Mathematicians have made a groundbreaking discovery by disproving the bunkbed conjecture, a widely believed assumption in physics about fluid flow through solids. The conjecture was debunked using hypergraphs, which has implications for how mathematicians approach problem-solving and question their assumptions. This result offers fresh guidance on related problems in physics and taps into deeper questions about how mathematics works.
A New Hypergraph Was Created
Background
Hollom created a small hypergraph whose edges each connected three vertices and found a counterexample. This result was then reworked by Gladkov and his colleagues into a normal graph that would disprove the original bunkbed conjecture.
The Counterexample
The counterexample is a massive graph with 7,222 vertices connected by 14,422 edges.
Implications for Physics
The bunkbed conjecture was related to problems in physics about properties of solid materials. It would have implied a widely believed assumption in physics about how likely a fluid is to travel through a solid. However, the debunking of the conjecture does not affect the physics statement that inspired it.
Importance of Questioning Assumptions
The result offers fresh guidance on related problems in physics and taps into deeper questions about how mathematics works. Mathematicians may need to question their assumptions more often and consider the possibility that things which intuitively look very likely to be true, might not be true at all.
The bunkbed conjecture was about navigating graphs stacked on top of each other like bunk beds and seemed natural and self-evident. However, the result offers fresh guidance on related problems in physics about properties of solid materials and taps into deeper questions about how mathematics works.
A Counterexample is Found
Lawrence Hollom disproved a version of the bunkbed problem in a different context using hypergraphs. He created a small hypergraph whose edges each connected three vertices, which was then reworked by Gladkov and his colleagues into a normal graph that would disprove the original bunkbed conjecture.
Impact on Physics
The bunkbed conjecture would have implied a widely believed assumption in physics about how likely a fluid is to travel through a solid. However, with the debunking of this conjecture, mathematicians may need to question their assumptions more often and consider alternative approaches.
Further Discussion Needed
A more active discussion is needed about the nature of mathematical proof, especially with computer- and AI-based lines of attack becoming more common in mathematics research. This will help to clarify how mathematics works and provide fresh insights into related problems in physics.
