Department of "Fundamental Mathematics" meets the requirements of the research university, was founded on the basis of pre-existing university departments, such as "Mathematical Analysis", "Geometry, Algebra and Mathematical logic", "Probability theory and Statistics" in 2011-2012 years. Since the founding of the department, the head of this department is a doctor of physical and mathematical sciences,Professor Kanguzhin Baltabek Esmatovich. Deputy head of the department of "Fundamental Mathematics" on academic affairs and educational work, candidate of physical and mathematical sciences, associate professor Kosherbaeva Ulbike Rahmanberdіkyzy. Deputy head of the department "Fundamental Mathematics" on scientific innovation work and international links affairs, PhD Nurakhmetov Daulet Bagdatuly. Nowadays, the staff of the department consists of three academicians, five doctors of physical and mathematical sciences, sixteen candidates of physical and mathematical sciences, four doctors of PhD.
Department of "Mathematical Analysis" was founded in 1936, it is one of the first departments based in Al-Farabi Kazakh National University in 1934. The first Kazakh man Ibadullah Akbergenov received his degree in physical and mathematical sciences in 1936, was invited from Leningrad. He developed items such as Functional Analysis, Computational Mathematics, scientific director, whom was a laureate of the "Nobel premium" L.V Kantorovich. Famous mathematicians have made some contribution to the formation and development of the department of Mathematical Analysis. Among them, the department led by such eminent mathematicians, the best teachers, textbook writers like I.P.Natanson, K.P.Persidsky, N.I.Ahiezer, M.Ya.Vygodsky, S.G.Mihlin, M.S.Livshits, O.A.Zhautikov, T.I.Amanov, D.Үmbetzhanov, V.H.Harasahal, A.A.Zhensikbaev, M.Otelbaev, N.K.Bliev, T.Sh.Kal’menov, N.T.Temirgaliev, R.Oynarov, A.Tungatarov.
Department of "Geometry, Algebra and Mathematical logic" was founded in 1995 on the basis of objects of Geometry, Algebra and Mathematical logic. Before that, there were at university department for research and teaching: department of Mathematics (1934-1938), department of Higher Geometry (1938-1986), department of Algebra (1938-1972), department Mathematical logic (1968-1972), department of Algebra and Mathematical logic (1972-1986), department of Algebra and Geometry (1986-1988), department of Geometry and Mathematics teaching methods (1988-1993), department of Geometry (1993-1995), Department of Algebra and Mathematical logic (1988-1995).
Professional staff of the department was founded by well-known professors, associate professors, invited at that time out of different scientific centers of the Soviet Union in the city of Almaty, and students of the Abai Pedagogical Institute. From 1935 to 1936 he taught geometry graduate of Moscow State University, Associate Professor L.I. Babushkin. The department of Higher Geometry taught such prominent scientists of the XX century, like A.D. Aleksandrov (1912-1999), B.N. Samorukov, V.F. Rogacheka, B.M. Urazbaev, M. Vygodski, F.D. Kramar, A.A. Fridman, E. I. Kim, A.D. Aleksandrov, A.Z. Zakarin, V.V. Streltsov, D.Sh. Yusupov, S.A. Ayapbergenov, E.I. Himelevski, V. M. Amerbaev, M.G. Peretyatkin and A.I. Omarov, have invested a certain contribution to the department and training process.
Department of "Probability theory and Statistics" was founded in 1989 under the title "Functional Analysis and Probability theory." The first head of the department was the winner of the Lenin Prize of the Kazakh SSSR, member of the National Academy of Sciences of Kazakhstan (to date, National Academy of Sciences of Kazakhstan) professor T.Sh.Kal’menov (1989-1991). Then, the department head were A.A.Bedelbaev (1991-1992), professor N.T.Temirgaliev (1992-1997), Academician of the National Academy of Sciences of Kazakhstan, professor M.Otelbaev (1997-2000), Academician of the National Academy of Sciences of Kazakhstan, professor N.K.Bliev (2000-2005) and associate professor N.Akanbay (2005-2011). In connection the need to change teaching plans of the Academic Council of Kazakh National University on May 26, 2009. Name of the department was changed to the "Probability theory and Statistics."
Today the department of “Fundamental Mathematics” of the faculty of mechanics and mathematics prepares bachelors, masters and doctors of philosophy (PhD) in various specialties.
In this department defended a five PhD doctors in 2012. They are Ahmed-Zaki Dinara, Kungozhin Almas, Mazhitova Akmaral, Mustafa Manat and Nurakhmetov Daulet. Current members Ahmed-Zaki D., Kanguzhin A., Mazhitova A., Nurakhmetov D. have engaged in research and teaching. Mustafa Manat enrolled the postdoctoral program of the Nanyang Technological University of Singapore.