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Comment by verroq | Hacker News Reader

I think it's much clearer to define everything in terms of vector spaces and linear operators.

I entirely agree. People tend to run away from abstract math, with the impression that it's difficult. But the whole point is that a more abstract view of these things makes them easier to understand, not harder.

The problem is that abstractions are designed to make hard problems harder. Someone who has never seen the type of problem that would make a given abstraction useful would not be able to understand it easily. If you work you're way up, then it becomes obvious.

> Someone who has never seen the type of problem that would make a given abstraction useful would not be able to understand it easily.

Whether or not someone is sufficiently motivated to study something should not affect their ability to understand it. Vector spaces and linear maps are actually much easier to understand, and I think that at some point in mathematics (probably your first analysis course) your motivation has to come from the beauty of the theory itself rather than some real-world application.

So mathematicians seek beauty instead of utility.

Should they deserve to starve like artists then?

Should taxpayers fund disciples (students) for them?

If yes, than should taxpayers be forced to fund students for any cult anyone wishes to start?

There is nothing quite like trolling a bunch of nerds with the opinion that the entire study of pure mathematics has been a wasted endeavor for mankind...

You deserve a round of applause!

(Also, mods, where are you?)

Newborns don't come out with all knowledge in their heads already. I'm simply alerting younger people to facts, there's absolutely no reason to get mods involved. Otherwise most of HN should be banned (since a lot of it is not completely fresh news). Why alert the mods, are you a scared pure mathematician?

My point was not that someone would not be motivated to learn the abstraction, it was that the abstraction would not make sense without a reason to use it. That reason could very well be an entirely theoretical application, but why would the concept of expressing a linear equation as a matrix make any sense to someone who has never dealt with more than 2 linear equations at a time?

Sure, but verroq was talking about vector spaces and linear maps, not matrices. The theory of vector spaces over a field is more general and can be applied to much more than systems of equations.

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