Hilda's mother was also a mathematician who had read mathematics at Newnham College, Cambridge, so perhaps it was not entirely surprising that William and his wife should have had children with outstanding mathematical talents who went on to study mathematics at Cambridge. Hilda had an older brother, R W H T Hudson, who was Senior Wrangler in the Mathematical Tripos at Cambridge in 1898 while her sister was bracketed with the 8th Wrangler in the Mathematical Tripos of 1900. At this time only the men were ranked in the Tripos Examination but women who took the examination were made aware of their place by being told they were placed between the nth and (n+1)st man or equal to the nth man. The fact that Hilda's sister was bracketed with the 8th Wrangler meaning that she had come 8th equal among the First Class students.
Hilda entered Newnham College, Cambridge in 1900, the year in which her sister sat the mathematical Tripos. In the examinations of 1903 she went one place better than her sister when she was bracketed with the 7th Wrangler meaning that she had come 7th equal among the First Class students but, as was still the custom, her achievement was still not officially classed. In the following year, 1904, there was tragedy for the Hudson family when Hilda's brother died in a mountaineering accident in Wales. This cut short what had promised to be a stunning mathematical career with his brilliant book Kummer's quartic surface being published by Cambridge University Press in the year of his death.
After leaving Cambridge, Hilda Hudson went to Germany for a year spending the time studying at the University of Berlin with Schwarz, Schottky, Edmund Landau and others. She returned to Cambridge in 1905 when she was appointed as a lecturer at Newnham College. After holding this position for five years she was appointed Associate Research Fellow at Newnham. In 1912 the International Congress of Mathematicians was held in Cambridge, England. In the list of participants Hilda Hudson is listed as accompanying her father Professor W H H Hudson, but in fact she gave a communication to the Congress, being the only woman to do so.
Hudson was Associate Research Fellow at Newnham College until the end of the academic year 1912-1913, but she spent this last academic year at Bryn Mawr College, a private women's college founded in 1885 in Pennsylvania in the United States. Charlotte Angas Scott, who had studied under Cayley and shared Hudson's interests in algebraic geometry, was Head of the Mathematics department there. It was a remarkably productive period for Hudson who published her first paper in the Proceedings of the London Mathematical Society in 1911, followed by three papers in 1912, and six papers on topics such as Cremona transformations, nodal curves, pinch-points, and algebraic surfaces in 1913.
After spending the academic year 1912-13 at Bryn Mawr, Hudson returned to England. She was appointed as a lecturer at West Ham Technical Institute where she worked for four years. One interesting monograph which she published during this time was Ruler and Compass in 1916. This was a work :-
... in which [Hudson] included a lot of elegant geometry in an exposition of the range and limitations of ruler and compass constructions.Of course World War I started while during her years at West Ham Technical Institute and, while the War was still underway, Hudson joined the Civil Service to undertake work for the Air Ministry. At this point she showed her versatility as a mathematician working on applied mathematics problems. Already while at West Ham Institute she had worked on applied probability problems, and now while working for the Air Ministry she published two papers in 1920, one on The strength of lateral loaded struts in The Aeroplane, the other on Incidence wires in the Aeronautical Journal.
In 1919, after the war had ended, Hudson was appointed as a technical assistant at Parnell and Company in Bristol. After two years she retired from this position to devote herself to writing the treatise Cremona transformations in plane and space which was published in 1927. She dedicated this work to her brother who had been so tragically killed in 1904. Semple describes this book in the following terms :-
This was indeed her magnum opus, the culminating achievement of many years of scholarly research, in which she gathered into one connected account all the essential elements of what had long been a fashionable field of research and supplemented it with an impressive bibliography (37 pages and 417 items) covering sixty to seventy years of publications on the subject.During the years in which she was writing her major treatise Hudson returned to publishing on Cremona transformations and algebraic surfaces. However she essentially gave up publishing mathematics after her treatise appeared in print, except for one notable exception which was an article on Analytic geometry, curve and surface in the 14th edition of Encyclopaedia Britannica published in 1929.
Semple writes :-
Miss Hudson was a distinguished mathematician, of great erudition and integrity; and she was also, throughout her long life, a woman of high ideals and standards. She will long be remembered by the mathematical world for her contributions to geometry and by Newnham and Cambridge as one of their distinguished alumni.She received a number of very significant honours for her outstanding contributions including a Sc.D. from Trinity College Dublin in 1913 and an O.B.E. in 1919.
Article by: J J O'Connor and E F Robertson