Scientists Disprove Bunkbed Conjecture
Mathematicians from Russia, including two HSE graduates, have disproven a well-known mathematical conjecture that, despite lacking solid proof, had been considered valid for 40 years. The ‘Bunkbed Conjecture’ belongs to percolation theory—a branch of mathematics that studies the formation of connected structures in independent environments.
The hypothesis was proposed in the 1980s by Dutch physicist Pieter Kasteleyn, who aimed to mathematically describe how liquids seep through porous surfaces, such as water saturating a sponge.
The conjecture is based on random connections between vertices in an imaginary graph resembling a bunkbed. It posits that the probability of a connection forming between two vertices on the same level is higher than the probability of a connection forming between levels.
While this statement seems intuitively true, no convincing proof had been found to confirm or refute it until recently. Sceptics argued that the claim was too general to hold true in all cases.
Mathematics typically focuses on proving the validity of statements, with disproofs being relatively rare. However, a team of Russian mathematicians—Igor Pak, Nikita Gladkov, and Aleksandr Zimin—managed to find a counterexample that invalidated the conjecture.
‘Actually, my colleague Nikita Gladkov and I first encountered the “bunkbed” concept during our freshman year at HSE. We were dorm roommates, and our room actually had a bunkbed,’ joked Aleksandr Zimin. ‘With this conjecture, we understood that it holds true for most cases. But we were curious—are there rare cases where it fails?’
Initially, the team tried to find a counterexample using machine learning methods. They trained a neural network to identify potential connections in graphs and attempted to explore all possible configurations. However, for graphs with more than nine vertices, the number of possible connections grew exponentially, quickly exceeding computational limits. No proof was found.
The researchers then adapted methods from hypergraph theory, where a disproof of the Bunkbed Conjecture already existed, to classical graphs. They constructed a highly complex structure containing thousands of vertices and edges. In this graph, the probability of a connection forming between the upper and lower levels was slightly higher than the probability of a connection forming on the lower level, thereby disproving the conjecture.
‘My co-authors Igor Pak and Nikita Gladkov—who are currently working at UCLA—and I complemented each other perfectly on this project. I prefer using numerical methods. In my opinion, to truly understand a problem, you need to be able to program it and explain it to a computer. Nikita, on the other hand, takes a different approach and prefers relying on a more abstract, intuitive level,’ says Aleksandr Zimin, one of the authors of the paper and a postgraduate student at the HSE Faculty of Mathematics.
Aleksandr Zimin
‘The conjecture resisted disproof for a long time—or perhaps no one wanted to disprove it because it was beautiful and elegant. However, in my view, disproving it does not destroy its beauty; rather, it proves that the world is far more interesting and complex than we thought,’ Zimin says.
The discovered counterexample raises fundamental questions for science about whether intuition can be relied upon, how critical thinking should be applied in mathematics, and how probabilistic evidence-based proofs should be interpreted.
See also:
HSE Neurolinguists Reveal What Makes Apps Effective for Aphasia Rehabilitation
Scientists at the HSE Centre for Language and Brain have identified key factors that increase the effectiveness of mobile and computer-based applications for aphasia rehabilitation. These key factors include automated feedback, a variety of tasks within the application, extended treatment duration, and ongoing interaction between the user and the clinician. The article has been published in NeuroRehabilitation.
'Our Goal Is Not to Determine Which Version Is Correct but to Explore the Variability'
The International Linguistic Convergence Laboratory at the HSE Faculty of Humanities studies the processes of convergence among languages spoken in regions with mixed, multiethnic populations. Research conducted by linguists at HSE University contributes to understanding the history of language development and explores how languages are perceived and used in multilingual environments. George Moroz, head of the laboratory, shares more details in an interview with the HSE News Service.
