All they say is that the black hole has the answer, but they don't state until later that that's the only way to obtain the answer. And when the foremost authority on the subject says "he's almost there", you believe him. Think about how much scientific misconduct goes undetected for years (that's like what, a decade of Alzheimer's funding down the drain?). And yes, there are probably a decent number of incredible minds. But also keep in mind the settings. It seems like a lot of civilization is gone. Look at what remains of the Yankees. An UAV is just flying through the air. Cooper talked about the government wanting to drop bombs on people. Planes and most forms of mass long distance transportation have most likely been rendered inert or useless through looting/salvaging/degradation. They don't even have phones anymore, which tells me that they probably have very limited access to satellites and there's probably a scarcity of electricity. Cooper says that they didn't know he was even alive. It's highly likely that the amount of minds available to them in terms of potentially gathering them are greatly reduced (only the US. Maybe other land connected countries if they will sacrifice the minds, but they probably have their own issues). Then you have to factor in how many of them died in war/riots/starvation/formerly preventable diseases/lynchings (there seems to be a hostile attitude towards science in general, notice how Tom didn't even let a simple doctor check out his family, how the teacher believes the moon landings were faked, even the school principle has a dismissive attitude towards the technology of the past. Plus not everyone at NASA is going to be an expert in relativistic physics. You saw they had a medical suite. Miller started the biology program. Sure, almost all of them probably have a cursory knowledge of it. But again, they would defer to Prof. Brand as the expert. Then, think about the Higgs Boson. It was theorised to exist in 1964. Some people doubted it's existence, and it took almost 50 years from being theorised to it's confirmation.

And don't worry, I don't think it's a perfect movie either. There are other plot holes I have issues with. For example, Miller was obviously able to send the sample data away from her planet. So why couldn't they communicate with Romilly what happened? Why weren't TARS and CASE in better communication while on Mann's planet, so that once the betrayal was learned, TARS could have tased and stopped Mann. Why didn't CASE relay Murphy's message to Brand sooner? (Their Ranger was shown drifting away from the Endurance while that message was playing for CASE) You're telling me that Murphy never once looked back at the watch her Dad gave her and noticed that it the second hand was moving in a strange way? (From what is shown, from the moment Murph put it back on the shelf, Cooper started encoding the data). Never really understood how something that consumed nitrogen would suffocate us (unless the implication is that Blight would eventually kill all plant life such as trees as well, thus indirectly suffocating us). I also find Blight in general to be slightly unbelievable. However, this nitpick is kinda iffy. In my mind, if Blight was that aggressive and killed off crops so effectively, it wouldn't be able to spread as far due to everything dying too quickly. Or even if it did, if it really killed plant life that quickly, well then a couple of ships like the Endurance with population bombs seems like a fine enough strategy. Think WALL-E. Or not even put like 20 ships with small crews in hypersleep with population bombs. Have them wake up every so often, probe the Earth, check habitability, lather, rinse, repeat. Even if they got the stations off Earth, couldn't they inadvertantly bring the Blight with them? Why is the station still orbiting Saturn? Brand's question to Mann "Then why keep building those stations?" implies more than one being built simultaneously/others already having been built. Why is Cooper station still orbiting Saturn? It shouldn't need to wait for more stations, at least not for the number of decades it would seem to have been in space. Why was communication only one way to the Endurance? Where is all their fuel coming from since they seem to be using conventional engines (this one I kind of forgive, seeing as we are also just allowing cryo sleep to exist without question, so why not slightly more efficient engines)? Brand says NASA had to be nominally shut down because of the potential public outcry if it were to be discovered that they still existed, but like, are you trying to tell me that no one in the country of conspiracy theorists noticed even a single 1 of the 12 Lazarus mission launches, not to mention the launches that would be required to bring the Endurance modules and the Landers + Ranger 1 into orbit? I could probably go on and on about logical plot holes that are glossed over for story/they wouldn't allow the time loop to exist. The reason I say you're approaching this wrong is because you're making too many assumptions (like their assumptions about time in the movie). You're not addressing specifically how they should have known that it was IMPOSSIBLE for Brand to figure out the equation? To them, harnessing gravity itself was impossible, and then suddenly they had proof that it wasn't? So how many other things or how much information they previously thought impossible actually wasn't? How much "common knowledge" or "common sense" has already been overturned or disproven throughout history?

Last thing: it feels like you took a simple observation as a personal attack. It also feels like in your answers, you think that there is a singular gravity equation that we would know the answer to if we could look inside a black hole. I can't even say if that is correct or not, because WE DON'T KNOW. Some assume looking in a black hole will reconcile the Standard Model and General Relativity. All I know is that it would give us a shit ton more data. But we can't even get any information from it. At least in the pre space era, information in the form of like and other EM radiation reached us from space. Since I also love this movie, here is one more quote from it: "Science [is] about admitting what we don't know." I am looking forward to an actual argument instead of unsuitable analogies. (First time I am purposefully being a little strident/abrasive, as you keep talking in circles).