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Omer ZAK's avatar

I am very interested in the following problem.

Suppose I have a practical problem in my business. How do I discover the right mathematical branches/theorems/concepts/models relevant to my practical problem?

There is no natural mapping among the vocabulary of my hypothetical practical problem and the vocabulary used to name mathematical concepts (usually combinations of names of prominent mathematicians).

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Kaleberg's avatar

A lot depends on what you want to measure. If you want to measure the pervasiveness of mathematics in the economy, you'll notice that it has been soaring. Someone has to develop the algorithms that control automobile engines, delivery scheduling, industrial processes, farm machinery and so on.

Something like a thermostat was high tech in its day, but optimally using a thermostat to control a coking oven was high tech in its day. It ended the expensive batch processing of coke and allowed continuous production. Back in the days of the USSR, mathematicians like Kolmogorov did theoretical work, but he also worked on problems in lubrication. It was considered remarkable at the time, but no one remarks nowadays when disposable diaper companies hire mathematicians.

You can try measuring mathematical progress in some abstract sense of advancing, but one problem with mathematics is that one often doesn't know whether one is advancing or not. Mathematicians do all sorts of mathematics for the beauty of it, and only centuries later does their work turn out to be useful in proving some intractable theorem or solving an applied problem.

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