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It seems to me that he was able to reformulate Maxwell's equations in a more understandable form and in fact come up with vector calculus without finishing high school would arguably cause him to be ranked with people like Galois and Ramanujan. Does this make sense?

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  • $\begingroup$ I think it is of very limited value to try to rank mathematicians, or anyone, according to ... well, what actually? $\endgroup$ Mar 15 at 21:58

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(Question whether Heaviside's achievements "would arguably cause him to be ranked with people like Galois and Ramanujan. Does this make sense?")

Yes, I would think it makes a lot of sense. Even taking into account that much of his achievement had applications in view (often in electrical engineering) rather than belonging to pure mathematics alone, the mathematical content of his work is notable in itself.

Some references to both aspects of his work may be found in "On Heaviside's contributions to transmission line theory: waves, diffusion and energy flux", C Donaghy-Spargo (2018). Some explanation, with references to some of the background and origin of his work including the Heaviside operational calculus and other scientific and engineering publications, is also given in this HSM answer, The origin of the Heaviside function.

Arguably Heaviside's work is now underrated, as it was during his lifetime (in spite of his eventual FRS). There have been some steps taken to remember him appropriately, e.g. in 2018 there was a theme issue of Philosophical Transactions of the Royal Society A on "Celebrating 125 years of Oliver Heaviside's ‘Electromagnetic Theory’". Nevertheless, the history remains that, relying on his mathematical analysis, he invented improvements in transmission lines for telephony that led to his proposal to reduce distortion, but the whole was later patented out of his hands by Michael Pupin in the USA, who sold the rights for much money, while Heaviside lived and died in poverty. (See also, besides the links already given above, e.g. the Heaviside condition, and 'Oliver Heaviside and the theory of transmission lines', by P T de Boer).

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  • $\begingroup$ i think nowadays Pupin could not have successfully patented something that was based on someone else' work, whether that person had tried to patent it or not. i also think Heaviside could have done better financially had he been so motivated. I read his annual income from a "civil list pension:" was something over 100 pounds which is hard to translate but may have meant he did not live in abject poverty. i like how this genius worked as a telegrapher as did once Edison -- they were roughly contemporaries, perhaps knew each other. $\endgroup$
    – releseabe
    Mar 15 at 17:49

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