_{Photo Credit: Quanta Magazine, Math’s ‘Bunkbed Conjecture’ Has Been Debunked. “Hollom found a counterexample to this version of the conjecture. He created a small hypergraph whose edges each connected three vertices.“}

A research team consisting of Professor Igor Pak, UCLA PhD Candidate Nikita Gladkov, and MIT PhD Candidate Aleksandr Zimin have proven the ‘Bunkbed Conjecture’ is false, offering a new perspective on how to approach related problems in probability. The research team formulated an explicit counterexample against the conjecture of Dutch physicist Pieter Kasteleyn, who wanted to model how liquids flow throughout solids. 

Recently featured in Quanta Magazine, the three mathematicians are commended for their persistence in proving their doubts about the bunkbed conjecture. After failed attempts using computers and machine learning, they found what they were looking for when Gladkov came across University of Cambridge Professor Lawrence Hollom’s paper disproving a version of the bunkbed conjecture. They reworked Hollom’s hypergraph to create a graph that led to their breakthrough. 

“Gladkov, Pak and Zimin replaced each three-vertex edge in the hypergraph with a massive cluster of points and normal edges. This gave them an enormous graph of 7,222 vertices connected by 14,422 edges. They then used the theoretical argument they’d built up after abandoning their artificial intelligence approach to prove that in this graph, finding an upper path was 1/10^6,500 more likely than finding a lower one – an unimaginably small but nonzero number. The bunkbed conjecture was wrong.” 

Read the official paper here.

Read Professor Pak’s blog post here.

Watch the featured video here. 

Read the full Quanta Magazine piece here.