Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-28T08:35:30.807Z Has data issue: false hasContentIssue false
  • English
  • Français

Two prime centenaries – a number theorem and a miscarriage of justice

Published online by Cambridge University Press:  01 August 2016

Colin R. Fletcher
Colin R. Fletcher*
Affiliation:
Department of Mathematics, University of Wales, Aberystwyth SY23 3BZ
Get access Rights & Permissions [Opens in a new window]

Extract

The prime numbers are often called the building blocks of number theory, a classic case of a ‘sine qua non’. If the corpus of the theory of numbers is looked upon as an architectural pile then the primes will be found amongst its foundations, and amongst its walls and buttresses, and indeed amongst the array of pinnacles and turrets which burst forth from it and stand proud, alone and magnificent. One such pinnacle had been discussed and planned for a hundred years before it was finally constructed in 1896 by two men working totally independently of each other (collapse of stout analogy). With this achievement, the prime numbers, those familiar yet raw beasts of mathematics, in one sense had been tamed. The long journey, which had begun with the tentative definitions of the ancient Greeks, was completed.

Type
Articles
Information
The Mathematical Gazette , Volume 80 , Issue 489 , November 1996 , pp. 476 - 484
Copyright
Copyright © The Mathematical Association 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Heath, T. L. A history of Greek mathematics, Vol. 1 Dover (1981).Google Scholar
2. Euler, L. Introductio in analysis infinitorum, Lausanne, (1748).Google Scholar
3. Euclid, , The Elements (trans, by Heath, T. L.), Dover (1956).Google Scholar
4. Hardy, G. H., Mathematician’s apology, Cambridge University Press (1969).Google Scholar
5. Legendre, A. M., Essai sur la théorie des nombres, Paris (1798 and 1808).Google Scholar
6. Gauss, C. F., Werke, II (1872) pp. 444–447.Google Scholar
7. Goldstein, L. J., A history of the prime number theorem Amer. Math. Monthly 80 (1973) pp. 599–615.CrossRefGoogle Scholar
8. Tchebycheff, P. L., Oeuvres I (1899).Google Scholar
9. Riemann, G. F. B., Gesammelte mathematische werke, Leipzig (1892).Google Scholar
10. Hadamard, J., Sur la distribution des zéros de la fonction ζ (s) et ses conséquences arithmétiques Bull. Soc. Math. France 14 (1896) pp. 199–220.Google Scholar
11. de la Vallée Poussin, C-J., Recherches analytiques sur la théorie des nombres premiers Annates de la Soc. Sc. de Bruxelles, 20B (1896) pp. 183–256.Google Scholar
12. Cartwright, M. L., Obituary of Jacques Hadamard Journal London Math. Soc. 40 (1965) pp. 722–748.Google Scholar
13. Greaves, G. R. H., Private communication (1995).Google Scholar
14. Chapman, Guy, The Dreyfus trials, Batsford, (1972).Google Scholar
15. Zola, E., J’accuse L’Aurore (13 January 1898).Google Scholar
16. Mandelbrojt, S., The mathematical work of Jacques Hadamard Amer. Math. Monthly 60 (1953) pp. 599–604.Google Scholar