Walter Hayman


Walter Kurt Hayman FRS (6 January 1926 – 1 January 2020) was a British mathematician known for contributions to complex analysis.[1] He was a professor at Imperial College London.[2]

Walter Hayman
Walter Hayman.jpg
Walter Kurt Hayman

(1926-01-06)6 January 1926
Cologne, Germany
Died1 January 2020(2020-01-01) (aged 93)
EducationUniversity of Cambridge
Known forTheory of subharmonic functions
Univalent function theory
Spouse(s)Margaret Hayman (née Crann)
AwardsBerwick Prize (1955)
Senior Berwick Prize (1964)
De Morgan Medal (1995)
Scientific career
FieldsComplex analysis
InstitutionsKing's College, Newcastle
University of Exeter
Imperial College

Life and workEdit

Hayman was born in Cologne, Germany, the son of Roman law professor Franz Haymann (1874-1947) and Ruth Therese Hensel, daughter of mathematician Kurt Hensel.[3] He was a great-grandson of acclaimed composer Fanny Mendelssohn. Because of his Jewish heritage, he left Germany, then under Nazi rule, alone by train in 1938. He continued his schooling at Gordonstoun School,[4] and later at St John's College, Cambridge under John Edensor Littlewood and his doctoral advisor Mary Cartwright. He taught at King's College, Newcastle, and the University of Exeter.[5]

In 1947, he married Margaret Riley Crann: together, they founded the British Mathematical Olympiad.[6]

He is known for his asymptotic results in Bieberbach conjecture in 1955,[7] and for Hayman's alternatives in Nevanlinna Theory. His work with Wolfgang Fuchs gave a solution to an inverse problem of the Nevanlinna theory for entire functions, predating David Drasin's 1976 work.

Honours and awardsEdit

Hayman was elected to the Royal Society in 1956 and of the Finnish Academy of Science and Letters in 1978:[8] he was elected "Foreign member" of the Accademia dei Lincei on 16 December 1985.[9] In 1992 he received an honorary doctorate from the Faculty of Mathematics and Science at Uppsala University, Sweden[10] In 1995 he was awarded the De Morgan Medal by the London Mathematical Society.[11] In 2008, an issue of the Journal Computational Methods and Function Theory was dedicated to him on the occasion of his 80th birthday.[12]

Selected publicationsEdit

Hayman presents a talk at the 2010 One Day Function Theory Meeting.


  • Hayman, W. K. (1952), "Functions with values in a given domain", Proceedings of the American Mathematical Society, 3 (3): 428–432, doi:10.1090/S0002-9939-1952-0049323-9, MR 0049323, Zbl 0048.31402.
  • Hayman, W. K. (1974), "The local growth of power series: a survey of the Wiman-Valiron method", Canadian Mathematical Bulletin, 17 (3): 317–358, CiteSeerX, doi:10.4153/CMB-1974-064-0, MR 0385095, Zbl 0314.30021.
  • Hayman, W. K.; Rossi, J. F. (1984), "Characteristic, maximum modulus and value distribution", Transactions of the American Mathematical Society, 284 (2): 651–664, doi:10.1090/S0002-9947-1984-0743737-2, MR 0743737, Zbl 0547.30023.
  • Hayman, Walter K. (1993), "A problem on Fourier series arising from an Isoperimetric inequality", in Ricci, Paolo Emilio (ed.), Problemi attuali dell'analisi e della fisica matematica. Atti del simposio internazionale dedicato a Gaetano Fichera nel suo 70o compleanno. Taormina, 15–17 ottobre 1992, Roma: Dipartimento di Matematica Università di Roma La Sapienza – Aracne Editrice, pp. 119–125, MR 1249093, Zbl 0851.42009.
  • Hayman, W. K. (2002), "Univalent and Multivalent Functions", in Kuhnau, Reiner (ed.), Geometric Function Theory, Handbook of Complex Analysis, vol. 1, Amsterdam: North-Holland, pp. 1–36, ISBN 978-0-444-82845-3, MR 1966188, Zbl 1069.30018.


