Mathematical Explanations in Euler’s Königsberg

I examine Leonhard Euler’s original solution to the Königsberg bridges problem. Euler’s solution can be interpreted as both an explanation within mathematics and a scientific explanation using mathematics. At the level of pure mathematics, Euler proposes three different solutions to the Königsberg problem. The differences between these solutions can be fruitfully explicated in terms of explanatory power. In the scientific version of the explanation, mathematics aids by representing the explanatorily salient causal structure of Königsberg. Based on this analysis, I defend a version of the so-called “Transmission View” of scientific explanations using mathematics against objections by Alan Baker and Marc Lange, and I discuss Lange’s notion of “distinctively mathematical explanations” and Christopher Pincock’s notion of “abstract explanations”.