Were I to guess they're talking about the different derivatives. Here's at least something that might introduce you to some of the shortcuts people take but it's far from complete [0] (you can probably find more if you search things like how physicists use the derivative wrong. (I make this critique as someone with a degree in physics too))
I often say that math is taught through a game of telephone. It's a fanatic example of the problem with "I just care that it works" type of attitudes. The problem is if that's your actual belief then you wouldn't be saying that because you'd need to dig deeper. Caring about it working is exactly the reason people do did deeper and bring up issues. The reason things fall apart less in math is because the language was specifically invented to make miscommunication difficult. That's why it's overly pedantic. That's why we use formal languages rather than natural ones. So we should rephrase "I just care that it works" is that it's actually "I just care that it works for this exact case." It makes it easier to see the problem. If you don't know the subject in more detail then you can't actually know if it breaks in that use case. The broken parts are completely invisible to you! Which undermines your own stated goal.
This goes for a lot more than math. But being a formal language it's just easier to point things out and how people misunderstand. If you're an expert in any field you've probably see this same phenomena in that domain though. People having over confidence and their refusal to get deeper knowledge actually just undermines their whole goal. I'd honestly call this a form of Murray-Gell-man Amnesia
I often say that math is taught through a game of telephone. It's a fanatic example of the problem with "I just care that it works" type of attitudes. The problem is if that's your actual belief then you wouldn't be saying that because you'd need to dig deeper. Caring about it working is exactly the reason people do did deeper and bring up issues. The reason things fall apart less in math is because the language was specifically invented to make miscommunication difficult. That's why it's overly pedantic. That's why we use formal languages rather than natural ones. So we should rephrase "I just care that it works" is that it's actually "I just care that it works for this exact case." It makes it easier to see the problem. If you don't know the subject in more detail then you can't actually know if it breaks in that use case. The broken parts are completely invisible to you! Which undermines your own stated goal.
This goes for a lot more than math. But being a formal language it's just easier to point things out and how people misunderstand. If you're an expert in any field you've probably see this same phenomena in that domain though. People having over confidence and their refusal to get deeper knowledge actually just undermines their whole goal. I'd honestly call this a form of Murray-Gell-man Amnesia
[0] https://m.youtube.com/watch?v=oIhdrMh3UJw