Twenty vs Ten: HSE Researcher Examines Origins of Numeral System in Lezgic Languages
It is commonly believed that the Lezgic languages spoken in Dagestan and Azerbaijan originally used a vigesimal numeral system, with the decimal system emerging later. However, a recent analysis of numerals in various dialects, conducted by linguist Maksim Melenchenko from HSE University, suggests that the opposite may be true: the decimal system was used originally, with the vigesimal system developing later. The study has been published in Folia Linguistica.
How many fingers do you need to count to forty? That depends on the language you are counting in. In Russian and most European languages, the decimal counting system is standard, with numbers like 40 formed as 4 × 10, 60 as 6 × 10, and so on. A vigesimal system is based on the number 20, so 60 is expressed as 3 × 20, and 50 as 2 × 20 + 10.
Counting by tens or twenties is not just a matter of convenience—it also has historical roots. In the Lezgic group of languages—which includes Lezgian, Tabasaran, Aghul, and Rutul—both numeral systems are found: some dialects use a base-10 system with numbers like 10, 20, 30, while others follow a base-20 system with numbers like 20, 40, 60, and so on. Until recently, it was believed that the vigesimal system in these languages was more ancient, but a new study by linguists at HSE University challenges this assumption.
Maksim Melenchenko, Research Assistant at the Linguistic Convergence Laboratory of the HSE Faculty of Humanities, analysed numerals in nine Lezgic languages and concluded that the decimal system may have existed earlier, rather than being a later borrowing. In some languages, he discovered supposedly archaic forms of the number 40, suggesting an alternative development of the counting system. These forms are called archaic because certain features make them appear older than modern numerals.
Maksim Melenchenko
'For the number 40, some Lezgic languages unexpectedly use a decimal system: even in villages where counting by twenties is common, 40 is expressed as 4 × 10. This may indicate that the overall system of numeral formation has changed, but earlier forms of the number forty have persisted in the language, reflecting an older numeral system,' explains Melenchenko.
Another detail noted by the linguist is the special suffixes found on all decimal numerals from 30 to 90. In some languages where these numbers are formed decimally, they end with a suffix that originally indicated the grammatical gender of the noun the numeral refers to.
'This suggests that, in earlier times, the suffixes of decimal numerals actually changed to reflect grammatical gender. This implies that the decimal system was not a later introduction but had been in use long enough for gender markers in decimal numerals to become fossilised,' the linguist notes.
Dialectal variations in numeral systems can sometimes occur on opposite sides of the same mountain. For example, in the northern areas where Aghul is spoken, people count by tens, while in the southern parts, they count by twenties. Sometimes both systems coexist side by side: the older generation sticks to the traditional system, younger people use the more recent one, and some numerals reflect a mix of both systems.
Such variability shows how vibrant and dynamic different elements of a language—including numerals—can be. The study suggests that numeral systems can be easily borrowed, adapted, and changed spontaneously. Their history is not simply a progression from 'primitive' to 'advanced' structures, but a complex process that deserves close study—especially in linguistically rich and diverse regions like the Caucasus.
The study was conducted with support from HSE University's Basic Research Programme within the framework of the Centres of Excellence project.
See also:
HSE University Scholars Uncover E-Learning Preferences of Top Students
HSE University experts have analysed students’ digital footprints and shown for the first time that final grades depend on one’s personal approach to an online course. Balanced students have proven to be more successful than those who follow a more traditional and practical approach. The findings from this study will help create a more adaptive and personalised educational system. This research has been published in the journal The Internet and Higher Education.
HSE Scientists Develop Method to Stabilise Iodine in Solar Cells
Scientists at HSE MIEM, in collaboration with colleagues from China, have developed a method to improve the durability of perovskite solar cells by addressing iodine loss from the material. The researchers introduced quaternary ammonium molecules into the perovskite structure; these molecules form strong electrostatic pairs with iodine ions, effectively anchoring them within the crystal lattice. As a result, the solar cells retain more than 92% of their power after a thousand hours of operation at 85°C. The study has been published in Advanced Energy Materials.
HSE Researchers Create Genome-Wide Map of Quadruplexes
An international team, including researchers from HSE University, has created the first comprehensive map of quadruplexes—unstable DNA structures involved in gene regulation. For the first time, scientists have shown that these structures function in pairs: one is located in a DNA region that initiates gene transcription, while the other lies in a nearby region that enhances this process. In healthy tissues, quadruplexes regulate tissue-specific genes, whereas in cancerous tissues they influence genes responsible for cell growth and division. These findings may contribute to the development of new anticancer drugs that target quadruplexes. The study has been published in Nucleic Acids Research.
Mathematician from HSE University–Nizhny Novgorod Solves Equation Considered Unsolvable in Quadratures Since 19th Century
Mathematician Ivan Remizov from HSE University–Nizhny Novgorod and the Institute for Information Transmission Problems of the Russian Academy of Sciences has made a conceptual breakthrough in the theory of differential equations. He has derived a universal formula for solving problems that had been considered unsolvable in quadratures for more than 190 years. This result fundamentally reshapes one of the oldest areas of mathematics and has potential to have important implications for fundamental physics and economics. The paper has been published in Vladikavkaz Mathematical Journal.
Scientists Reveal How Language Supports Complex Cognitive Processing in the Brain
Valeria Vinogradova, a researcher at HSE University, together with British colleagues, studied how language proficiency affects cognitive processing in deaf adults. The study showed that higher language proficiency—regardless of whether the language is signed or spoken—is associated with higher activity and stronger functional connectivity within the brain network responsible for cognitive task performance. The findings have been published in Cerebral Cortex.
HSE AI Research Centre Simplifies Particle Physics Experiments
Scientists at the HSE AI Research Centre have developed a novel approach to determining robustness in deep learning models. Their method works eight times faster than an exhaustive model search and significantly reduces the need for manual verification. It can be applied to particle physics problems using neural networks of various architectures. The study has been published in IEEE Access.
Scientists Show That Peer Influence Can Be as Effective as Expert Advice
Eating habits can be shaped not only by the authority of medical experts but also through ordinary conversations among friends. Researchers at HSE University have shown that advice from peers to reduce sugar consumption is just as effective as advice from experts. The study's findings have been published in Frontiers in Nutrition.
HSE University Establishes Cybersecurity Department
The HSE University Moscow Tikhonov Institute of Electronics and Mathematics (MIEM) has established a new Department of Cybersecurity. This move consolidates MIEM’s educational, scientific, and expert resources in information and computer security, expands its portfolio of educational programmes, strengthens partnerships with industry leaders, and enhances HSE’s position as a leading centre of cybersecurity competence.
HSE University to Host Second ‘Genetics and the Heart’ Congress
HSE University, the National Research League of Cardiac Genetics, and the Central State Medical Academy of the Administrative Directorate of the President will hold the Second ‘Genetics and the Heart’ Congress with international participation. The event will take place on February 7–8, 2026, at the HSE University Cultural Centre.
HSE University Develops Tool for Assessing Text Complexity in Low-Resource Languages
Researchers at the HSE Centre for Language and Brain have developed a tool for assessing text complexity in low-resource languages. The first version supports several of Russia’s minority languages, including Adyghe, Bashkir, Buryat, Tatar, Ossetian, and Udmurt. This is the first tool of its kind designed specifically for these languages, taking into account their unique morphological and lexical features.