Alexander Mikhailovich Lyapunov, a Russian scientist and Doctor of Mathematical Sciences, is known as the founder of modern stability theory for equilibrium and motion of mechanical systems with a finite number of parameters. His work in the fields of differential equations and hydrodynamics has also received wide recognition.

Lyapunov was born on June 6, 1857, in Yaroslavl to the astronomer Mikhail Vasilyevich, who was then the director of the Demidov Lyceum. In 1870, Alexander entered the third grade of a gymnasium in Nizhny Novgorod, where he showed an interest in the exact sciences in the senior classes.

After graduating from the gymnasium with a gold medal in 1876, Lyapunov enrolled in the Faculty of Physics and Mathematics at St. Petersburg University. Initially, he was fascinated by chemistry and attended lectures by Dmitri Mendeleev, but soon switched to the mathematics department, inspired by the lectures of Pafnuty Chebyshev, which had a significant impact on his subsequent scientific and teaching career.

In 1880, Lyapunov graduated from the university and published his first works on the equilibrium of solid bodies and the potential of hydrostatic pressure the following year. In 1885, he defended his master's thesis on the stability of ellipsoidal forms of equilibrium of a rotating fluid, which attracted the attention of scientists worldwide. After that, Lyapunov began teaching at Kharkov University, where he worked until 1902.

From 1888, Lyapunov published several works on the stability of motion of mechanical systems and defended his doctoral dissertation on this topic in 1892. In 1900, he was elected a corresponding member of the St. Petersburg Academy of Sciences, and in 1901, an ordinary academician in applied mathematics. In 1902, he moved to St. Petersburg to fully devote himself to science.

During this period, Lyapunov studied the forms of equilibrium of uniformly rotating fluids, making significant contributions to world science and refuting some results of foreign scientists. In 1906, he published a work in French on the equilibrium figures of homogeneous rotating fluids. Lyapunov developed a rigorous theory of stability for equilibrium and motion of mechanical systems, creating a general method for solving stability problems.

His works contain many fundamental results in the theory of ordinary differential equations. Lyapunov was recognized by the global community and was an honorary member of several universities and academies.

In 1908, he participated in the IV International Mathematical Congress in Rome and in the publication of the complete works of Leonhard Euler.

After the death of his wife on October 31, 1918, Lyapunov attempted to take his own life. He was taken to the hospital in an unconscious state, but he could not be saved. Alexander Mikhailovich Lyapunov passed away on November 3, 1918, in an Odessa hospital and was buried in a local cemetery.