Word problems: Why?

 Perhaps none of us escaped from doing good old word problems in mathematics and in many other areas. Surprisingly, we can trace its roots all the way to more than 5000 years ago, which would counter the argument that word problems are made by the modern education system for whatever goals it intends to serve.

The idea of pure vs applied mathematics seems to stem mostly from academic areas, where scholars jokingly say that math is at the top with applied math below it, with other sciences coming in the order of physics, chemistry, biology and so on. I feel that this is analogous to asking whether the egg came first or the hen came first. Some areas of mathematics, namely number theory, primes and divisors, seem to be more of a matter of taste, as some of us couldn't care less if there are Mersenne primes or sum of divisors being equal to itself. Recent technological breakthrough in computing requires more secure encryption, and surprisingly, there is quite a bit of number theory driving the changes. Those questions about divisors and primes could date back to 5000 years ago before they had computers and likely, they weren't thinking about how to apply it to encryption.

My opinion would simply be the following: if we call it pure mathematics, it is likely we haven't found use of it in something observable.

Given that scientific knowledge has been branching out ever since its discovery, I would say that abstraction is at the core of every subject. A mathematician is likely not an expert biologist, and it would be absurd to expect every biologist to be a great mathematician as well. Abstraction allows us to study what we do best, and collaborate for practical purposes: discovery of new knowledge.