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April 22, 2026Notices of the American Mathematical Society0 citations

Throwing Darts at the Real Line

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JHJoel Hamkins

Key Points

  • To explore how existence claims can be proven without providing specific examples, using randomness.
  • Mathematical proof techniques involving random selection from a defined class.
  • Analysis of probabilities associated with randomly chosen instances.
  • Establishes a framework for existence claims based on nonzero probabilities.
  • Shows that randomness can affirm properties in various mathematical contexts.

Abstract

There is an elegant style of mathematical argument by which one proves an existence claim not by exhibiting any particular instance, but rather by proving that a randomly chosen instance from a suitable class exhibits the property with nonzero probability.

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Cite This Study

Joel Hamkins (2026) studied this question.

synapsesocial.com/papers/69e865476e0dea528dde9d4bhttps://doi.org/10.1090/noti3315
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