[nabla9]

I can learn to understand basics of many advanced concepts outside engineering math to the level where I can read/skimp some research papers and understand the thinking behind it. But it's very hard to recognize the concept on my own and the utility 'on the wild' unless someone else is pointing it out and explains it.

Take for example Sheaf[1]. The basics are not that hard if you spend some time. But once you have learned it in abstract. Can you see use for it [2] in data analytic, signal processing, or machine learning? How long you have to work for it to really click to the point where you can see and utilize the concept?

I think this is the reason why mathematicians are needed more in every area. They should walk around pointing things out.

[1]: https://en.wikipedia.org/wiki/Sheaf_(mathematics)

[2]: http://www.drmichaelrobinson.net/20131024_overview.pdf

[j2kun]

Oh, if only I could make a career of pointing math things out :)

Joking aside, I think a lot of researchers will oversell the applications of their technology, so it's just as important to be able to recognize when a particular math thing will help, and when it's more harm than good. The first rule of statistics is: if the decision maker already has their heart set on a particular action, you shouldn't waste your time and money designing a statistical study with fancy tests and inference techniques.