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There often are "areas" of math

Example: topology, geometry, abstract algebra etc...

But can these "areas" be rigorously defined?

For example given a sentence $\phi$ in ZFC can one deduce which "subject" this sentence belongs to?

Of course a lot here needs to be made rigorous:

How do we formally defined the subjects How do we decide if a particular sentence belongs to a particular subject Does there exist more than one natural way to do this?

But I'm curious if a generic sentence to subject recognizer could be built.

An idea:

Perhaps one can compute "identifying" elements of the different subjects of mathematics, say using LDA with ngrams of sequences of symbols in a sentence that a human has already decided belongs to some subject.

Sidharth Ghoshal
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  • Divisibility belongs to number theory, of course, doesn't it? And yet, the famous Euclidean algorithm to find the gcd of two numbers was first published in the Elements as a geometric construction ... - but regarding sentences in ZFC, I'd say: Any sentence that is short enough to fit into just a few lines in the language of ZFC is about set theory, simply because there is not enough room to define the notion of, say, smooth manifold – Hagen von Eitzen Aug 13 '16 at 07:44
  • This occurs a lot. I still grow curious, the idea of teaching machines to recognize the subject of a problem, however superficial sounding, seems intriguing to consider. On points like this perhaps the algorithm ought to suggest both Number Theory and Geometry, perhaps weighted differently. – Sidharth Ghoshal Aug 13 '16 at 07:46

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