In fact, this is happening now, with companies such as Infosys, Tata Consultancy, Cognizant, HCL, Wipro, and iGate Patni. For example, iGate Patni is a Silicon Valley headquartered, Indian IT outsourcing company with over 26,000 well-educated employees who perform such tasks as writing smartphone apps, handling complex financial matters, and optimizing business logistics processes.
Every mathematical skill, procedure, or technique I learned over six years at university is now essentially obsolete from a US market perspective.
(This is why I am not unduly worried for my own future. I learned two things at university far more valuable than a bunch of techniques: I learned to think a certain way -- as a mathematician -- and I learned how to master new techniques quickly whenever I need them.)
The first category comprises people who, given a mathematical problem (i.e., a problem already formulated in mathematical terms), can find its mathematical solution.
The second category comprises people who can take a new problem, say in manufacturing, identify and describe key features of the problem mathematically, and use that mathematical description to analyze the problem in a precise fashion, picking up whatever mathematical techniques are required along the way.
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