“menifolds”
I created these menifolds for my dissertation defense presentation. “Menifold” is a portmanteau of “men” and “manifold.” The “manifold” is a foundational mathematical idea, which encompasses a variety of spatial forms. It was introduced in the nineteenth century by Bernhard Riemann. I represented each of the “men” below with exactly one one-dimensional manifolds, which are effectively continuous curved lines. (In other words, were I to recreate these with pen and paper, I would never lift the pen off the page.) The menifolds lightly poke fun at two widespread ideas about mathematics: that it is widely the province of men, and that these men are effectively disembodied heads, brains without bodies. In the following, I show how Riemann in “On the hypotheses” constructed his identity with reference to, and with the help of, a handful of other scholars.
Bernhard Riemann, mathematician
My dissertation focuses on Riemann. I diverge from most scholarship, which portrays him as wholly distinctive: unparalleled in his creative thinking, one of the greatest mathematicians ever, etc. And then there are the accompanying tropes: shy and inward turning, frail, prone to gloominess. While there is some truth to all of this, that truth is limited; from another perspective, Riemann was a relatively typical scholar of his time, whose “genius” identity was constructed by his predecessors after his death. Riemann too had a hand in forming this identity, which he cultivated in part by linking himself to lionized scholars like Gauss and Herbart.
Wilhelm Weber, physicist
Weber’s primarily contributions to securing Riemann’s success arguably took place behind the scenes. Weber was a staunch advocate throughout Riemann’s career, and wrote several times to the Hannoverian ministry on his behalf. Over the years, Weber helped Riemann secure a permanent position at Göttingen, several different sources of income, and even a place to live in the Göttingen observatory. Riemann didn’t mention Weber explicitly in his habilitation lecture, but perhaps his presence can be felt in the lecture’s nods to physics and the natural sciences.
Carl Friedrich Gauss, polymath
There are many ways in which Riemann’s habilitation lecture reveals his scholarly debts to Gauss, and especially Gauss’s work on surfaces. It is also possible to see Gauss’s scholarly identity as a model for Riemann’s own. Gauss is listed as a “polymath” because disciplinary boundaries were less clearly delineated when he entered the scholarly world. Gauss’s work spanned abstract treatises to measurements of earth’s magnetism. While scholars have argued that the world of the polymaths had all but disappeared by Riemann’s time, Riemann in his habilitation lecture crossed the boundaries of subjects and insisted on relations among different subjects. Riemann positioned his habilitation lecture as spanning several subject areas, including mathematics and philosophy, and presented himself as a scholar in Gauss’s mold.
Johann Friedrich Herbart, philosopher
In Riemann’s telling, his reading of Herbart’s works led him to new approaches to questions about the physical world. This fact is supported by the Göttingen University Library’s borrowing records, which suggest Riemann borrowed Herbart’s collected works extensively. The library record suggests that for Riemann, Herbart was to philosophy as Gauss was to mathematics: Riemann’s anchor in the subject. So insofar as Riemann’s lecture made forays into philosophy, he was following a path that Herbart had carved—a fact that many scholars have supported with specific details, though not all agree. Although Herbart had passed away long before Riemann arrived at Göttingen, Herbart’s work played a considerable role in Riemann’s scholarly activity.
