Of course the main reason for using natural language is that we apply mathematics and so an important part of learning is the interpretation of the symbolic notation for application. You can't ask questions in symbols just because you haven't introduced the necessary meta-mathematical symbolic language. But you easily could and write something like ?x[13+78=x]. But then you would still need to teach the natural language interpretation. Brent On 12/2/2017 11:06 PM, Scott Kim wrote:
I'm thinking about teaching the problem solving process in mathematics, and have run into a curious question: can one ask a mathematical question purely in mathematical notation? I believe the answer is no — mathematical questions always require human language in addition to mathematical notation. Problem statements are therefore always extramathematical in nature.
In practice, school kids frequently see problems stated in forms like: 13+78 = ___, which means "what is the sum of thirteen and seventy eight?" But that involves a nonmathematical symbol (the blank), AND ends up misleading kids to think that the equals sign means "the answer is". Very sloppy. We can do better.
This is an extension of something that has always bothered me: if mathematics is so rigorous, then how come it is conducted in a mish mosh of English and formal notation? The practical reason for mixing in human language is clear…like a computer program, a formal mathematical proof is more readable if it is annotated with comments. But too much reliance on human language means that formal proofs are not checkable by computer — a weird situation at best. I suppose that makes me a formalist, or a computer scientist…I've certainly got the latter bias because I don't trust anything I can't program.
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