So narrowly educated

In a tribute to the mathematician Israel Moiseevich Gelfand (Notices of the AMS, vol. 60, no. 2, p. 162), Dusa McDuff recalls meeting Gelfand in Moscow.

Then [Gelfand] gave me his recent paper on Gelfand-Fuchs cohomology to read. It was titled “The cohomology of the Lie algebra of vector fields on a manifold”, but I had been so narrowly educated that I didn’t know what cohomology was, what a Lie algebra was, what a vector field was, or what a manifold was.

I know one definition of a vector field, but it’s probably not the same as the one in the paper mentioned. Right now I also don’t know the definitions of the other three terms.

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