Naum Illich Akhiezer. On the 125th Anniversary of the Birth of the Outstanding Scholar and Founder of the Kharkiv Mathematical School

Naum Illich Akhiezer (March 6, 1901 – June 3, 1980) was an outstanding mathematician, a specialist in function theory, approximation theory, and functional analysis, as well as a talented educator. He was the brother of the renowned theoretical physicist Alexander Illich Akhiezer. Doctor of Physical and Mathematical Sciences (1936), Professor (1941), Corresponding Member of the All-Ukrainian Academy of Sciences (1934). He was awarded the P. L. Chebyshev Prize of the USSR Academy of Sciences (1949) for his monograph “Lectures on Approximation Theory. For his significant achievements in mathematical sciences, he received the Leonard Euler Medal of the USSR Academy of Sciences (1957).

Naum Illich was born on March 6, 1901, in the town of Cherikov, Mogilev Province (now Belarus), into the family of a zemstvo doctor. He graduated from the classical gymnasium in Mstislavl (1918), where he mastered German, French, Latin, and mathematics. He taught mathematics, physics, and chemistry at the first school-commune in the country — the Lemelska School. He graduated from the Department of Mathematics of the Kyiv Institute of Public Education (now Taras Shevchenko National University of Kyiv) in 1923 and completed his postgraduate studies in 1928. He defended his dissertation on the topic «Aerodynamic Experiments»(1928).

He taught at Kyiv University, the Kyiv Aviation Institute, and the Nizhyn Institute of Public Education (1928–1933). He served as Head of the Department of Function Theory at Kharkiv State University (1933–1941), and later headed the Department of Mathematical Physics, where he worked as a professor until the end of his life (1980). At the same time, he lectured on aerodynamics and hydrodynamics at the Kharkiv Aviation Institute. He served as Director of the Institute of Mathematics and Mechanics at Kharkiv State University (1935–1940). The degree of Doctor of Physical and Mathematical Sciences was conferred upon him in 1936. He worked at the Moscow Power Engineering Institute (1943–1947). At the Kharkiv Institute for Low Temperature Physics of the Academy of Sciences of the Ukrainian SSR, he headed a department (1961–1963), and from 1963 served as a senior researcher; from 1970 he was a scientific adviser.

At the Kharkiv Polytechnic Institute, he served as Head of the Department of Theoretical and Mathematical Physics (1941–1943), and later became the organizer and first Head of the Department of Applied Mathematics (1947–1955). Concurrently, he remained a professor at Kharkiv University. N. I. Akhiezer was an excellent teacher and a brilliant lecturer. He taught courses such as «Mathematical Physics», «Variational Calculus», «Constructive Function Theory», and others. His «Lectures on Integral Transforms», published posthumously in Ukraine and abroad, continue to attract considerable interest among specialists.

The mathematician’s scientific achievements made a significant contribution to the development of function theory, spectral analysis, functional analysis, and approximation theory. His research and monographs became foundational for many areas of modern mathematics. He actively worked on the theory of function approximation, with special attention to the study of best approximations of functions by polynomials in various metrics, the proof of important theorems concerning the behavior of best-approximation polynomials, and the development of methods for approximating analytic functions. He proposed a method for solving the inverse spectral problem for important classes of spectral planes. This method later enabled the solution of several nonlinear equations in mathematical physics. A central place in his scientific heritage is occupied by the study of orthogonal polynomials and their spectral properties. A significant portion of his research was devoted to the spectral theory of operators and the classical moment problem. His works in constructive complex analysis and potential theory contributed to the development of new directions in mathematical research.

N. I. Akhiezer was the author of more than 150 scientific works, including 10 monographs, 9 of which were translated and published in many countries. He headed the Kharkiv Mathematical Society for 25 years (from 1947), edited its journal, and led various mathematical seminars. He was the initiator of the creation of the Kharkiv Mathematical School (now Kharkiv Physics and Mathematics Lyceum No. 27) and the Correspondence Youth Mathematics School at Kharkiv State University.

Naum Illich Akhiezer passed away on June 3, 1980, in Kharkiv. In 2018, the National Academy of Sciences of Ukraine established the N. I. Akhiezer Prize, awarded for outstanding scientific works in theoretical physics and plasma physics. In Kharkiv, the N. I. Akhiezer Foundation was created to support young Kharkiv mathematicians (students, postgraduate students, early-career researchers). The Foundation awards scholarships to young mathematicians and annually organizes competitions of scientific works, awarding the winners. The founder and sponsor of the Foundation is American mathematician Professor Mikhail Brin. A memorial plaque dedicated to Professor Naum Akhiezer was unveiled on the façade of the building at 17 Bagaleia Street in Kharkiv (2018). A street in the Saltivka district of Kharkiv was named in honor of the Akhiezer brothers (2019).

We invite faculty, students, and all interested readers to acquaint themselves with the works of Naum Illich Akhiezer (Scientific and Technical Library of NTU «KhPI», room 45).

More information about Naum Illich is available on the website of the Scientific and Technical Library of NTU “KhPI” at: https://library.kpi.kharkov.ua/uk (Electronic catalog, Repository, History of KhTI in Persons – Academic Staff)