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Sounds like what math grad students did 50 years ago, before we solved all the pure math even tenuously related to the 4 dimensional reality we live in.

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You are just wrong. For example, algebraic topology is one of the most abstract subjects I hear conversations about week. It has applications in physics, data analysis, and numerical computing.

Also, saying that reality is 4-dimensional is hooding yourself. The machine learning techniques we use everywhere depend on the math of higher-dimensional spaces, and they wouldn't work if reality couldn't be meaningfully viewed as many-dimensional.

Please share a link to an example paper published by a pure math department.

http://arxiv.org/pdf/1303.2807.pdf

Went to the Arxiv into the Algebraic Topology category. Any comments?

Here's one I've been struggling with lately: Parallel coordinates representations of smooth hypersurfaces. I'm not aware of extensive reseach of the parallel coordinates geometry prior to 50 years ago.

http://www.cs.usc.edu/assets/004/83248.pdf

Machine learning casts a problem into higher dimensions in order to linearize it. Linear problems are easier solve, and can be projected back into the original space. An extra dimension is literally just another variable, which doesn't necessarily have a physical meaning.

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