
Still I'd say that the thing holding back mathematicians from being good developers is simply that research mathematics does not provide development experience.
If I really take a step back and re-think this whole thread, I'd say the main different between mathematical researchers and programmers is just incentives. Funding and output are just fundamentally measured differently and the work is done very differently with respect to cooperation with others.
Still I'd say that the thing holding back mathematicians from being good developers is simply that research mathematics does not provide development experience.