I am reading H.T.H. Piaggio's "An Elementary Treatise on Differential Equations and their Applications", published 1920 originally; I have the 1952 edition.

The first chapter "Historical Introduction" goes:

"The geometrical interpretation [of differential equations] was given by Lagrange in 1774, but the theory in its present form was not given until much later by Cayley (1872) and M.J.M. Hill (1888)."

And again:

"These theories [of partial differential equations] still remain in an unfinished state; contributions have been made by Chrystal (1892) and Hill (1917)."

Who is this "M.J.M. Hill"? Piaggio cites him a few times during the course of the text, citing papers in Philosophical Transactions and Proceedings of the London Mathematical Society, etc., but I can't find anything more than his footprint in the journals.

Anyone with any information about him?


There's a Wikipedia page: Micaiah John Muller Hill.

Hill is ofted cited in Ramanujan's biographies, here there is something more than in the Wikipedia page:

[...] Hill was born at Berhapore, Bengal (narrowly escaping death during the Indian mutiny) and was Professor of Mathematics at University College, London, from 1884 until 1926. He had a reputation as a sympathetic and painstaking teacher. He had been at Peterhouse in Cambridge as an undergraduate, and was classed as 4th Wrangler (equal) in the Mathematical Tripos in 1879. Hill did research on hydrodynamics and differential equations, but at the time of Griffith's letter [Griffith sent some Ramanujan works to Hill, see here for something about him] was primarly interested in Euclid's axioms [...]. In 1907 and 1908, Hill published two papers giving an asymptotic formula for partial sums of certain hypergeometric series [...]. It is unfortunate that no one at that time knew of this mutual interest of Hill and Ramanujan [...]

  • $\begingroup$ Thank you, that was everything I needed to know. Cheers $\endgroup$ – Prime Mover Aug 24 '20 at 13:04

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