
13The role of testimony in mathematicsSynthese 112. 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

1‘The End of Proof’? The integration of different mathematical cultures as experimental mathematics comes of ageIn Brendan Larvor (ed.), Mathematical Cultures. The London Meetings 2012–2014. pp. 139160. 2016.

Shaping Mathematics as a Tool: The Search for a Mathematical Model for QuasicrystalsIn Johannes Lenhard & Martin Carrier (eds.), Mathematics as a Tool. Tracing New Roles of Mathematics in the Sciences, Springer Verlag. pp. 6990. 2017.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 openended, truly interdisciplinary collaborations. The present paper addresses the role of mathematical models in the openended process of conceptualizing new phenomena. It does so by suggesting a notion of cultures of mathematizat…Read more

10Mathematics Unbound: The Evolution of an International Mathematical Research Community, 1800?1945  Edited by Karen H. Parshall and Adrian C. Rice (review)Centaurus 49 (2): 179181. 2007.

3Cultivating the Herb Garden of Scandinavian Mathematics: The Congresses of Scandinavian Mathematicians, 19091925Centaurus 55 (4): 385411. 2013.

2Patrick PopescuPampu. What Is the Genus? xvii + 184 pp., figs., bibl., index. Cham, Switzerland: Springer, 2016. $59.99 (review)Isis 109 (2): 367368. 2018.

11David Aubin and Catherine Goldstein , The War of Guns and Mathematics: Mathematical Practice and Communities in France and Its Western Allies around World War I. Providence, RI: American Mathematical Society, 2014. Pp. xviii + 391. ISBN 9781470414696. $126.00 (review)British Journal for the History of Science 50 (3): 557558. 2017.

12Mathematicians writing for mathematiciansSynthese 118. 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

210Making Philosophy of Science Relevant for Science StudentsCentre 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

12Abel and his mathematics in contextsNTM Zeitschrift für Geschichte der Wissenschaften, Technik und Medizin 10 (13): 137155. 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 wellknown biography, this article illustrates two aspe…Read more

41Exploratory experimentation in experimental mathematics: A glimpse at the PSLQ algorithmIn Benedikt Löwe & Thomas Müller (eds.), PhiMSAMP. Philosophy of Mathematics: Sociological Aspects and Mathematical Practice, College Publications. pp. 341360. 2010.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 socalled 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

2Representations as means and ends: Representability and habituation in mathematical analysis during the first part of the nineteenth centuryIn Bart Van Kerkhove (ed.), New Perspectives on Mathematical Practices: Essays in Philosophy and History of Mathematics, World Scientific. pp. 114137. 2009.

5Rüdiger Campe, The Game of Probability: Literature and Calculation from Pascal to Kleist. Stanford: Stanford University Press, 2012. Pp. viii+486. ISBN 9780804768658. $35.00 (review)British Journal for the History of Science 47 (4): 727728. 2014.

217Experimental mathematics in the 1990s: A second loss of certainty?Oberwolfach Reports (12): 601604. 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.
Areas of Specialization
1 more
Philosophy of Mathematics 
History of Mathematics 
Mathematical Practice 
Epistemology of Mathematics 
Computer Proof 
Nondeductive Methods in Mathematics 