Wikipedia:Reference desk/Archives/Mathematics/2019 May 18

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May 18

Analytic and algebraic topology of locally Euclidean metrizations of infinitely differentiable Riemannian manifolds, Bozhe moi

Now this, I know from nothing.[1]

My question: is it a real math topic at all? What means it? Who has studied it? What is "analytic topology"--is that what they called differential topology back in the 1950s? What do they mean about topology of metrizations since I thought the idea of topology was that if metrics were involved then it would be geometry? Thanks.... 67.164.113.165 (talk) 21:04, 18 May 2019 (UTC)

Tom Lehrer did go to graduate school in Math (though he never finished his dissertation), so he was familiar with mathematical jargon. The song was not meant to be taken seriously though, so I'm fairly sure that he took some liberties to make it sound (even) more abstruse than it actually is. See Analytic geometry, Algebraic geometry, Algebraic topology, Locally Euclidean space, Metrization theorem, Riemannian manifold, and an infinitely differentiable manifold is another name for a Smooth manifold. --RDBury (talk) 23:58, 18 May 2019 (UTC)

Thanks, yeah, I know about Lehrer and I know more or less what most of those words mean when taken separately, but couldn't make much sense of the purported topic described by the whole phrase. If it's just nonsense I'm a little bit disappointed but oh well, thanks. 67.164.113.165 (talk) 08:20, 19 May 2019 (UTC)

On the other hand New Math was an actual thing at the time Lehrer wrote a song about it, and everything in that song is mathematically valid (almost). --RDBury (talk) 09:45, 19 May 2019 (UTC)