أزمة اللانهائي في الفكر الرياضي المعاصر

الملخص EN

Mathematics, since it was established as a theoretical science in the Greeks, is considered a higher model of reasonableness, accuracy and certainty, and the various emerging sciences seek to simulate it.

the development of mathematical through out the ages had different stations, and perhaps the most prominent of all was what happened at the end of the 19th century and the beginning of the 20th century, of severe crises in mathematical construction, the most important of which was what was known as the foundations crisis.

which raised a major problem in the philosophy of sports (mathematics), and created confusion and turmoil in the ranks of athletes (mathematicians) and philosophers of sports (mathematics) alike, as a result of searching for a unified and stable basis to achieve the certainty and rigor that characterizes them.

other problems, no less serious, branched out from this problem, among them and fore most among them what was known as the paradoxes that appeared in contemporary mathematical thought after mathematician abandoned spatial intuition as a basis, and the adoption of the number as an alternative, where research in this context led to the establishment of the theory of groups, whose absoluteness and sovereignty did not last long until contradictions and various paradoxes appeared in it, based in their essence on what is known as the infinite, but in a new form that differs in form and content from what was known in ancient times, and where the purely mathematical concept replaced the infinite metaphysics that had long dominated human thought.