
7What is an experiment in mathematical practice? New evidence from mining the Mathematical ReviewsSynthese 203 (2): 121. 2024.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 computerassisted 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

43The role of testimony in mathematicsSynthese 199 (12): 859870. 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

22Adapting practicebased philosophy of science to teaching of science studentsEuropean Journal for Philosophy of Science 11 (3): 118. 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

9‘The End of Proof’? The integration of different mathematical cultures as experimental mathematics comes of ageIn Brendan Larvor (ed.), Mathematical Cultures: The London Meetings 20122014, Springer International Publishing. pp. 139160. 2016.

3Shaping Mathematics as a Tool: The Search for a Mathematical Model for QuasicrystalsIn Martin Carrier & Johannes Lenhard (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

15Mathematics 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.

5Cultivating the Herb Garden of Scandinavian Mathematics: The Congresses of Scandinavian Mathematicians, 19091925Centaurus 55 (4): 385411. 2013.

5Patrick PopescuPampu. What Is the Genus? xvii + 184 pp., figs., bibl., index. Cham, Switzerland: Springer, 2016. $59.99 (review)Isis 109 (2): 367368. 2018.

14David 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.

26Mathematicians writing for mathematiciansSynthese 198 (Suppl 26): 62336250. 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

13In Honour of Kirsti AndersenCentaurus 52 (1): 13. 2010.During the first half of the nineteenth century, mathematical analysis underwent a transition from a predominantly formulacentred practice to a more conceptcentred one. Central to this development was the reorientation of analysis originating in AugustinLouis 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

71Exploratory 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

3Representations 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.

7Rüdiger 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.

363Experimental 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.

370Making 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

21Abel 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
Areas of Specialization
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Philosophy of Mathematics 
History of Mathematics 
Mathematical Practice 
Epistemology of Mathematics 
Computer Proof 
Nondeductive Methods in Mathematics 