A particularly charming aspect of Dutch doctoral dissertations is the use of “stellingen”: a list of succinct claims that summarise the argument of the dissertation in a direct fashion. (See for example the stellingen of Brouwer’s 1907 dissertation [English translation available in his collected works].)

“Stelling” is the Dutch word for “proposition” (or literally simply “putting,” in keeping with the Dutch way of speaking). In this context it means something like “propositions to be defended by the candidate.” It evokes days of yore when a doctoral dissertation had to be defended in a proper disputation.

It’s too bad that the practice of concise, no-nonsense stellingen and feisty, no-holds-barred disputations has fallen out of favour these days; it could do much to combat the vague babble and polite circumlocution that plague academia today.

Stellingen are no longer an official part of Dutch dissertations, sadly, but in honour of this beautiful tradition of the country that hosted me for my Ph.D. research I offer here my ten stellingen:

1. That which is known is that which is constructed.

2. Descartes, Leibniz, Newton, et al. modelled their mathematics, science, and philosophy on what they perceived as the method of Euclidean geometry.

3. Key conflicts between these figures in all these fields trace back to their divergent interpretations of the method of Euclidean geometry.

4. Leibniz was the last proponent of ancient rigour in mathematics.

5. Euler and Lagrange were opportunists who abandoned ancient standards of rigour; Leibniz had too much intellectual integrity to do the same.

6. For this reason Leibniz et al. resisted reliance on analytical representations of curves, despite being well aware of the advantages of such an approach.

7. The term “rigorous” as used today is an inconsequential social construct and dubious honorific.

8. History shows that “where there’s a will there’s a way”: if a certain idea did not develop at a certain time, it was as a rule for lack of motivation and desire rather than lack of ability or imagination.

9. Understanding a historical development means explaining why it should have happened thus and not otherwise.

10. In history, that which makes more sense happens before that which makes less sense.