Timeline for Why is the Leibniz rule a definition for derivations?
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| Dec 28, 2012 at 5:02 | comment | added | user30180 | @Qiaochu: I agree that "algebra is dual to geometry" is a useful principle for those with enough experience to appreciate its non-formal aspects, but I also think that answers should (try to) be understandable to the person who asked the question (even if partially aimed at a wider audience). | |
| Dec 28, 2012 at 3:48 | comment | added | Qiaochu Yuan | @ayanta: it is a good example of a powerful general pattern in mathematics, roughly encapsulated by the slogan "algebra is dual to geometry." Most people encounter it first in algebraic geometry but I think the realization that it can be used to make sense of certain parts of differential geometry is also valuable. If you disagree, well, you can write your own answer. It is okay to have different answers with different points of view, and answers are not only for the person who asked the question. | |
| Dec 28, 2012 at 2:17 | comment | added | user30180 | The question is about differential geometry, by someone just getting started. How is introducing the consideration of $\mathbf{R}$-algebra homomorphisms from $C^{\infty}(M)$ into $\mathbf{R}[t]$ supposed to illuminate the situation for such a person? | |
| Dec 28, 2012 at 1:38 | history | edited | Qiaochu Yuan | CC BY-SA 3.0 |
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| Dec 28, 2012 at 1:31 | history | answered | Qiaochu Yuan | CC BY-SA 3.0 |