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 simplified Maxwell's equations to the current form which uses vector calculus.
Between 1880 and 1887 he developed the operational calculus[?], 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 telephone cable in order to correct the distortion which it suffered. For political reasons, this was not done.
In 1902 he predicted the existence of the Kennelly-Heaviside Layer which bears his name. It was finally detected in 1923.
He also developed the Heaviside step function.
In later years his behaviour became quite eccentric.
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