There's a certain cultural thing in mathematics that is kind of hard to convey unless you've been around other mathematicians about what is a definition and wha

There's a certain cultural thing in mathematics that is kind of hard to convey unless you've been around other mathematicians about what is a definition and what constitutes proof. And these things definitely change culturally with time. Our current standards of analysis are quite modern. From a modern viewpoint, nobody really bothered to define continuity and limits until the 19th century, even though calculus is from the 17 century. The 19th century cultural fixes had a purpose: actual misunderstandings and/or errors crept up in previously published works. So when we get pedantic about what things and use early 20th century formalism, we do so kind of as a reaction to historical misunderstandings. When we ask, "what is the derivative of f at 0?", we're trying to show holes in understanding that have been patched by more modern frameworks.