Edge Rewrite
everything Source code View original
// HTMLRewriter · presentation

This page was redesigned at the edge.

Cloudflare fetched the original article and streamed it through HTMLRewriter to apply an entirely new visual system without rebuilding the source page.

// request.cf · coarse context

A page that knows where it met you.

Only coarse request metadata is shown. This demo does not display or persist visitor IP addresses.

Country
US
Cloudflare location
CMH
Connection
HTTP/2
Language
Not provided

Ray ID: a44a97207ee3a151

Jump to content

// Workers AI · dad joke modeIs Graeme Cohen a good golfer? Cohen-cidentally yes.

Add links
From Wikipedia, the free encyclopedia
Graeme Cohen
EducationUniversity of Sydney (BSc, MSc)
University of New South Wales (PhD)
University of Technology Sydney (MA)
Known forCounting Australia In
Lower bounds for odd perfect numbers
Infinitary divisors
AwardsHonorary member (2006) and fellow, Australian Mathematical Society
Fellow, Royal Society of New South Wales (2020)
Scientific career
FieldsNumber theory
History of mathematics
WorkplacesUniversity of Technology Sydney
Thesis Generalised quasiperfect numbers  (1982)

Graeme Laurence Cohen is an Australian mathematician and historian of mathematics. He was an associate professor at the University of Technology Sydney, and much of his research concerned odd perfect numbers.

Cohen's undergraduate textbook A Course in Modern Analysis and its Applications was published in 2003. Three years later he published Counting Australia In, a history of the people and institutions of Australian mathematics, and in 2007 Figuring Sport, written with Neville de Mestre. His novel The Possibly True Story of Martin Gardiner followed in 2022. He is an honorary member and fellow of the Australian Mathematical Society, and was elected a fellow of the Royal Society of New South Wales in 2020.

Education and career

[edit]

Cohen took a Bachelor of Science with honours and a Master of Science at the University of Sydney, and later a Master of Arts at the University of Technology Sydney.[1] He completed a doctorate at the University of New South Wales in 1982, with a thesis titled Generalised quasiperfect numbers.[2]

He taught at the University of Technology Sydney for thirty-six years, retiring in 2002 as an associate professor in the School of Mathematical Sciences.[3][4] Cohen was one of the founders of Shalom College at the University of New South Wales in 1968, and became part-time Hillel director in Sydney in 1971.[5] He was a member of the Klein Design Team, formed for the Klein Project, an initiative of the International Mathematical Union and the International Commission on Mathematical Instruction.[6] He edited the Australian Mathematical Society's Gazette in the 1980s and was joint editor of its Bulletin from 2011 to 2014,[4][7] and later the Society's history of mathematics resource.[8]

Research

[edit]

Most of Cohen's research concerned odd perfect numbers.[9] In 1978 he showed that the sum of the reciprocals of the prime divisors of such a number is less than log 2.[10] His 1982 doctoral thesis gave a substantial lower bound on the number of prime factors an odd perfect number must have, counted with multiplicity.[11] With Richard Brent and Herman te Riele he showed in 1991 that any odd perfect number would have to run to at least 300 digits,[9] and with Peter Hagis he proved in 1998 that every one has a prime factor greater than a million.[12]

Cohen also defined the infinitary divisors of an integer,[13] and with te Riele the (m, k)-perfect numbers.[14] With Ronald Sorli he introduced the harmonic seed,[15] and with Hagis he worked on quasiperfect numbers and on a conjecture of Lehmer about the Euler totient function.[16]

Books

[edit]

Cohen's undergraduate textbook was published in 2003 by Cambridge University Press, as the seventeenth title in the Australian Mathematical Society Lecture Series. It was reprinted in 2021 in association with the Harbin Institute of Technology Press for distribution in mainland China.[17] Rod Nillsen, in the Gazette of the Australian Mathematical Society, found it a coherent work for a wide readership, well written and largely self-contained. He thought its applications rather than its treatment of standard material made it distinctive, but found the application to quantum mechanics underdeveloped.[18]

Cohen wrote Figuring Sport with Neville de Mestre. It was published in 2007 and covers the mathematics of tennis, cricket, golf, rowing, weightlifting, football, billiards and athletics, along with the design of tournaments and the selection of teams. Jagannath Mazumdar reviewed the book for the Gazette of the Australian Mathematical Society and wrote that it is a friendly monograph that assumes little beyond elementary calculus and probability. However, he pointed out that no solutions are given for the exercises.[19]

Cohen's book Counting Australia In: The People, Organisations and Institutions of Australian Mathematics was published in 2006. Ian Sloan reviewed it in The Mathematical Intelligencer, calling it a fine book deserving a wide readership. He found it enjoyable, and wrote that it does not avoid the discipline's internal quarrels. However, he found the detail sometimes overwhelming.[20]

The Possibly True Story of Martin Gardiner

[edit]

Cohen's novel The Possibly True Story of Martin Gardiner was published in 2022. It is a historical account of Martin Gardiner, an Irish-Australian mathematician born in Dublin around 1833 who came to Melbourne in 1856. Gardiner published more than a dozen research papers but never got the academic post he wanted.[21]

