{"id":155545,"date":"2026-01-27T23:12:35","date_gmt":"2026-01-27T21:12:38","guid":{"rendered":"https:\/\/prohoster.info\/blog\/novosti-interneta\/rossijskij-matematik-nashel-klyuch-k-nereshaemym-uravneniyam-xix-veka-eto-uprostit-raschety-v-fizike-i-kosmonavtike"},"modified":"2026-01-30T17:57:27","modified_gmt":"2026-01-30T15:57:27","slug":"rossijskij-matematik-nashel-klyuch-k-nereshaemym-uravneniyam-xix-veka-eto-uprostit-raschety-v-fizike-i-kosmonavtike","status":"publish","type":"post","link":"https:\/\/prohoster.info\/en\/blog\/news\/rossijskij-matematik-nashel-klyuch-k-nereshaemym-uravneniyam-xix-veka-eto-uprostit-raschety-v-fizike-i-kosmonavtike","title":{"rendered":"A Russian mathematician has found the key to the 'unsolvable' equations of the 19th century: this will simplify calculations in physics and space exploration.","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

National Research University Higher School of Economics (HSE) reported<\/a>, mathematician Ivan Remizov from Nizhny Novgorod has discovered a way to obtain a conditionally simple solution to second-order differential equations with variable coefficients. For almost two centuries, such equations have been considered unsolvable. However, they play a key role in mathematics and natural sciences as they are used to describe dynamic processes.<\/p>\n

\"A<\/p>\n

Historically, the limitation was associated with the results of French mathematician Joseph Liouville, who, as early as 1834, demonstrated that solutions of such equations cannot be expressed using a finite number of standard operations and elementary functions. As a result, mathematicians were forced to either seek particular solutions or use approximations, which excluded universal methods and greatly complicated calculations. In other words, a general formula that could simply plug in 'numbers' to yield a solution did not exist.<\/p>\n

Ivan Remizov proposed a new approach by expanding the class of permissible mathematical operations. He did not argue with Liouville but simply added another mathematical tool to the equations\u2014the limit of a sequence. To do this, the mathematician utilized Chernoff's theorem and Laplace transform. This allowed him to construct a universal formula that formally provides a solution to any equation from the 'unsolvable' class, circumventing the classical limitations of the theory.<\/p>\n

\"The essence of the idea is that a complex, constantly changing process is broken down into an infinite number of simple steps. For each of these segments, a separate approximation is constructed\u2014a elementary fragment that describes the behavior of the system at a specific point. Individually, these pieces provide only a simplified picture, but as their number approaches infinity, they seamlessly combine into a perfectly accurate graph of the solution,\" explained the press release from HSE.<\/p>\n

Second-order differential equations are used not only for modeling real-world events but also for defining new functions that cannot be specified otherwise. These include, for example, the so-called special functions of Mathieu and Hill, which are critically important for understanding how satellites move in orbit or how protons behave in the Large Hadron Collider.<\/p>\n

A slightly more complex mathematical language about the discovery can be read<\/a> found on the HSE website. The work is available in English published<\/a> entirely in the 'Vladikavkaz Mathematical Journal'.<\/p>\n

Source:<\/strong><\/p>\n