Gödel's Incompleteness Theorem has little to do with complexity theory. Complexity theorists routinely find out if two complexity classes are included in each other or not.
Why would Gödel's Incompleteness Theorem stop them for P=NP in particular?
Why is the current definition of P or NP insufficiently formal or clear?
PS: Citing YouTube Videos in mathematical discussions is a big red flag indicating you have not really understood things.
I would advise listening to Professor Thorsten Altenkirch brief introduction about the subject, and consider delaying argumentum ad hominem opinions a few minutes.
> "not really understood things"
Something currently impossible to prove is by definition confusing. lol =3
The ad-hominem was maybe unwarranted, sorry. Let's get back to the subject matter by me repeating the material question in my comment above, which you ignored: "Complexity theorists routinely find out if two complexity classes are included in each other or not. Why would Gödel's Incompleteness Theorem stop them for P=NP in particular?"
PS: I read through the transcript of the YouTube video you linked (and also know the material from my CS degree education) so I do in fact know what Gödel's Incompleteness Theorem is. Note that the video is really not about P=NP at all, not any more than it is about 1+1=2. The use of P=NP in the video was just to give an example of "what is a statement."
Personally I never saw degrees as an excuse to post nonsensical answers or troll people with personal barbs. P!=NP can be shown true for certain constrained sets, but P=NP was shown it can't currently be proven.
People can twist it anyway they like, but stating they can "sort of" disprove or prove P=NP is 100% obfuscated BS. That is why the million dollar prize remains unclaimed.
Why would Gödel's Incompleteness Theorem stop them for P=NP in particular?
Why is the current definition of P or NP insufficiently formal or clear?
PS: Citing YouTube Videos in mathematical discussions is a big red flag indicating you have not really understood things.