Slim vs Fat: Overweight Russians Earn Less
Overweight Russians tend to earn significantly less than their slimmer counterparts, with a 10% increase in body mass index (BMI) associated with a 9% decrease in wages. These are the findings made by Anastasiia Deeva, lecturer at the HSE Faculty of Economic Sciences and intern researcher in Laboratory of Economic Research in Public Sector. The article has been published in Voprosy Statistiki.
Scientists Reveal Cognitive Mechanisms Involved in Bipolar Disorder
An international team of researchers including scientists from HSE University has experimentally demonstrated that individuals with bipolar disorder tend to perceive the world as more volatile than it actually is, which often leads them to make irrational decisions. The scientists suggest that their findings could lead to the development of more accurate methods for diagnosing and treating bipolar disorder in the future. The article has been published in Translational Psychiatry.
Scientists Develop AI Tool for Designing Novel Materials
An international team of scientists, including researchers from HSE University, has developed a new generative model called the Wyckoff Transformer (WyFormer) for creating symmetrical crystal structures. The neural network will make it possible to design materials with specified properties for use in semiconductors, solar panels, medical devices, and other high-tech applications. The scientists will present their work at ICML, a leading international conference on machine learning, on July 15 in Vancouver. A preprint of the paper is available on arxiv.org, with the code and data released under an open-source license.
HSE Linguists Study How Bilinguals Use Phrases with Numerals in Russian
Researchers at HSE University analysed over 4,000 examples of Russian spoken by bilinguals for whom Russian is a second language, collected from seven regions of Russia. They found that most non-standard numeral constructions are influenced not only by the speakers’ native languages but also by how frequently these expressions occur in everyday speech. For example, common phrases like 'two hours' or 'five kilometres’ almost always match the standard literary form, while less familiar expressions—especially those involving the numerals two to four or collective forms like dvoe and troe (used for referring to people)—often differ from the norm. The study has been published in Journal of Bilingualism.
Overcoming Baby Duck Syndrome: How Repeated Use Improves Acceptance of Interface Updates
Users often prefer older versions of interfaces due to a cognitive bias known as the baby duck syndrome, where their first experience with an interface becomes the benchmark against which all future updates are judged. However, an experiment conducted by researchers from HSE University produced an encouraging result: simply re-exposing users to the updated interface reduced the bias and improved their overall perception of the new version. The study has been published in Cognitive Processing.
Mathematicians from HSE Campus in Nizhny Novgorod Prove Existence of Robust Chaos in Complex Systems
Researchers from the International Laboratory of Dynamical Systems and Applications at the HSE Campus in Nizhny Novgorod have developed a theory that enables a mathematical proof of robust chaotic dynamics in networks of interacting elements. This research opens up new possibilities for exploring complex dynamical processes in neuroscience, biology, medicine, chemistry, optics, and other fields. The study findings have been accepted for publication in Physical Review Letters, a leading international journal. The findings are available on arXiv.org.
Mathematicians from HSE University–Nizhny Novgorod Solve 57-Year-Old Problem
In 1968, American mathematician Paul Chernoff proposed a theorem that allows for the approximate calculation of operator semigroups, complex but useful mathematical constructions that describe how the states of multiparticle systems change over time. The method is based on a sequence of approximations—steps which make the result increasingly accurate. But until now it was unclear how quickly these steps lead to the result and what exactly influences this speed. This problem has been fully solved for the first time by mathematicians Oleg Galkin and Ivan Remizov from the Nizhny Novgorod campus of HSE University. Their work paves the way for more reliable calculations in various fields of science. The results were published in the Israel Journal of Mathematics (Q1).
Large Language Models No Longer Require Powerful Servers
Scientists from Yandex, HSE University, MIT, KAUST, and ISTA have made a breakthrough in optimising LLMs. Yandex Research, in collaboration with leading science and technology universities, has developed a method for rapidly compressing large language models (LLMs) without compromising quality. Now, a smartphone or laptop is enough to work with LLMs—there's no need for expensive servers or high-powered GPUs.