👉 Experimental mathematics involves using computational methods to explore mathematical concepts, often where traditional proofs are difficult or impossible to achieve. Researchers employ algorithms and computer simulations to test hypotheses, discover new patterns, and even generate conjectures about mathematical structures. For instance, they might use numerical methods to approximate solutions to complex equations or employ machine learning techniques to identify relationships between seemingly unrelated mathematical objects. This approach has led to breakthroughs like the proof of Fermat's Last Theorem using modular forms and the discovery of new fractal patterns through iterative algorithms. By leveraging computational power, experimental mathematicians can explore vast mathematical landscapes, validate or refute conjectures, and sometimes even propose entirely new theories that can later be rigorously proven through traditional methods.
