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2 results

  • 7 - Mathematical Wonderland

  • Paul Embrechts, Swiss Federal University (ETH), Zürich, Marius Hofert, The University of Hong Kong, Valérie Chavez-Demoulin, Université de Lausanne, Switzerland
  • Book:
    Risk Revealed
    Published online:
    05 April 2024
    Print publication:
    11 April 2024, pp 82-93

  • Summary

    Time for a break! Chapter 7 takes you for a guided walk through a tiny part of mathematical wonderland. We will encounter several mathematical personalities. An important one is Andrew Wiles, who solved Fermat’s Last Theorem. The story about how he finally obtained a proof is a must-read. We learn about the Fields Medal, the equivalent of a (non-existing) Nobel Prize in mathematics. We also tell you about the four-yearly International Congresses of Mathematicians and their influence on the field. There will be a first step on the ladder towards a theory of randomness; key names here are Jacob Bernoulli and Andrei Nikolajewitsch Kolmogorov. Randomness also comes to us through the famous discussion between Niels Bohr and Albert Einstein on “God throwing dice”. Of course, we include Leonhard Euler and his most beautiful formula of mathematics.

  • CAUCHY–MIRIMANOFF AND RELATED POLYNOMIALS

  • Part of
  • PAUL M. NANNINGA
  • Journal:
    Journal of the Australian Mathematical Society / Volume 92 / Issue 2 / April 2012
    Published online by Cambridge University Press:
    27 September 2012, pp. 269-280
    Print publication:
    April 2012
    • Article
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  • In 1903 Mirimanoff conjectured that Cauchy–Mirimanoff polynomials En are irreducible over ℚ for odd prime n. Polynomials Rn, Sn, Tn are introduced, closely related to En. It is proved that Rm, Sm, Tm are irreducible over ℚ for odd m≥3 , and En, Rn, Sn are irreducible over ℚ, for n=2qm, q=1,2,3,4,5 , and m≥1 odd.