Understanding MathematicsThis article is an attempt to explain the structure of the process of understanding mathematical objects such as notions, definitions, theorems or mathematical theories. Understanding is an indirect process of cognition that involves grasping the meaning of what is to be understood, manifested in the ability to apply what is understood in other circumstances and situations. Thus, understanding must be treated functionally: as the acquisition of meaning. We can distinguish three fundamental levels on which the process of understanding mathematics takes place. The first is the plan for understanding the meaning of notions and terms existing in mathematical considerations. A mathematician must know what the given symbols mean and what the corresponding notions denote. On the second level, understanding concerns the structure of the object of understanding where it is the meaning of the sequences of notions and terms applied which is important. The third plan – understanding the “role” of the object of understanding – involves fixing the meaning of the object of understanding in the context of a larger entity, i.e. it is of an investigation into the background of the problem. Furthermore, the understanding of mathematics, to be sufficiently complete, must take into account (besides theoretical planes) at least three other related considerations – historical, methodological and philosophical – because ignoring them results in a superficial and incomplete understanding of mathematics. In PJ Davis and R. Hersh's book, The Mathematical Experience, there is a short chapter devoted to the crisis of understanding mathematics. Alas, this fragment only focuses on presenting the d...... middle of paper ...... and does not allow one to learn mathematics without in-depth understanding. My postulate is that, in the process of teaching mathematics, we must take into account both the history and the philosophy (with methodology) of mathematics, because neglecting them makes the understanding of mathematics superficial and incomplete.Bibliography1. Philip J. Davis and Reuben Hersh, The Mathematical Experiment, Birkhäuser Boston, 1981.2. Izydora Dąmbska, W sprawie pojęcia rozumienia, in: Ruch Filozoficzny 4, 1958.3. John R. Searle, Minds, Brains and Programs, in: Behavioral and Brain Sciences 3, Cambridge University Press 1980, p.417-424.4. Danuta Gierulanka, Zagadnienie swoistości poznania matematycznego, Warszawa 1962.5. Roger Penrose, The Emperor's New Mind, Oxsford University Press 1989.6. Andrzej Lubomirski, O uogólnieniu w matematyce, Wrocław 1983.