Katie has a PhD in maths, specializing in the intersection of dynamical systems and number theory. She reports on topics from maths and history to society and animals. Katie has a PhD in maths, ...
Reviewed by Robert C. KellyFact checked by Yarilet PerezReviewed by Robert C. KellyFact checked by Yarilet Perez Arrow's impossibility theorem is a social-choice paradox illustrating the flaws of ...
Mathematics has many different ways of distinguishing “big” sets from “small” sets. I will introduce another, ultrafilters, and discuss their definition, construction, and some properties. Next, we ...
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Why every voting system breaks down under math
Democracy feels intuitive, fair, and rational, yet mathematics tells a far more troubling story. In the mid-20th century, a formal proof showed that no voting system can fairly translate individual ...
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