标题：The Problem of Intuition in Mathematics in the Thoughts and Creativity of Selected Polish Mathematicians in the Context of the Nineteenth-Century Breakthrough in Mathematics
摘要：In the article,I examine the presence and importance of intuitive cognition in mathematics.I show the occurrence of mathematical intuition in four contexts: discovery,understanding,justification,and acceptance or rejection.I will deal with examples from the history of mathematics,when new mathematical theories were being created (the end of the nineteenth and the beginning of the twentieth century will be particularly important,including the period of establishing the Polish mathematical school).I will also refer to the research (mainly) of Polish philosophers and mathematicians in this field.The goal of the article is also an attempt to understand the breakthrough that took place in mathematics at the turn of the nineteenth century.The analysis also shows,by highlighting the specifics of intuition and mathematical creativity,the difficulties that arise when acquiring new concepts and mathematical arguments.Research goes in the direction of deepening research on the very phenomenon of intuition in cognition,by pointing to the universal nature of mathematical intuition.
关键词：mathematical intuition;studying of the foundations of mathematics;universality of mathematics;Polish School of Mathematics;mathematics of the turn of the 19th and 20th centuries;mathematics paradoxes
