This paper discusses the idea of fundamental nature of the university mathematics education. In the conditions of university education there are three interconnected groups of factors, which form the basis of the conceptual model of mathematicians training fundamentalization. The first group of factors is focused on updating the ways of specialist training of the increased creative potential – training for modern mathematicians. The second group of factors is connected with the need of strengthening fundamental and humanitarian training, ensuring interdisciplinary communication within educational process, interrelation of mathematical, technical and humanitarian knowledge. The third group of factors includes the concept of university principle of education, the concept of fundamentalization and the concept of humanitarization of technical education at classical university. There is a model of the fundamental nature for training mathematicians.