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Volume 76 - November 1992

Contents

Page 4 of 8

Notes

Research Article

  • A gemstone in matrix algebra

  • Tony Crilly
  • Published online by Cambridge University Press:
    01 August 2016, pp. 182-188

  • The history of mathematics is an abundant field for making surprising discoveries. Some luck is necessary, but whereas the literary tradition has been extensively explored by scholars, finding a nugget in the history of mathematics is not so difficult as turning up a new fragment by Jane Austen, or a lost piece by Mozart. In my case I struck lucky in the theory of matrices.

    As is well known, the theory of matrices arose during the 1850s – a useful benchmark is the publication of Arthur Cayley's celebrated memoir of 1858, A memoir on the theory of matrices, a paper which generations of mathematicians have taken as signalling the beginning of matrix theory. Even today the opening paragraphs serve as a useful introduction to the subject.

Notes

Research Article

  • The remarkable Ibn al-Haytham

  • John D. Smith
  • Published online by Cambridge University Press:
    01 August 2016, pp. 189-198

  • ‘I saw that I can reach the truth only through concepts whose matter are sensible things and whose form is rational.’

    The achievements in experimental and theoretical science of the Arab scholar al-Haytham (also known as Alhazen, from his latinized first name al-Hasan) make him as much a figure of the sixteenth and seventeenth centuries as of his own tenth and eleventh centuries.

    When his writings become known in the West the importance of his contribution to optics was widely recognized and he was studied by Galileo, Kepler, Fermat, Snell and Descartes. Mathematicians remember al-Haytham chiefly for Alhazen's Problem on the reflection of light from a circular mirror, which he solved by the method of conic sections; Huygens, Gregory, l'Hospital, Barrow (and many others) later took up the problem with the new analytical methods of geometry. Al-Haytham also wrote a commentary on the postulates of Euclid, and his attempted proof of the parallel postulate has similarities to Lambert's quadrilateral and Playfair's axiom in the eighteenth century. His theory of cognition may produce yet further interest in his work.

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Page 4 of 8