....or maybe they discovered complex numbers then invented calculus to help explain them?

Newton developed his fluxional calculus in an attempt to evade the informal use of infinitesimals in his calculations.

Once you have the idea of roots, the problem of what happens when you try to find an even root of a negative number immediately falls out.

The idea that you can add up an infinite number of infinitely small things and get a finite result is totally weird and counterintuitive and it takes a Newton or a Leibniz to come up with it in the first place.

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They just had a lot of free time to sit around and think about stuff.