  • Hayman, W. K. (1964), Meromorphic functions, Oxford Mathematical Monographs, Oxford: Clarendon Press, pp. XIV+191, MR 0164038, Zbl 0115.06203.
  • Hayman, W. K. (1967), Research Problems in Function Theory, London: Athlone Press, pp. vii+56.
  • Hayman, W. K.; Kennedy, P. B. (1976), Subharmonic functions. Volume 1, London Mathematical Society Monographs, vol. 9, London–New York: Academic Press, pp. XVII+284, ISBN 978-0-12-334801-2, MR 0460672, Zbl 0419.31001.[13]
  • Hayman, W. K. (1988), Subharmonic functions. Volume 2, London Mathematical Society Monographs, vol. 20, London: Academic Press, pp. xiii+875, ISBN 978-0-12-334802-9, MR 1049148, Zbl 0699.31001.[14]
  • Hayman, W. K. (1994) [1958], Multivalent functions, Cambridge Tracts on Mathematics, vol. 110 (Second ed.), Cambridge: Cambridge University Press, pp. xii+263, ISBN 978-0-521-46026-2, MR 1310776, Zbl 0904.30001.[15]
  • Hayman, W. K. (2014), My Life and Functions, Logic Press, pp. iv+138, ISBN 978-1-326-03020-9
  • Hayman, W. K.; Lingham, E. F. (2019), Research Problems in Function Theory - Fiftieth Anniversary Edition, Problem Books in Mathematics, Springer, pp. VIII+284, ISBN 978-3-030-25164-2


  1. ^ Johnston, John (7 January 2019). "Professor Walter Hayman (1926-2020)". London Mathematical Society. Retrieved 8 January 2019.
  2. ^ Imperial College webpage
  3. ^ O'Connor, John J.; Robertson, Edmund F., "Walter Hayman", MacTutor History of Mathematics archive, University of St Andrews
  4. ^ Obituary
  5. ^[dead link]
  6. ^ As stated by (Quadling 1995, p. 127) in his commemoration of Hayman's wife.
  7. ^ Royal Society biography
  8. ^ According to the academic list of foreign members.
  9. ^ See (Accademia Nazionale dei Lincei 2012, p. 88).
  10. ^ "Honorary doctorates - Uppsala University, Sweden".
  11. ^ See the LMS announcement.
  12. ^ See (Ruscheweyh 2008).
  13. ^ Helms, L. L. (1979). "Review: Subharmonic functions, vol. 1, by W. K. Hayman and the late P. B. Kennedy" (PDF). Bull. Amer. Math. Soc. (N.S.). 1 (2): 376–379. doi:10.1090/s0273-0979-1979-14604-4.
  14. ^ Baernstein II, Albert (1991). "Review: Subharmonic functions, vol. 2, by W. K. Hayman" (PDF). Bull. Amer. Math. Soc. (N.S.). 25 (2): 458–467. doi:10.1090/s0273-0979-1991-16091-x.
  15. ^ Jenkins, James A. (1959). "Review: Multivalent functions by W. J. Hayman" (PDF). 65 (3): 163–166. {{cite journal}}: Cite journal requires |journal= (help)


Biographical referencesEdit

  • Accademia Nazionale dei Lincei (2012), Annuario dell'Accademia Nazionale dei Lincei 2012 – CDX dalla Sua Fondazione (PDF) (in Italian), Roma: Accademia Nazionale dei Lincei, p. 734, archived from the original (PDF) on 4 March 2016, retrieved 6 December 2014. The "Yearbook" of the renowned Italian scientific institution, including an historical sketch of its history, the list of all past and present members as well as a wealth of information about its academic and scientific activities.
  • Quadling, Douglas (1995), "Obituary: Margaret Hayman", The Mathematical Gazette, 79 (484): 127, doi:10.1017/S0025557200147813, JSTOR 3620019.
  • Finnish Academy of Science and Letters (2014), Ulkomaiset jäsenet – Foreign Members, retrieved 21 December 2014.

General referencesEdit

  • Drasin, David (May 2015), "My Life and Functions by Walter K. Hayman", Notices of the American Mathematical Society, 68 (5): 517–520, doi:10.1090/noti1250. The review of the autobiographical book of Hayman.
  • Ruscheweyh, S., ed. (2008), "Special Volume. Dedicated to Walter K. Hayman on the occasion of his 80th birthday", Computational Methods and Function Theory, Lemgo, 8 (1–2): xliii+640, ISSN 1617-9447 (online ISSN 2195-3724).

External linksEdit