Tao on coordinate vs coordinate-free math reasoning

[dmm]

> On when to use coordinates and other concrete constructions in mathematics, and when to use coordinate-free formulations and abstractions:

> 1. If your priority is to perform computations in mathematics, use coordinates and concrete constructions.
> 2. If your priority is to generalize to as broad a range of use cases as possible, use coordinate-free formulations and abstractions.
> 3. If your priority is to actually understand what is going on behind the mathematical formalism, learn how the coordinate-based and coordinate-free approaches are equivalent.

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