Comment by pfdietz
The critique of calculus as lacking in rigor goes much further back than that. Bishop Berkeley famously argued calculus was no more dependable than theology. It was only with Cauchy and the formalization of analysis in the 19th century that this issue would be put to bed.
https://en.wikipedia.org/wiki/The_Analyst
I wonder if the issues that this essay claims came up in Italy persisted in any way. I ask that, because there was later (1885-1935) an infamous breakdown in Italian mathematics (the "Italian School of Algebraic Geometry") due to foundational issues.
https://en.wikipedia.org/wiki/Italian_school_of_algebraic_ge...
History doesn't repeat but it sometimes rhymes.
From a contemporary viewpoint, Berkeley seems to have been a bit of an edgelord in his defense of faith: https://en.wikipedia.org/wiki/Appeal_to_the_stone#Origin
(or am I doing him an injustice and he was running with the whole Cartesian Demon thing to see just how far he could take it?)
Mumford (a grand-advisee of Castelnuovo's) on the infamous school: https://ftp.mcs.anl.gov/pub/qed/archive/209