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.
Alexander Zimin
See also:
The 'Second Shift' Is Not Why Women Avoid News
Women are more likely than men to avoid political and economic news, but the reasons for this behaviour are linked less to structural inequality or family-related stress than to personal attitudes and the emotional perception of news content. This conclusion was reached by HSE researchers after analysing data from a large-scale survey of more than 10,000 residents across 61 regions of Russia. The study findings have been published in Woman in Russian Society.
Resource Race and Green Transition: Three Unexpected Conclusions from Foresight Centre’s Research on Climate and Poverty
Beneath the surface of green energy—which most people associate with solar panels, electric vehicles, and reduced CO2 emissions—lies a complex web of geopolitical interests, international inequality, and resource constraints. Researchers from the Laboratory for Science and Technology Studies (LST) at the HSE ISSEK Foresight Centre have published a series of articles in leading international journals on hidden and overt conflicts surrounding critically important metals and minerals, as well as related processes in the energy sector.
Immersion in Second Language Environment Influences Bilinguals’ Perception of Emotions
Researchers at the Cognitive Health and Intelligence Centre at the HSE Institute for Cognitive Neuroscience have discovered how bilingual individuals process emotional words in their native (first) and non-native (second) languages. It was found that the link between word meaning and bodily sensations is weaker in a second language than in a first language. However, the more a person is immersed in a language environment, the smaller this difference becomes. The article has been published in Language, Cognition and Neuroscience.
Researchers Find More Effective Approach to Revealing Majorana Zero Modes in Superconductors
An international team of researchers, including physicists from HSE MIEM, has demonstrated that nonmagnetic impurities can help more accurately reveal Majorana zero modes—quantum states considered promising building blocks for quantum computing. The researchers found that these impurities shift the energy levels that typically obscure the Majorana signal, while leaving the mode itself largely unaffected, thereby making its spectral peak more distinct. The study has been published in Research.
New Development by HSE Scientists Helps Design Reliable Electronics Faster at a Lower Cost
Scientists from HSE MIEM have developed a new approach to modelling electrothermal processes in high-power electronic circuits on printed circuit boards (PCB). The method allows engineers to quickly and accurately predict how electronic components heat up during operation, helping prevent overheating and potential failures. The results have been published in Russian Microelectronics.
The Future of Cardiogenetics Lies in Artificial Intelligence
Researchers from the AI and Digital Science Institute at the HSE Faculty of Computer Science have developed a program capable of analysing regions of the human genome that were previously inaccessible for accurate interpretation in genetic testing. The program adapts large generative AI (GenAI) models for cardiogenetics to predict how specific mutations affect the function of individual genes.
HSE Researchers: Young Russians Have Sufficient Knowledge About Money but Lack Money Management Skills
Adolescents and young adults in Russia today are well versed in financial terminology: they know what bank cards, loans, interest rates, and online payments are. However, as researchers at HSE University have found, real money-management skills remain poorly developed among most young people. The study ‘Financial Literacy, Financial Culture, and Financial Autonomy of Youth’ has been published in Monitoring of Public Opinion: Economic and Social Changes.
Why Weaker Competitors Give Up—and How to Keep Them in the Game
Anastasia Antsygina, Assistant Professor at HSE University’s Faculty of Economic Sciences, has developed a prize distribution model that maximises competitor engagement. She proposed revising the traditional ‘winner-takes-all’ approach and, in certain cases, offering a small reward even to those who have lost. According to her, this could increase participant motivation and make the competition more intense. The findings of her research were published in the Economic Theory journal.
HSE Researchers Compile Scientific Database for Studying Children’s Eating Habits
The database created at HSE University can serve as a foundation for studying children’s eating habits. This is outlined in the study ‘The Influence of Age, Gender, and Social-Role Factors on Children’s Compliance with Age-Based Nutritional Norms: An Experimental Study Using the Dish-I-Wish Web Application.’ The work has been carried out as part of the HSE Basic Research Programme and was presented at the XXVI April International Academic Conference named after Evgeny Yasin.
New Foresight Centre Study Identifies the Most Destructive Global Trends for Humankind
A team of researchers from the HSE International Research and Educational Foresight Centre has examined how global trends affect the quality of human life—from life expectancy to professional fulfilment. The findings of the study titled ‘Human Capital Transformation under the Influence of Global Trends’ were published in Foresight.