The existence of provably equivalent mathematical redescriptions of the same phenomenon—as in Euler's bridges and graph-theoretic reformulations—entails that explanatory success tracks modal structure, not particular abstract objects.

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Euler(as a historical example of mathematical problem-solving): Leonhard Euler was an 18th-century Swiss mathematician who solved a famous puzzle about bridges in the city of Königsberg, which became one of the first problems in graph theory.
Euler's bridges(as a concrete example of a problem that can be described in multiple ways): A classic puzzle asking whether you can cross all seven bridges in Königsberg exactly once; Euler proved it was impossible and created graph theory in the process.
Explanatory success(as used in epistemology and philosophy of science): When a theory or description actually works well at predicting what happens and helping us understand why things occur the way they do.
Graph theory(as an alternative way to describe the bridge problem): A branch of mathematics that studies networks made of points (called nodes) connected by lines (called edges), useful for solving puzzles and real-world problems like finding the best route.

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