In 1901, under the supervision of David Hilbert, Werner Boy wrote his dissertation „Über die Curvatura integra und die Topologie geschlossener Flächen“\cite{Boy}. It is noticeable that in this thesis the global formulation of the well-known Gauss-Bonnet theorem appeared for the first time.

In particular his work contained a discussion of the theorem for non-orientable surfaces. This lead to a construction of an immersion of the real projective plane $\mathbb{R}P^2$ into $\mathbb{R}^3$ which was, until then, thought to be unlikely possible\cite{KP}.

Rob Kusner and Robert Bryant found a particularly appealing parameterisation of the so called \textit{„Boy’s surface“} \cite{Kus} which minimises the „Willmore functional“ $$W(f)=\frac{1}{4}\int_M (\kappa_1 + \kappa_2)^2\ dA\ .$$
Willmore surfaces are perceived to be exceptionally attractive as they do not possess any unnecessary dents.

Boy’s surface is related to Kusner surfaces as you can obtain the former from a Kusner surface of degree 3 by applying a suitable sphere inversion.