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What other parts of mathematics use Fields? They seem significant, but I dont understand the significance or the meaning.
by ghthor 7y ago
What other parts of mathematics use Fields? They seem significant, but I dont understand the significance or the meaning.
- dboreham 7y agoHmm...everything? https://en.m.wikipedia.org/wiki/Field_(mathematics) https://en.m.wikipedia.org/wiki/Field_(mathematics) IANAM but for me the significance and meaning is to do with being able to reason about problems at a higher level of abstraction. E.g. the proof using Galois Field Theory that the heptagon is unconstructable: https://en.m.wikipedia.org/wiki/Constructible_polygon https://en.m.wikipedia.org/wiki/Constructible_polygon
- ur--whale 7y agoAside from the obvious fact that the set everyday numbers (both rationals and reals) are fields, most crypto heavily relies on finite fields. [edit] and come to think of it, I might be mistaken I don't think the notion of vector space and therefore the whole of linear algebra would work without a field for the underlying coordinates.