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Mathematics will only get you so far. There are many real-life events which cannot be accurately predicted through theroretical calculations, or may be more easily determined through physical testing.
Besides, when it comes down to it, the only way to know for *sure* if something works is to test its designed function. In the case of aircraft windshields it's MUCH cheaper to find out if they will fail on the ground, than in the air.

-Cordite

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