In physics, the relationship between conceptual intuition and mathematical formalism is usually a feedback loop. Normally, a scientist uses intuition to form a guess, builds a mathematical model to test it, and then uses the results to refine their mental picture. However, when a principle is extremely counterintuitive, such as quantum entanglement or non-locality, this traditional cycle breaks down because our mental images fail to represent the reality correctly.
When thought experiments no longer provide a clear visual guide, the role of mathematical formalism shifts from being a mere tool to becoming the primary source of truth. In these cases, the math acts as a guide to lead the mind where intuition cannot reach. Instead of using math to describe an existing mental image, scientists use the mathematical structure to dictate what the new physical reality must be. This forces a shift from intuitive reasoning to formal reasoning. Eventually, through rigorous mathematical work, a new type of intuition often emerges. This updated intuition is not based on simple visual patterns but is a deeper conceptual understanding derived directly from the logic of the equations themselves.
