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How closely does MathOverflow track the interests of mathematicians as measured in other ways?

For instance, the Tags page here suggests that $$\frac{\text{interest}_{tags}\text{(algebraic geometry and number theory)}}{\text{interest}_{tags}\text{(algebraic topology and differential geometry)}}> 2$$

Would other measures, counting numbers of people or papers or talks, give similar results?

My guess is that MathOverflow gets a higher number for the above ratio than other metrics, since its format is more suited to things like 47867742232066880047611079 than to geometric diagrams.

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    $\begingroup$ While I agree that algebraic geometry and number theory are over-represented on MO relative to mathematics as a whole, I think your tag count here is misleading. Algebraic geometry and number theory are enormously broad areas; however, for cultural reasons people still usually tag most questions about them as algebraic geometry and number theory. Algebraic topology and differential geometry, however, are more specialized and precise. For instance, I suspect that lots of questions about hyperbolic geometry or the topology of manifolds are tagged using different tags. $\endgroup$ – Andy Putman Jan 9 '14 at 21:10
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    $\begingroup$ If only... it seems that getting a job in logic and set theory would be much easier if MO tag sizes were an accurate depiction of reality. $\endgroup$ – Asaf Karagila Jan 10 '14 at 8:13
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    $\begingroup$ There are almost exactly twice as many questions tagged in logic than in analysis-of-pdes. $\endgroup$ – Scott Armstrong Jan 10 '14 at 12:33
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I would expect not.

To a very large extent, the relative activities of various fields on MathOverflow reflects the relative activities of those fields on MathOverflow earlier. The interests of the founders and early adopters could have had a very big effect. (Perhaps like small variations in the cosmic background radiation leading to the formations of galaxies!)

We also know there are large variations in the degree to which various fields use the arXiv, and it's very plausible that there are similar variations more generally for use of the internet to do mathematics.

I'd be interested to see someone calculate some other measures, but I think they would say more about the forums (MathOverflow, blogs, the arXiv, AMS conference participation, etc) than about mathematics as a whole.

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  • $\begingroup$ I just checked some easily accessed data on the arXiv: recent submissions in the four areas I mentioned give a ratio of (45+39)/(15+44), which is <1.5. Interesting. $\endgroup$ – Matt F. Jan 9 '14 at 22:36
  • $\begingroup$ These four number $45, 39, 15, 44$ (or rather either of them divided by their sum) give much more info than the ratio you computed. So what is the point of doing so (not only for your comment, but also for the above question)? $\endgroup$ – Christian Stump Jan 11 '14 at 20:07

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