•  217
    Experimental mathematics in the 1990s: A second loss of certainty?
    Oberwolfach Reports (12): 601--604. 2010.
    In this paper, I describe some aspects of the phenomenon of "experimental mathematics" in order to discuss whether it constitutes a subdiscipline or a particular style of mathematics. My conclusion is that neither of these notions accurately capture the complex culture of experimental mathematics.
  •  210
    Making Philosophy of Science Relevant for Science Students
    Centre for Science Studies, University of Aarhus. 2012.
    Since 2004, it has been mandated by law that all Danish undergraduate university programmes have to include a compulsory course on the philosophy of science for that particular program. At the Faculty of Science and Technology, Aarhus University, the responsibility for designing and running such courses were given to the Centre for Science Studies, where a series of courses were developed aiming at the various bachelor educations of the Faculty. Since 2005, the Centre has been running a dozen di…Read more
  •  41
    In the present paper, I go beyond these examples by bringing into play an example that I nd more experimental in nature, namely that of the use of the so-called PSLQ algorithm in researching integer relations between numerical constants. It is the purpose of this paper to combine a historical presentation with a preliminary exploration of some philosophical aspects of the notion of experiment in experimental mathematics. This dual goal will be sought by analysing these aspects as they are presen…Read more
  •  13
    The role of testimony in mathematics
    with Line Edslev Andersen, Hanne Andersen, and Henrik Kragh Sørensen
    Synthese 1-12. forthcoming.
    Mathematicians appear to have quite high standards for when they will rely on testimony. Many mathematicians require that a number of experts testify that they have checked the proof of a result p before they will rely on p in their own proofs without checking the proof of p. We examine why this is. We argue that for each expert who testifies that she has checked the proof of p and found no errors, the likelihood that the proof contains no substantial errors increases because different experts w…Read more
  •  12
    Abel and his mathematics in contexts
    NTM Zeitschrift für Geschichte der Wissenschaften, Technik und Medizin 10 (1-3): 137-155. 2002.
    200 years ago, on August 5, 1802, Niels Henrik Abel was born on Finnøy near Stavanger on the Norwegian west coast. During a short life span, Abel contributed to a deep transition in mathematics in which concepts replaced formulae as the basic objects of mathematics. The transformation of mathematics in the 1820s and its manifestation in Abel’s works are the themes of the author’s PhD thesis. After sketching the formative instances in Abel’s well-known biography, this article illustrates two aspe…Read more
  •  12
    Mathematicians writing for mathematicians
    with Line Edslev Andersen and Mikkel Willum Johansen
    Synthese 1-18. forthcoming.
    We present a case study of how mathematicians write for mathematicians. We have conducted interviews with two research mathematicians, the talented PhD student Adam and his experienced supervisor Thomas, about a research paper they wrote together. Over the course of 2 years, Adam and Thomas revised Adam’s very detailed first draft. At the beginning of this collaboration, Adam was very knowledgeable about the subject of the paper and had good presentational skills but, as a new PhD student, did n…Read more
  •  10
    In Honour of Kirsti Andersen
    with Jesper Lützen
    Centaurus 52 (1): 1-3. 2010.
  •  7
    Reviews (review)
    with Charlotte Methuen
    Centaurus 48 (1): 66-68. 2006.
  •  3
    The importance of mathematical surplus
    Metascience 1-4. forthcoming.
  • Vedkommende videnskabsteori
    with Hanne Andersen, Louis Klostergaard, Henrik Knudsen, Helge Kragh, Keld Nielsen, and Kurt Mã¸Ller Pedersen
    Aktuel Naturvidenskab (1): 32--35. 2009.
  • Teaching reader engagement as an aspect of proof
    with Kristian Danielsen and Line Edslev Andersen
    ZDM 51 (5): 835-844. 2019.
  • with Reinhard Siegmund-Schultze
    . 2006.
  • Although the use of mathematical models is ubiquitous in modern science, the involvement of mathematical modeling in the sciences is rarely seen as cases of interdisciplinary research. Often, mathematics is “applied” in the sciences, but mathematics also features in open-ended, truly interdisciplinary collaborations. The present paper addresses the role of mathematical models in the open-ended process of conceptualizing new phenomena. It does so by suggesting a notion of cultures of mathematizat…Read more
  • . 2006.