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Comment by sykh | Hacker News Reader

It is dismissive because if it was just that then knowing the mathematics would be sufficient to do research in theoretical quantumn mechanics but it isn't. One needs to know the physics and have physical intuition. To say that theoretical quantumn mechanics is just a small branch of mathematics is ignorance. It is not insightful at all.

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.

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> It is dismissive because if it was just that then knowing the mathematics would be sufficient to do research in theoretical quantumn mechanics but it isn't.

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.

Isn’t it true that commutative algebra is contained within set theory? Aren’t all the objects sets?

> Isn’t it true that commutative algebra is contained within set theory? Aren’t all the objects sets?

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.

A ring is a set. So is a group. At least this is how almost every working commutative algebraist views things. Category theory and its like are gaining traction but the objects are still viewed as sets.

> A ring is a set.

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!

I don't understand the complaint here, Quantum Field Theory is physics just as much as Quantum Mechanics?

The mathematician who made the quote I mentioned said that quantum mechanics was just <some branch of mathematics that I’ve forgotten> in dimension 1. I don’t know what quantumn field theory is. If it is a branch of physics then it’s not the theory the mathematician I referred to mentioned. Some mathematicians view mathematics as superior to physics and are dismissive about physics. They tend to believe that since they mastered mathematics then learning physics is easy.

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