What is reasoning? What is logic? What is math? Common sense tells us that concepts such as numbers, relations, and logical structures feel inherently familiar—almost intuitive. They seem so obvious, but why? Do they have deeper origins? What is the number? What is addition? Why do they work in this way? Basic axioms of math, their foundation seems to be very intuitive, but absolutely mysteriously appear to the human mind out of nowhere. In a way their true essence magically slips (...) away unnoticed from the consciousness, in an attempt to pinpoint its foundation. This paper delves into the fundamental nature of mathematics, logic, and rational reasoning, examining their "unreasonable effectiveness" in understanding and shaping the world. By drawing parallels between advancements in artificial neural networks and human cognition, the work introduces a novel perspective on intuition as the cornerstone of higher cognitive systems. Intuition is presented not only as a tool for pattern recognition but as the foundation upon which complex reasoning processes, such as mathematical abstraction and logical frameworks are constructed. This perspective redefines the role of consciousness, highlighting its capacity for innovation and exploration within abstract domains. Beyond theoretical insights, the paper outlines potential pathways for advancing artificial general intelligence by leveraging the interplay between intuition and conscious reasoning. (shrink)