4 ms·

> 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.

> 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_Effectiveness_of_Mathematics_in_the_Natural_Sciences 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.

sykh 8y ago
Isn’t it true that commutative algebra is contained within set theory? Aren’t all the objects sets?
- throwaway37585 8y ago
  > 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 https://news.ycombinator.com/item?id=16080027.
  - sykh 8y ago
    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.
    - throwaway37585 8y ago
      > 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!

sykh 8y ago

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

throwaway37585 8y ago
> 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 https://news.ycombinator.com/item?id=16080027.
- sykh 8y ago
  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.
  - throwaway37585 8y ago
    > 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!