•  7
    From a purely formalist viewpoint on the philosophy of mathematics, experiments cannot (and should not) play a role in warranting mathematical statements but must be confined to heuristics. Yet, due to the incorporation of new mathematical methods such as computer-assisted experimentation in mathematical practice, experiments are now conducted and used in a much broader range of epistemic practices such as concept formation, validation, and communication. In this article, we combine corpus studi…Read more
  •  43
    The role of testimony in mathematics
    Synthese 199 (1-2): 859-870. 2020.
    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
  •  22
    Adapting practice-based philosophy of science to teaching of science students
    with Sara Green, Hanne Andersen, Kristian Danielsen, Claus Emmeche, Christian Joas, Mikkel Willum Johansen, Caio Nagayoshi, and Joeri Witteveen
    European Journal for Philosophy of Science 11 (3): 1-18. 2021.
    The “practice turn” in philosophy of science has strengthened the connections between philosophy and scientific practice. Apart from reinvigorating philosophy of science, this also increases the relevance of philosophical research for science, society, and science education. In this paper, we reflect on our extensive experience with teaching mandatory philosophy of science courses to science students from a range of programs at University of Copenhagen. We highlight some of the lessons we have l…Read more
  •  8
    Reviews (review)
    with Charlotte Methuen
    Centaurus 48 (1): 66-68. 2006.
  •  3
    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
  •  26
    Mathematicians writing for mathematicians
    Synthese 198 (Suppl 26): 6233-6250. 2019.
    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
  • . 2006.
  •  13
    In Honour of Kirsti Andersen
    with Jesper Lützen
    Centaurus 52 (1): 1-3. 2010.
    During the first half of the nineteenth century, mathematical analysis underwent a transition from a predominantly formula-centred practice to a more concept-centred one. Central to this development was the reorientation of analysis originating in Augustin-Louis Cauchy's (1789–1857) treatment of infinite series in his Cours d’analyse. In this work, Cauchy set out to rigorize analysis, thereby critically examining and reproving central analytical results. One of Cauchy's first and most ardent fol…Read more
  • with Reinhard Siegmund-Schultze
    . 2006.
  •  71
    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
  •  363
    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.
  • Vedkommende videnskabsteori
    with Hanne Andersen, Louis Klostergaard, Henrik Knudsen, Helge Kragh, Keld Nielsen, and Kurt Mã¸Ller Pedersen
    Aktuel Naturvidenskab (1): 32--35. 2009.
  •  370
    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
  •  21
    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