The problem is that mathematics by itself doesn't have a robust account of a system. It can imply the boundary and initial conditions which are effective, but are removed from some of the messy problems we get in modeling.
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These issues were there since even Archimedes's mechanical method but they began to show their face in the medieval times in areas such as algebra-fluid mechanics (Kitab al-jabr val Muqallaba), optics (Al-Hazen), air-pump (Torricelli and Hobbes), etc.
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