I took humans thousands of years, then hundreds of years, to come to terms with very basic concepts about numbers.
Its amazing to me when people talk about recombining things, or following up on things as somehow lesser work.
People can't separate the perspective they were given when they learned the concepts, that those who developed the concepts didn't have because they didn't exist.
Simple things are hard, or everything simple would have been done hundreds of years ago, and that is certainly not the case. Seeing something others have not noticed is very hard, when we don't have the concepts that the "invisible" things right in front of us will teach us.
It's why the invention of teaching has been so important. Took a long time for humans to develop calculus. A long time to then refine it and make it much more useful. But then in a year or two an average person can learn what took hundreds of years to invent. It's crazy to equate these tasks as being the same. Even incremental innovation is difficult. You have to see something billions of people haven't. But there's also paradigm shifts and well... if you're not considered crazy at first then did you really shift a paradigm?
And yet it is still taught in less than optimal form, lacking algebraic closure in ways that are completely unnecessary.
It isn't a secret, but the percentage of people who don't know that, plus the percentage of mathematicians who vaguely or more directly know that, but habitually use the broken, more difficult (i.e. less algebraic) notation is ... virtually everyone.
I am not trying to pick on calculus, this is everywhere. Important and useful concepts are right in front of all of us, that we don't see even in the context of what we are relatively fluent with.
Because we learn quickly, where we have (almost always inherited) the right preparatory perspectives (earned over lifetimes by others), we vastly overrate our ability to reason independently.
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
Its amazing to me when people talk about recombining things, or following up on things as somehow lesser work.
People can't separate the perspective they were given when they learned the concepts, that those who developed the concepts didn't have because they didn't exist.
Simple things are hard, or everything simple would have been done hundreds of years ago, and that is certainly not the case. Seeing something others have not noticed is very hard, when we don't have the concepts that the "invisible" things right in front of us will teach us.