[FOM] 827: Tangible Incompleteness Restarted/1

[Timothy Y. Chow]

This line of discussion seems to be reaching its limits and I won't 
protest if the moderator decides to close it, but Annatala Wolf asked a 
specific question.

On Thu, 26 Sep 2019, Annatala Wolf wrote:
> I have a question. I'm curious about what might make a mathematical 
> researcher view an area of math as non-mathematical. Do you think it is 
> that there is not enough active research in the area? Or is it that the 
> subject is "too easy" to qualify? Or is it simply when the domain has 
> real-world applications? If the latter, I might agree that research is 
> not in some sense "pure" when it is directed toward a specific applied 
> purpose, but that's about as far as I would take the qualification—I 
> don't find it useful to label something mathematical based on whether it 
> finds utility in other scientific fields.

Of course when someone like this makes a judgment that "this is not math" 
they are not necessarily denying that it may technically satisfy some 
dictionary definition of the word "math."  Instead they are making some 
judgment that the field in question is unrepresentative of what they 
consider to be the essence of mathematics.  In some ways it is not unlike 
the complaint one sometimes hears from professional mathematicians that 
the math that is taught in schools is unrepresentative of "what math 
really is."  While the features suggested by Wolf may play a role, I think 
that ultimately such people are making an aesthetic judgment, that there 
is a subset of mathematical knowledge that exhibits features such as 
unity, interrelatedness, and depth, that they regard as capturing what is 
most beautiful about mathematics.  Areas of mathematics that are perceived 
of as being insufficiently unified with this paradigmatic subset, or that 
are perceived of as lacking depth, are downgraded to second-class status.

Tim