Oliver Heaviside
Although he was a good scholar, he left school at 16 and became a telegraph operator. However he continued to study and, in 1872, while working as a chief operator in Newcastle upon Tyne, he started to publish papers on electricity.
He also re-formulated and reduced in complexity Maxwell's equations to the current form which uses vector calculus.
Between 1880 and 1887 he developed the operational calculus (involving the D notation for the differential operator, to which he is credited of creating), a method of solving differential equations by transforming them into ordinary algebraic equations which caused a great deal of controversy when first introduced, owing to the lack or rigour in his derivation of it.
In 1887, he proposed that induction coils should be added to the transatlantic telegraph cable in order to correct the distortion which it suffered. For political reasons, this was not done.
In 1902 he proposed the existence of the Kennelly-Heaviside Layer which bears his name (which was originally researched by Nikola Tesla). It was finally detected in 1923.
He also developed the Heaviside step function, which he used to model the flow of current in an electric circuit.
In later years his behaviour became quite eccentric, having been at odds with the scientific establishment for most of his life. Most of his recognition he gained post mortem.
