The Hodgkin and Huxley Model
The currently accepted model of transmission of information on the nerve membrane through the creation and propagation of an action potential only dates from the early 1940s, thanks to the work of Drs. Hodgkin and Huxley.
Using a squid giant axon and special microelectrodes, they were able to measure the membrane potential as well as the depolarization and hyperpolarization that compose the action potential. They received the Nobel prize in Physiology and Medicine in 1963 for this work, alongside Sir John Carew Eccles for his own work on neuron synapses.
Figure 1: The results of Drs. Hodgkins and Huxley.
In a series of 5 papers, Drs Hodgkin and Huxley developed the now-standard model of an action potential, with the last paper covering the mathematical model. It was the first quantitative description of electrical excitability in nerve cells, even allowing them to predict the behavior of ion channels that were undiscovered at the time. Coupled with their improvement of the voltage clamp technique, they defined an equation able to predict an action potential time course.
Historically, by doing so they also proved that the previous consensus was inaccurate, i.e. based on the idea that the axon membrane would break down punctually to allow the passage of ions, thus bringing the membrane potential to zero for a short moment. As we now know, the membrane does not break and channels are responsible for the controlled transfer of ions, bringing the membrane potential to even +45 mV.