The bricks of Mathematical Research: from Antyquity to the Era of Artificial Intelligence

Abstract

Mathematical research began in ancient times when humanity faced the need for precise measurements and calculations to solve practical problems, leading to the emergence of disciplines such as arithmetic and geometry. A significant milestone in building mathematics as a logically rigorous and consistent theory was Euclid's work Elements, in which he introduced the axiomatics system: he substantiated the truth of the known geometric statements of the time by deriving them from axioms – basic statements accepted as true (based on intuitive reasoning). However, as was later revealed, there are mathematical propositions whose proofs or disproving may take centuries, and a vivid example of this is Fermat's Last Theorem, the truth of which was confirmed only over 350 years after the author wrote it in his notes. With the advent of new technologies such as neural networks, the process of mathematical discovery began to accelerate. Neural networks can model complex logical relationships and quickly explore possible solution variants. This opens new horizons for scientific research, allowing the combination of classical mathematical methods with innovative approaches that may significantly change the way mathematical problems are solved.