I tried to solve some engineering problems with PGA few years ago. Seemed to work OK up to a point, and at least for me was easier to approach than say Lie algebra or differential geometry.

TFA denigrates papers and websites that are "non-theoretical" or "trivial". As a user of the formalisms, these kinds of materials are exactly what I need. I don't care about proofs or theoretically problematic corner cases that "real mathematics" seems to be almost exclusively interested in.

I did hit a wall quite soon with GA, and got a feel that it may indeed be overhyped, but at least the scene seems to be interested about applied use.

There seems to be similar debate about nonstandard calculus. For my modest use it has provided some tools that can give me results that I don't know how to get with epsilon-delta etc. I don't really care if I don't "really understand" it because the underlying proofs need some heavy machinery. I don't understand those for standard calculus either, and in applied use you either manipulate infinitesimals without any proper algebra, or just hope what you need is in some table.

I can't comment on deeper theoretical or philosophical questions about these, and I don't really care about them. But to me maths communication often seems analogous to making people learn turing machines and lambda calculus before they are allowed to program in Javascript.

I don't think the author necessarily disagrees with me much, but this is maybe a kinda mini rant from a perspective of someone who is just an "end user" of mathematics.

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NooneAtAll3 3 hours ago | parent | next [-]

> I did hit a wall quite soon with GA

can you give an example of what's impossible/hard to do?

	▲	jampekka 3 hours ago \| parent [-]
		I don't recall the details anymore, and the work never amounted to anything, but generally it was about finding expressions for some properties of the visual flow field under curvilinear motion. I can't really say if the problem was with me or GA. Probably more like GA didn't end up providing tools for my level of math skills to solve the problem. But neither did the the traditional branches.

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srean 3 hours ago | parent | prev [-]

> I don't care about proofs or theoretically problematic corner cases that "real mathematics" seems to be almost exclusively interested in.

That is a rather strange take for a software engineer.

When implementing something I do need to know what the corner cases are, whether the runtime can enter such a state. I need to think how to put in checks so that they cannot be reached, or alternatively, how to recover gracefully. That's my job after all, why would anyone pay me if I didn't.

Perhaps a topical example is a gimbal lock. I need to be aware that it can happen and I need to know how to prevent it.

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jampekka 2 hours ago | parent [-]

I didn't mean corner cases like that. I mean stuff that has no practical consequences, at least for most practical use.

E.g. whether or not Navier-Stokes can form singularities doesn't really change how you analyze fluid dynamics in engineering. This doesn't mean it is not a mathematically important question worth extensive study, but it's not relevant for practitioners.

	▲	srean an hour ago \| parent [-]
		Got you.