Clifford Gilmore, in the Irish Mathematical Society Bulletin found the book an entertaining and at times shocking portrait.[21] Reviewing the book in the Australian Journal of Biography and History, Kiera Lindsey wrote that the unlikability of its subject made the novel compelling and added that Cohen's approach "raises rich questions regarding the relationship between history and literature". She questioned whether a subject as well documented as Gardiner justified speculative methods at all.[22] Jeffrey Cohen, in the Gazette of the Australian Mathematical Society, called it a "page-turner".[23]

Honours

[edit]
  • 2006 - Honorary Membership and Fellowship, Australian Mathematical Society[24]
  • 2020 - Fellowship, Royal Society of New South Wales[1]

References

[edit]
  1. 1 2 "Fellows of the Royal Society of New South Wales". The Royal Society of NSW. Retrieved September 24, 2026.
  2. ↑ Hare, Kevin G. (2007). "New techniques for bounds on the total number of prime factors of an odd perfect number". Mathematics of Computation. 76 (260): 2241–2248. doi:10.1090/S0025-5718-07-02033-9.
  3. ↑ "Special sale: Counting Australia In". Gazette of the Australian Mathematical Society. 40 (3). 2013.
  4. 1 2 "Cover and back matter". Journal of the Australian Mathematical Society. 40 (2). 1986.
  5. ↑ Bersten, Helen (2008). "Book review: History of the Shalom Institute (Incorporating Shalom College and the Hillel Foundation of NSW) by Graeme Cohen". Australian Jewish Historical Society Journal. 19 (1): 143–145.
  6. ↑ Weigand, Hans-Georg (2025). "The Klein Project: elementary mathematics from a higher standpoint". EMS Magazine (137): 62–65. doi:10.4171/MAG/254.{{cite journal}}: CS1 maint: unflagged free DOI (link)
  7. ↑ The Australian Mathematical Society (Inc): reports for the fifty-fifth annual general meeting and the one hundred and eleventh council meeting (Report). Australian Mathematical Society. 2011. Bulletin of the Australian Mathematical Society: Editor's report to Council 2011.
  8. ↑ "History of Mathematics in Australia". Australian Mathematical Society. Retrieved September 24, 2026.
  9. 1 2 Gimbel, Steven; Jaroma, John H. (2003). "Sylvester: ushering in the modern era of research on odd perfect numbers". Integers: Electronic Journal of Combinatorial Number Theory. 3: Paper A16.
  10. ↑ Zelinsky, Joshua (2025). "The sum of the reciprocals of the prime divisors of an odd perfect or odd primitive non-deficient number". Integers: Electronic Journal of Combinatorial Number Theory. 25: #A59. doi:10.5281/zenodo.15756036.
  11. ↑ Iannucci, D. E.; Sorli, R. M. (2003). "On the total number of prime factors of an odd perfect number". Mathematics of Computation. 72 (244): 2077–2084. doi:10.1090/S0025-5718-03-01522-9.
  12. ↑ Jenkins, Paul M. (2003). "Odd perfect numbers have a prime factor exceeding 107". Mathematics of Computation. 72 (243): 1549–1554. doi:10.1090/S0025-5718-03-01496-0.
  13. ↑ Haukkanen, Pentti (2000). "On the k-ary convolution of arithmetical functions". Fibonacci Quarterly. 38 (5): 440–445.
  14. ↑ Yamada, Tomohiro (2009). "Linear equations involving iterates of σ(N)". Integers: Electronic Journal of Combinatorial Number Theory. 9 (Supplement): Article 15.
  15. ↑ Goto, Takeshi; Okeya, Katsuyuki (2007). "All harmonic numbers less than 1014". Japan Journal of Industrial and Applied Mathematics. 24 (3): 275–288. doi:10.1007/BF03167540.
  16. ↑ Guy, Richard K. (1981). Unsolved Problems in Number Theory. New York: Springer-Verlag. Sections B1, B2 and B37. ISBN 0-387-90593-6.
  17. ↑ "AustMS Lecture Series in China". Gazette of the Australian Mathematical Society. 48 (3). 2021.
  18. ↑ Nillsen, Rod (2005). "A Course in Modern Analysis and its Applications". Gazette of the Australian Mathematical Society. 32 (1): 55–56.
  19. ↑ Mazumdar, Jagannath (2009). "Figuring Sport, by Graeme Cohen and Neville de Mestre". Gazette of the Australian Mathematical Society. 36 (1): 54–56.
  20. ↑ Sloan, Ian H. (2008). "Counting Australia In". The Mathematical Intelligencer. 30 (2): 63–65. doi:10.1007/BF02985739.
  21. 1 2 Gilmore, Clifford (2024). "The Possibly True Story of Martin Gardiner". Irish Mathematical Society Bulletin (94): 94–95. doi:10.33232/BIMS.0094.94.95.
  22. ↑ Lindsey, Kiera (2026). "Review of The Possibly True Story of Martin Gardiner". Australian Journal of Biography and History (11): 267–272.
  23. ↑ Cohen, Jeffrey (2022). "The Possibly True Story of Martin Gardiner". Gazette of the Australian Mathematical Society. 49 (5): 223–224.
  24. ↑ "Fellows of the Australian Mathematical Society". Australian Mathematical Society. Retrieved September 24, 2026.
Retrieved from "https://en.wikipedia.org/w/index.php?title=Graeme_Cohen&oldid=1377999765"