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Concerning the role of mathematics in technological inventions: which books would you suggest that examine the historical relation between mathematical analysis & practical wisdom?

For example, if Leonardo Da Vinci had known Newton's laws of motion, would he design much more effective machines, or would he continue to work through trial-and-error guided by his own genius?

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    $\begingroup$ Your second paragraph is speculation on a counter-factual. Could you tighten your question a bit? $\endgroup$
    – Rory Daulton
    Commented Feb 1, 2019 at 0:56
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    $\begingroup$ There is no such thing as "practical wisdom." $\endgroup$
    – Carl Witthoft
    Commented Feb 1, 2019 at 13:34
  • $\begingroup$ Are you interested in how "practical wisdom" advances mathematical/theoretical developments, or vice versa? The theory-to-practice connection is well covered in the standard histories, for the influence in the other direction see e.g. Aristotle, Archimedes, Euclid, and the Origin of Mechanics by Damerow-Renn. However, counterfactual speculations on do not fit our format very well, I am afraid. $\endgroup$
    – Conifold
    Commented Feb 2, 2019 at 1:41
  • $\begingroup$ @Conifold: I'm interested in clarifying which of the following elements made possible the design & functioning of some basic machines (like steam-engines, airplanes, motors, or any other kind): a) an ingenious configuration of parts, without mathematical caclulations b) precise algebro-geometric calculations c) precise calculations using differential equations $\endgroup$
    – exp8j
    Commented Feb 3, 2019 at 18:22
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    $\begingroup$ None of the above, and especially not c), basic machines were built already in antiquity. And although many were very ingenious, people who built them, like Ctesibius and Archemedis, were well versed in geometry and mechanics. It is not calculations that matter but understanding of structure that theory provides. $\endgroup$
    – Conifold
    Commented Feb 4, 2019 at 5:14

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