The Ancient Greeks and Romans also used the same or similar empirical geometric methods to generate ellipses, parabolas, and hyperbolas in their architecture. The difference is, they were still 1000-2000 years away from having formalized calculus.
Doing it faster and with less doubts over fidelity and existence of a solution too.
Solving partial differential equations numerically and vetting the solution so obtained is not a trivial matters. Many things can go wrong in non obvious ways.
Analogue computers are a worthy alternative when applicable.
In a way that's like doing the math, but using real-world physics as your 'calculator'. No doubt Gaudi was a smart dude.
He also died crossing the tram track, presumable not looking both ways before crossing. To be clear, I've also nearly been hit by the Barcelona tram too, so I don't blame him, but "smart" is always relative.
Strictly speaking, it isn't "math" as math is the science of quantity and structure, both of which are objective features of reality. We all perceive structure and quantity as it is instantiated in concrete things and ensembles of concrete things and so on. We all respond to and reason about quantifiable and structural properties of reality at varying depths all the time. All math does is pursue them intentionally and methodically. It isn't surprising, then, that a competent artist should intuit various mathematical truths. Indeed, quantity and structure as essential to art. The artist is therefore closer to a domain-specific application where such properties are understood in relation to the subject matter. This introduces a domain-specific aesthetic dimension that is not present in abstracted properties, though one can certainly make aesthetic judgements about abstracted properties.