Arif Alihaydar oglu Babayev was born on November 11, 1934. He graduated from the Faculty of Physics and Mathematics on mathematics (1957). In 1960 he became a PhD, in 1966 - doctoral of science.
In 1976 he was elected as a corresponding member of the Azerbaijan Academy of Sciences. He worked as a teacher, associate professor, Professor, head of department and dean at the mechanics and mathematics department of Azerbaijan State University (1979-1994).
A.Babayev proved a number of new theorems on the existence of a solution and on the uniqueness of nonlinear singular integral equations, studied the singular integral for the integration of an uneven closed curve and applied it in linear and nonlinear singular integral equations.
He introduced a new method for studying a singular integral operator with a Cauchy nuclei along an open curve, was created method based on a local theory of nonlinear singular integral equations.
The discrete analogs of the singular integral and space, which are affected by this integral, as well as the application of these concepts for the approximate solution of nonlinear singular integral equations was given.
With the participation and leadership of A.Babayev were developed a local theory of nonlinear singular integral equations, approximate methods for solving these equations, a local theory of equations and multidimensional singular integral operators on a domain, and applied in function space input theorems and others. Under the leadership of A.Babayev more than 40 PhD and doctoral theses were defended.
He was awarded the Order "Badge of Honor" (1976) and in 1992 he was awarded the "Honored Scientist".
Corresponding member of ANAS Arif Babayev died in 1998 in Baku.