University mathematics at the turn of the century unpublished recollections of W. H. Young

Annals of Science

Volumn 28, Issue 4, 1972, Pages 369-384

  Grattan Guinness, I ^a  

^a MIDDLESEX UNIVERSITY   (United Kingdom)

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[No Author keywords available]

Indexed keywords

EID: 0347305140     PISSN: 00033790     EISSN: 1464505X     Source Type: Journal    
DOI: 10.1080/00033797200200291     Document Type: Article

References (29)

1. There is no adequate bibliography of Young’s writings, but some are listed in the obituary by G. H. Hardy; ‘William Henry Young’, J. Lond. Math. Soc, (1) 1942, 17, 218-237=OM«. Not. Fellows Boy. Soc, 1943, 4, 307-323.
2. Joint authorship applies also to two books: The First Book of Geometry (London, 1905); and The Theory of Sets of Points (Cambridge, 1906). A reprint of this latter volume is planned, for which I have prepared an appendix on Mrs. Young’s plans for an (abortive) second edition. The reprint will be published by the Chelsea Publishing Company.
3. See M. I. Cartwright, ‘Grace Chisholm Young’, J. Lond. Math. Soc, (1) 1944, 19, 185-192.
4. The story is told in my ‘A mathematical union: William Henry and Grace Chisholm Young’, Ann. Sci., 1972, 29 (forthcoming). The papers are kept by their eldest daughter, Dr. R. C. H. Tanner, 13, Boundary Road, Wallington, Surrey, England.
5. AlthofFs enormous Nachlass is a source of the first importance for the history of education in Prussia at the end of the last century. It is kept in the Deutschos Zentral-archiv, Merseburg, East Germany, D.D.R.
6. See G. Mittag-Leffler, ‘Sophie Kovalevsky. Notice biographique’, Acta Math., 1892, 16, 385-392.
7. W. H. Young, ‘On systems of one-vectors in space of n dimensions’, Proa. Lond. Math. Soc, (1) 1897-98, 29, 478-487.
8. A. Schonflies, ‘Mengenlehre’, Enc der Math. Wiss., Arith. und Anal., pt. 1 1898-1904, 1, 185-207.
9. Influential also on the Youngs was Schonflies’s ‘Die Entwicklung der Lehre von der Punktmannigfaltigkeiten’, Jber. dtsch. Math.—Ver., 1900, 8, pt. 2.
10. See especially his ‘On the general theory of integration’, Phil. Trans. Boy. Soc London, (A) 1905, 204, 221-252; road 19 May 1904. Whilst writing this paper Young encountered Lehesgue’s work and incorporated some remarks on it. They do not appear to have been in personal contact at this time.
11. ‘Bimbo’ was the family name for Frankie. ‘Auntie May’ was Young’s sister, who helped Mrs. Young look after the family. ‘Dortchen’ was their second daughter Janet, born in 1901.
12. Unpublished note by Mrs. Young; quoted in sect. 11 of my forthcoming article (footnote 4)
13. The vagueness of his references makes the identification of these sources rather difficult, but he seems to have drawn mostly on various volumes published in the early 1910s under the auspices of the International Commission for Mathematical Education.
14. For interesting recollections of the situation at Cambridge around the time when the Youngs were students there, see A. B. Forsyth, ‘Old Tripos Days at Cambridge’, Math. Gaz., 1935, 19, 162-179.
15. This is a reference to Philippa Faweett, who was placed ‘above the Senior Wrangler’ in 1891, For Mrs. Young’s reminiscences of the occasion, see sect. 3 of my forthcoming article (footnote 4).
16. These are quoted in extenso in sects. 5 and 6 of my forthcoming article (footnote 4).
17. Ernst Ritter (1857-1895); see Klein’s obituary in Jber. dtsch. Math.-Ver., 1894-95, 4, 52-54.
18. See especially Hehnhottz’s ‘Uber Integrale der hydrodynamischen Gleichungen, …’, J. rei. ang. Math., 1858, 55, 25-55
19. and ‘Uber discontinuirliehe Flfissigkeltsbewegungen’, Monatsb. Akad. Wise. Berlin, 1868, 215-228 (Wissenschaftliche Abhandlungen, vol. 1, pp. 101-134 and pp. 146-157; reprinted in Ostwald’s Klassiker, vol. 79, Leipzig, 1896).
20. K. H. A. Sehwarz, ‘Ueber diejenigen Falle, in welchen die Gaussisehe hypergeometriseche: Reihe…’, J. rei. ang. Math., 1873, 75, 292-335 (Gesammelte mathematisehe Abhandlungen, vol. 1, pp.: 211-259).
21. E. Study, ‘Spharisehe Trigonometric, orthogonale Substitionen und elliptische Funkgionen’, Abh. math.-phys. K1. Konigl. Sachs. Gesell Leipzig, 1893, 20, no. 2.
22. G. Chisholm, Algebraiseh-gruppentheoretische Untersuchungen zur sphSrischen Trigonometrie, Gottingen, 1895. The work belonged to Klein’s development of group theory, and was praised by him in his Elementary mathematics from an advanced standpoint (trans. E. R. Hedrick and C. A. Noble), vol. 1, London, 1932, pp. 179-181.
23. K. Hattendorff (ed.), Partlelle Differentialgleiehungen and deren Andwendung auf physikatisehe Fragen… 3rd edition, Braunsehweig, 1882.
24. Namely, Isabel Maltby, u fellow student also admitted under Althoff’s programme for women’s education.
25. G. Peano, ‘Sur une courbe, qui remplit route une aire plane’, Math. Ann., 1890, 36, 157-160 (Opere Seelte, vol. 1, pp. 110-114). Doubtless they also discussed Hilbert’s ‘Uber die stetige Abbildung einer Linle auf ein Flachenstuk’, Math. Ann., 1891, 38, 359-360 (Gesammelte Abhandlungen, vol. 3, pp. 1-2).
26. For a photograph of this Society taken in 1902, including Klein and Mrs. Young, see C. Reid, Hilbert, Berlin, 1970, p. 228.
27. Hilbert’s work was printed in a series of papers in the Nach, of the Gottgingen Academy and collectively as Grundzuge einer allgemeinen Theorie der integralgleichugan, Leipzig and Berlin, 1912.
28. C. Posse, Rapport sur l’enseignement mathgmatique … … en Russie St. Peterburg, 1910. This is one of the International Commission pamphlets mentioned in footnote 13.
29. This remark is not very accurate; many papers were published in French. The main journals concerned are the Comptes Rendus and Bulletin de l’Acadgmie des Sciences de Cracovie, and the Comptes Rendus de la Societe Seieutifique de Varsovle. In 1920, shortly after Young wrote this passage, Sierpiuski and his colleagues started a new journal, Fundamenta Mathematieae, in which French was the main language used.