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Science isn't designed to solve any problems.
Also yes, if you were to systematize science like it should be, you'd develop an algebraic/arithmetic like system with the structures and come across similar issues in mathematics, not to mention science (especially physics) total and utter dependence on mathematics.
And further mathematics is all bullshit divined from simplistic/god-given structures like natural numbers and basic geometry (dealing with spaces, counting, number, etc).
