Unlike traditional Multi-Layer Perceptrons (MLPs), which have fixed activation functions on nodes, KANs have learnable activation functions on edges. This seemingly simple change allows KANs to outperform MLPs in terms of accuracy and interpretability, particularly for small-scale artificial intelligence and scientific tasks. The text explores the mathematical foundations of KANs, highlighting their ability to overcome the curse of dimensionality and achieve faster neural scaling laws than MLPs. Additionally, the text showcases KANs' potential for scientific discovery by demonstrating their effectiveness in uncovering mathematical relations in knot theory and identifying phase transition boundaries in condensed matter physics.