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The Hodgkin-Huxley equations (1952) quantitatively describe how voltage-gated sodium and potassium channels produce the action potential. They remain one of the most successful mathematical models in biology.
Hodgkin and Huxley used squid giant axons to measure ion currents and built a coupled differential-equation model whose predictions match experimental waveforms with near-perfect fidelity. The 1963 Nobel honored the work. Subsequent neurons (cortical, hippocampal, dopaminergic) require additional ion channels, but the H-H framework remains the foundation. Modern computational neuroscience builds from H-H to entire circuit and brain-scale simulations.