Natan Krougliak graduated from the Department of Mechanics and Mathematics of the Moscow State University in 1971. In 1979 he received the PhD degree for an investigation on fast-convergent iteration method and its applications. In 1996 he received the degree "Doctor of Science" (a Russian degree which is higher than PhD) after a second dissertation, devoted to interpolation of operators, and subsequently the title of Professor in 1999.
From 1981 till 1988 he worked in the industry as a deputy chief of the department of innovations at a large Computer Centre of the Northern Railroad (Russia). During this period he originated several projects, aiming at developing computer-aided management of railway operation and was the leader of the developing team. The developed programmes were widely introduced across Russian Railroads. One of them (monitoring and management of operation of railway depot) was exhibited at VDNH (Exhibition of National Economic Achievement) in Moscow and Natan Krougliak was awarded a silver medal for its development.
After teaching at the Yaroslavl University for 9 years Natan Krougliak became Full Professor in 1997. During this time he supervised PhD and Master theses. Among courses taught by him at the Yaroslavl University were courses in Theoretical and Applied Mathematics, including Functional Analysis, Theory of Approximation, Applied Theory of Approximation, and Applied Linear Algebra. Apart from this, in 1992-1993 Natan Krougliak was on Lady Davis Fellowship at Technion Israel Institute of Technology, and he worked at Chicago University of Illinois (2000) and at Florida Atlantic University (2000-2002). Since 2002 he has been employed at the Luleå University of Technology.
Natan Krougliak is well known for his results in the theory of interpolation, he has been involved in joint scientific research with mathematicians from the USA, Canada, Spain, France, Israel, and Sweden. In 1991 he published (jointly with Yu. Brudnyi) a book on Interpolation of Operators, which was based on the authors' new results in interpolation of operators. One of the main accomplishments was solving of a number of long-standing problems, for example, it was shown that the problem of K-divisibility has a positive solution. This result was then used to construct a general theory of real interpolation.
Natan Krougliak's main research interests are theory of interpolation, theory of approximation, functional spaces and their applications. Present research focuses on covering theorems and their application to singular integral operators in limiting cases (when these operators are unbounded).