This week’s topic is one of several suggested again by Mr Wu, blogger and Singaporean mathematics tutor. He’d suggested several topics, overlapping in their subject matter, and I was challenged to pick one.
The reputation of mathematics has two aspects: difficulty and truth. Put “difficulty” to the side. “Truth” seems inarguable. We expect mathematics to produce sound, deductive arguments for everything. And that is an ideal. But we often want to know things we can’t do, or can’t do exactly. We can handle that often. If we can show that a number we want must be within some error range of a number we can calculate, we have a “numerical solution”. If we can show that a number we want must be within every error range of a number we can calculate, we have an “analytic solution”.
There are many things we’d like to calculate and can’t exactly.
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