A New Bridge Links the Math of Infinity to Computer Science
17 hours ago
- #computer-science
- #infinity
- #descriptive-set-theory
- Descriptive set theory explores the fundamental nature of sets, especially infinite ones, unlike most mathematicians who take set behavior for granted.
- Anton Bernshteyn discovered a deep connection between descriptive set theory and computer science, showing that infinite set problems can be rewritten as network communication problems.
- The bridge between set theory and computer science was unexpected due to their different languages (logic vs. algorithms) and focuses (infinite vs. finite).
- Bernshteyn's work allows mathematicians to translate problems between the two fields, leading to new theorems and reorganizing the hierarchy of set theory.
- Descriptive set theory originated with Georg Cantor's discovery of different sizes of infinity, leading to concepts like measure (e.g., Lebesgue measure) and unmeasurable sets.
- Bernshteyn studied infinite graphs and coloring problems, avoiding the axiom of choice to ensure measurable sets, which led to his breakthrough connecting set theory and distributed algorithms.
- Distributed algorithms in computer science, like coloring finite graphs for router frequency assignments, share structural similarities with infinite graph problems in set theory.
- Bernshteyn proved that efficient local algorithms correspond to measurable colorings of infinite graphs, enabling cross-disciplinary insights and problem-solving.
- The discovery has practical implications, such as classifying previously unclassifiable problems in set theory using computer science frameworks.
- Bernshteyn aims to make infinity more accessible and relevant to mathematicians, bridging the gap between abstract set theory and applied mathematics.