The paper by John H. Conway and Joseph Shipman on "extreme" proofs of irrationality of $\sqrt{2}$,
"We shouldn’t speak of ‘‘the best’’ proof, because different people will value proofs in different ways. [...] It is enjoyable and instructive to find proofs that are optimal with respect to one or more such value functions [...] Indeed, because at any given time there are only finitely many known proofs, we may think of them as lying in a polyhedron [...] and the value functions as linear functionals, as in optimization theory, so that any value function must be maximized at some vertex. We shall call the proofs at the vertices of this polygon the extreme proofs.
Terence Tao mentions this paper here, and describes his interaction with some of Conway's contributions to mathematics and with Conway himself. He closes his post with
Conway was arguably an extreme point in the convex hull of all mathematicians. He will very much be missed.
ADDENDUM:
CONWAY published an interesting paper with R.H. Hardin, and N.J.A. Sloane regarding Packings in Grassmannian Space and it were adressed this question how should N n-dimensional subspaces of m-dimensional Euclidean space be arranged so that they are as far apart as possible? , He gives a way to describe $n$-dimensional subspaces of $m-space $ as$m$-space as points on a sphere in dimension $(m-1)(m+2)/2$
