Well, quantum mechanics is "just" 0+1 quantum field theory which is actually a good insight and not at all dismissive.
Is commutative algebra just a branch of set of theory? Are set theorists generally equipped to understand research papers on Galois Cohomology? No. Set theory is used in these areas but to suggest that these areas "are just aspects of set theory" is not all insightful.
This not at all the same. QM is a special case of QFT.
> To say that theoretical quantumn mechanics is just a small branch of mathematics is ignorance.
It’s not. That statement is objectively true.
> It is not insightful at all.
It is.
https://en.m.wikipedia.org/wiki/The_Unreasonable_Effectivene...
> Is commutative algebra just a branch of set of theory? Are set theorists generally equipped to understand research papers on Galois Cohomology? No. Set theory is used in these areas but to suggest that these areas "are just aspects of set theory" is not all insightful.
Intersection (overlap) is not the same as containment, so I have no idea why you’re bringing this up.
Sets are one way (among others) to encode such mathematical structures. This doesn’t mean these structures are sets. For example, is the empty set an element of pi? This question is meaningless because the answer would have to depend on the encoding being used, and not on the properties of pi itself. It’s imposing additional structure above and beyond that of the mathematical structure in question.
See here for more discussion: https://news.ycombinator.com/item?id=16080027.
No. It is a set together with additional structure. Without this additional structure you just have a set, not a ring.
> So is a group.
Again, no. It is a set together with additional structure.
Note: The collection of all groups is not even a set!
You have missed the point of my comment. Do you think Feynman lacked a vast amount of physics knowledge that he memorized (to use his phrasing)? Part of acquiring expertise in any area is the fact that you end up storing lots of information about that area so that you don’t need to look up every little detail or fact.
If you are going to have a serious discussion with biologists about cell processes you need to have lots of knowledge, names, etc. at the ready. Can't go looking up every little thing as you go along. It would be impossible communicate if you did that.
Feynman was being a jerk with that comment. His dismissiveness reminds me of comment that a well respected mathematician once made. “Quantumn mechanics is just such and such theory in dimesion 1.” Only ignorance allows one to hold such a belief.