Mathematical Adventures
Mathematics is a subject with surprising depth hiding in unexpected places — a routine exercise becomes a research problem, a question in linear algebra finds answers in the depths of set theory. This blog documents that kind of exploration, alongside reflection on mathematics as a social practice — its philosophy, its history, and its politics. The current series, Pathological Periodicity, digs into the fasinating world of periodic functions that admit what may be called “incommensurable decompositions.”
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Start here: Pathological Periodicity
Nonconstant continuous periodic functions cannot have dense period sets, and if two continuous functions have no (nonzero) periods in common, their sum won’t be periodic. Neither of these facts holds in general, and they fail in especially fascinating ways for nonmeasurable functions. This series explores the surprisingly rich family of pathological counterexamples that emerges once continuity, and then measurability, are abandoned.