
63The 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

3The Role of Experiments in Experimental MathematicsIn Bharath Sriraman (ed.), Handbook of the History and Philosophy of Mathematical Practice, Springer. pp. 24312458. 2024.This chapter is devoted to discussions about the nature of experiments in mathematics during the formative period of experimental mathematics and to a quantitative and qualitative analysis of the journal Experimental Mathematics founded in 1992. Particular attention is paid to interpret the roles of experiment and observation in the mathematical practices surrounding Experimental Mathematics.

11What 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

38Adapting 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

15‘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.

7Shaping 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

24Mathematics 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.

15Cultivating the Herb Garden of Scandinavian Mathematics: The Congresses of Scandinavian Mathematicians, 19091925Centaurus 55 (4): 385411. 2013.

Tusind Engle pÃ¥ et KnappenÃ¥lshoved: Matematikken i MiddelalderenIn Ole Hã¸Iris & Per Ingesman (eds.), Middelalderens Verden: Verdensbilledet, Tã¦Nkningen, Rummet Og Religionen, Aarhus Universitetsforlag. pp. 91104. 2010.

Reading MittagLeffler's biography of Abel as an act of mathematical selffashioningIn Benjamin Wardhaugh (ed.), The History of the History of Mathematics, Peter Lang. pp. 115144. 2012.

13Patrick PopescuPampu. What Is the Genus? xvii + 184 pp., figs., bibl., index. Cham, Switzerland: Springer, 2016. $59.99 (review)Isis 109 (2): 367368. 2018.

Poul Heegaard (18711948)In Fulvia Furinghetti & Livia Giacardi (eds.), The First Century of the International Commission on Mathematical Instruction (19082008): Portrait Gallery, . 2008.

Matematik pÃ¥ det store lÃ¦rred: Stereotyper om matematik og matematikere eksemplificeret ved tre nyere amerikanske filmIn Kristian Danielsen & Laura SÃ¸vsÃ¸ Thomasen (eds.), Fra Laboratoriet Til Det Store Lã¦Rred, Department of Science Studies, University of Aarhus. pp. 4058. 2011.

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.

En matematisk student krydser sit spor: TvÃ¦rfaglighed pÃ¥ Ã SG, 19982008In Ole Bã¸Ttzauw, Anton Vinderslev, Marianne Hã¸Gsgaard, Janne Yde & Anne Merete Frederiksen (eds.), 50 Ã Rhus Statsgymnasium, Ã Rhus Statsgymnasium. pp. 4647. 2008.

35Mathematicians 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

At begribe det ubegribelige: Matematikkens antikke verdenIn Ole Hã¸Iris & Birte Poulsen (eds.), Antikkens Verden, Aarhus Universitetsforlag. pp. 121136. 2011.

1Aksel Frederik Andersen (18911972)In Fulvia Furinghetti & Livia Giacardi (eds.), The First Century of the International Commission on Mathematical Instruction (19082008): Portrait Gallery, . 2008.

Abel, Niels HenrikIn Noretta Koertge (ed.), New Dictionary of Scientific Biography, Thomson Gale. pp. 58. 2007.

7In Peter C. Kjã¦Rgaard (ed.), Matematik Og Statistik, Aarhus Universitetsforlag. pp. 193216. 2006.

6In Henry Nielsen & Kristian Hvidtfelt Nielsen (eds.), Matematik, Statistik Og Datalogi, Aarhus Universitetsforlag. pp. 105124. 2006.

22In 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

27Abel 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

76Exploratory experimentation in experimental mathematics: A glimpse at the PSLQ algorithmIn Benedikt Löwe & Thomas Müller (eds.), PhiMSAMP: philosophy of mathematics: sociological aspsects 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

5Representations 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.

11Rüdiger 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.
Areas of Specialization
1 more
Philosophy of Mathematics 
History of Mathematics 
Mathematical Practice 
Epistemology of Mathematics 
Computer Proof 
Nondeductive Methods in Mathematics 