Hermes's Suitcase of Göttingen
Computing the 65537-gon
While studying and teaching mathematics in Prussia and Germany, Johann Gustav Hermes (1846–1912) spent 10 years on a 200-page manuscript focusing on the construction of the 65537-gon. After the Second World War, Hermes's manuscripts were moved to the Mathematical Institute in Göttingen, where they can now be viewed in the so-called "suitcase of Göttingen."
The 65537 sides in Hermes's computation are of interest because 65537 is the largest known Fermat prime. As such, it corresponds to the largest known "basic" (i.e. not having a number of sides which is a multiple of side counts of smaller constructible polygons) regular polygon that is constructible using classical Greek method involving compass and straightedge. However, despite the Herculean effort in computation and perseverance on the part of Hermes, the assessment of geometer H. S. M. Coxeter that "Hermes wasted ten years of his life on the 65537-gon" reflects the fact that not only do these calculations contain no new mathematics but—especially following the advent of symbolic computer algebra—they can be fully automated.