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Nesbitt's Inequality can be found all over the internet: $$\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b}\geq\frac{3}{2}$$

This appears to have been first published in 1902 in Education Times, by A.M. Nesbitt.

Is the identity of this person in an way retrievable, or is he or she lost in history?

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    $\begingroup$ I don't have time to double-check the details, but the google search "A M Nesbitt" + math + "Corpus Christi" is a start. Note that his degree (undergraduate or MA, I'm not sure which) was in 1876, so Nesbitt was almost certainly not a student in the early 1900s. This led me to this search, (continued) $\endgroup$ Aug 24, 2022 at 8:57
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    $\begingroup$ where I found Alfred Mortimer Nesbitt, and then this search and this web page, where it appears he was born 27 December 1854, and from this page he died 3 July 1926. $\endgroup$ Aug 24, 2022 at 8:57
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    $\begingroup$ Can't find info on Education Times First search I tried -- Nesbitt + "Educational Times". Click on one of these (all are freely available to read online or to download, at least where I am) and search for "Nesbitt" inside to get all references to Nesbitt. For 1902 Educational Times, I just clicked on "More editions" and then date restricted to 1902. This can also be read online or downloaded. $\endgroup$ Aug 24, 2022 at 17:15
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    $\begingroup$ If you can't get copies of ET's from 1902 to 1904, send me an email (thus providing me with an email address for replying) and I'll try to locate and download copies and (hopefully be able to, assuming their individual sizes are not too large) email them to you. One of my many-years on-going "spare time" projects has been downloading and archiving in simple to use folders, for my own use, older volumes of various journals. At this point I have essentially complete runs of over 100 math, physics, astronomy, general science, general scholarly, etc. journals (continued) $\endgroup$ Aug 24, 2022 at 18:20
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    $\begingroup$ from 1700s to early 1920s. I don't have all volumes of ET yet, in particular I don't have those you're interested in. The only volume of ET from the 1900s I have at this time (ET has not been something I've tried to complete my collection of yet) is named (by me) "57 #513 to 58 #536 (Jan 1904 - Dec 1905)", so getting those volumes is something I'd be doing at some later time anyway. $\endgroup$ Aug 24, 2022 at 18:20

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Nesbitt's inequality was posed as problem 15114 in The Educational Times. According to an online database of the publication maintained by Western Carolina University, it was published in May of 1902. A collection of selected problems and solutions from this publication can be found in Constance I. Marks (ed.), Mathematical Questions and Solutions from "The Educational Times," with many Papers and Solutions in addition to those published in "The Educational Times". New Series. Volume III. London: F. Hodgson 1903. On pages 37 and 38 one finds the problem (proof of the inequality) with three solutions, one of them by Nesbitt himself. On page 3 of the publication he is listed as

Nesbitt, A.M., M.A.: Melbourne

Doing a Google search on this information immediately led me to a website "A biographical register of Australian colonial musical personnel–N" by Dr. Graeme Skinner (University of Sydney) that provides detailed bits of biographical background on Nesbitt (including a photo), confirming information already identified by Dave L Renfro in comments.

Alfred Mortimer Nesbitt was born on December 27, 1854 in England and died July 3, 1926 in East Malvern, Victoria, Australia, which is a suburb of Melbourne. His parents were the physician Pearce R. Nesbitt, M.D. and his wife Arabella. Nesbitt studied mathematics at the University of Oxford, graduating in 1876. In 1877 he was appointed mathematical master of Manchester Grammar School. He married in 1880, as reported in The Medical Times and Gazette, Vol. 2, London: J. & A. Churchill 1880, p. 227:

NESBITT-HILL. — On August 5, at Hampstead, Alfred Mortimer Nesbitt, M.A., of Corpus Christi College, Oxford, youngest son of P. R. Nesbitt, M.D., to Margaret, only daughter of the late John Cartwright Hill, Esq.

In 1882 he was selected as head master of the Grammar School in Toowoomba, Queensland, Australia. The Manchester Grammar School Magazine, Vol. 10, No. 67, October 1882, p. 38:

The cause of athletics in the School has suffered a severe loss by the departures of Mr. H. C. Barnes-Lawrence, M.A., to Giggleswick Grammar School, and of Mr. A. M. Nesbitt, M.A., to the Headmastership of Toowoomba School, Queensland. [...] Mr. Barnes-Lawrence came with our High Master in January, 1877, and Mr. Nesbitt in September of the same year.

In 1888 he became an assistant lecturer of mathematics and natural philosophy at Trinity College in Melbourne. The Melbourne University Calendar 1889-90, University of Melbourne, p. 362 lists him as:

College Teaching Staff.
[...]
Mathematics and Natural Philosophy.
[...] (3) A. M. Nesbitt, M.A., late Scholar of Corpus Christi College, Oxford; First-class Honorman in Mathematics at Graduation, 1876.

In addition to being a mathematician, he appears to have been a competent musician and composer. He won first prize in the Jubilee Ode Competition of the Brisbane Musical Union, which presumably was set up for Queen Victoria's Golden Jubilee, which was celebrated in June 1887.

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