Copied from a bio of Johann Bernoulli: "Johann Bernoulli had already solved the problem of the catenary which had been posed by his brother in 1691. [...] At this stage Johann and Jacob were learning much from each other in a reasonably friendly rivalry which, a few years later, would descend into open hostility. For example they worked together on caustic curves during 1692-93 although they did not publish the work jointly. Even at this stage the rivalry was too severe to allow joint publications and they would never publish joint work at any time despite working on similar topics."

Whitehead-Russell

Let me second J.M.'s request, can you please elaborate?

This kind of statement is folklore knowledge in some epsilon neighbourhood of Miles Reid; I don't know a reference for this particular statement. But in one direction, a linear section of $Gr(2,5)$ is clearly an elliptic curve of degree $5$. In the other direction, by Riemann-Roch you get an embedding of $E$ into $P^4$, which is projectively Gorenstein; by Eisenbud-Buchsbaum, its equations are the Pfaffians of a skew matrix. Googling, I also found Tom Fisher: Pfaffian representations of elliptic normal curves, in Trans AMS 263 (2010), which does a lot more of this sort of thing.