At the end of the 19th century Oliver Heaviside developed a formal calculus of differential operators in order to solve various physical problems. The pure mathematicians of his time would not deal with this unrigorous theory, but in the 20th century several attempts were made to rigorise Heaviside's operational calculus. These attempts can be grouped in two classes. The one leading to an explanation of the operational calculus in terms of integral transformations (Bromwich, Carson, Vander Pol, Doetsch) and the other (...) leading to an abstract algebraic formulation (Lévy, Mikusiński). Also Schwartz's creation of the theory of distributions was very much inspired by problems in the operational calculus. (shrink)

Through 1886 to 1889 understanding of the mechanism of telephone transmission was transformed from an electrostatic and traditional view to an electrodynamic one conforming with Maxwell's scheme. Observed at the level of commercial application this painful adjustment occurred via a sequence of controversies connected with self-induction—on techniques of telephony, on electrical measurement, on lightning conductors and on matters of professional ethics—in which the parts played by evidence, by theory, and by authority were strangely mixed. The well-known confrontation of O. Heaviside (...) and W. H. Preece was at the centre of the debate. An open division between traditionalists and progressives amongst electrical engineers was provoked, and the effectiveness of mathematical theory as against pure pragmatism at the practical level had in the end to be conceded. (shrink)