AFTERWORD: THE VEIL OF MAYA

1. (Nietzsche 1974), Preface to the second edtion, paragraph 3; translation slightly modified. Stephen Strogatz’s book The Joy of x, published in 2012 may not be about the same joy, but it must be about the same x.

2. The discussion of the last two paragraphs is taken from chapter 21 of (Hadot 2006).

3. (Hausdorff 2011).

4. Hausdorff made major contributions to set theory, probability, functional analysis, and several other branches of mathematics as well as mathematical physics. His notion of continuous (or fractional) dimension is the starting point of Benoît Mandelbrot’s theory of fractals. But he is best known among mathematicians for his development of topology.

5. The comedy, entitled The Surgeon of his Honor [Der Arzt seiner Ehre], ridiculed the Prussian code of honor that came to an end with the war.

6. Quotations from (Purkert 2008; Monist 1900); see also (Epple 2006). Mongré was also concerned to disprove Nietzsche’s doctrine of eternal return, and to this end he appealed to Cantor’s infinities.

The author was not surprised to learn that philosophers have revived the term “transcendental nihilism,” specifically in connection with the book Nihil Unbound by Ray Brassier. There are parallels with the thoughts of Mongré’s Truth-seeker, but neither Mongré nor Hausdorff is cited as a precursor.

7. Translation from (Purkert 2008, p. 40).

8. (Stegmaier 2004).

9. See (Epple 2007): “According to Hausdorff, experience limits the range of possible mathematical conceptions of notions like time, space, motion, temperature, dimension, … but it is the task of mathematics to explore the full Spielraum of possibilities within these limits.” Hausdorff’s considered empiricism in some ways anticipated the positions of the Vienna Circle, specifically the early work of Moritz Schlick; see (Epple 2006: Stegmaier 2004).

10. Hausdorff, quoted in (Stegmaier 2004, note 22). For “very large indeed,” see (Epple 2006, p. 282).

11. In contrast, the word freedom is nowhere to be seen in Hardy’s Apology, nor in Russell’s Principles of Mathematics. When it appears in Jacques Hadamard’s Psychology of Mathematical Invention, it is associated with the arts, or with dreams; Poincaré uses the word liberté in Science et Hypothèse only to talk about the “limite imposée à la liberté” [the limits of freedom] and to remind us that “la liberté n’est pas arbitraire” [freedom is not arbitrary].

12. Hausdorff could not resist inserting a “glimmer of [dark] humor” in his suicide note. Mongré had published poetry; before advising the friend to whom the letter was addressed how to dispose of his property, Hausdorff alluded to the likelihood of depor-tation from Endenich, where he and his wife were about to be interned, in a two-line verse:

auch Endenich
ist noch vielleicht das Ende nich!
[Endenich may not be the End either!]

13. (Purkert 2008), from the introduction by David E. Rowe, p. 36 and p. 37. The expression “Dionysian mathematician” was due to Hausdorff’s contemporary, the writer Paul Lauterbach.