# Henrik Kragh SørensenUniversity of Copenhagen · Department of Science Education

Henrik Kragh Sørensen

PhD, MSc

## About

136

Publications

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216

Citations

Introduction

DH4PMP - Digital Humanities for Philosophy of Mathematical Practice: We use methods of big data, machine learning and digital humanities to explore philosophically interesting questions about contemporary mathematical research practices.

## Publications

Publications (136)

Do mathematicians only think in formulas? We surveyed mathematicians' use of mental imagery via the OSIVQ test (n=232) and four open questions (n=222). Combining expert judgement and text mining count of the number of diagrams in 3799 arXiv articles, we investigated whether the amount of visuo-spatial thinking (if any) is related to an article's su...

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...

This chapter contains the biographical portraits of the 54 members of the Central/Executive Committee of ICMI who passed away in the first 100 years of ICMI.Each of these portraits consists of a section of general biographical information and a section containing contributions to education and dissemination of mathematical culture. In the same vein...

Recent case studies in the philosophy of mathematical practice have pointed out that certain types of diagrams play epistemic roles in mathematical proofs. To complement such case studies and provide a quantitative basis for further analysis and discussions, we undertake an empirical study based on a large and contemporary corpus of mathematical te...

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...

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...

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 mandat...

In the Diagrams 2020 conference, we (Mikkel Willum Johansen and myself) reported on our first successes with machine-learning agents identifying and counting diagrams in mathematical papers. One year later, we have progressed, and in this paper I present and discuss ways of creating evidence on the use of diagrams in mathematical publications. Stud...

In this article we consider important developments in artificial intelligence within automated and interactive theorem provers (ATP/ITP). Our focus is to describe and analyze key challenges for interactive theorem provers in mainstream mathematical practice. Our broader research program is motivated by studying the functions of visual internal and...

The role and use of diagrams in mathematical research has recently attracted increasing attention within the philosophy of mathematics, leading to a number of in-depth case studies of how diagrams are used in mathematical practice. Though highly interesting, the study of diagrams still largely lack quantitative investigations which can provide vita...

For the past decade, philosophers of mathematical practice have examined the nature and function of proofs in mathematical practice, most often in mathematical research practice. More recently they have examined how mathematicians assess and get to know a proof not just by reading it, but through active engagement with the proof. For example, mathe...

We present and discuss initiatives to develop source-centered teaching materials in history of mathematics for upper secondary education, aiming at meeting the objective of the Danish curriculum to make history of mathematics relevant. To this end we present the design template for such multi-purpose materials we developed, which allows devising ma...

Henrik Kragh Sørensen: “When a Triangle is More than a Triangle. Mathema-tics and Literature in the Long 19th Century”Mathematical concepts such as triangles are very precisely defined in their geometrical context. Yet, these concepts gain new life outside the strict mathematical use. And outside of mathematics, triangles can have all kinds of symb...

David Aubin and Catherine Goldstein (eds.), 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 978-1-4704-1469-6. $126.00 (hardback). - Volume 50 Issue 3 - Henrik Kragh Sørensen

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...

This essay juxtaposes a particular a set of novel mathematical ideas from the early nineteenth century with a synchronous development in literary criticism. Important mathematical discoveries of the 1820s, such as non-Euclidean geometries, new impossibility results, and new proof ideals, exhibit structural similarities with notions of Romantic iron...

During the first decade of its existence, the American Mathematical Monthly regularly published short biographies of mathematicians. When read as appropriations of past lives, these biographies can be analysed to provide new insights into the images of mathematics, and of American mathematics in particular, held by groups of authors and welcomed by...

This book addresses the historiography of mathematics as it was practiced during the 19th and 20th centuries by paying special attention to the cultural contexts in which the history of mathematics was written.
In the 19th century, the history of mathematics was recorded by a diverse range of people trained in various fields and driven by different...

We prove that each maximal partial Latin cube must have more than 29.289% of its cells filled and show by construction that this is a nearly tight bound. We also prove upper and lower bounds on the number of cells containing a fixed symbol in maximal partial Latin cubes and hypercubes, and we use these bounds to determine for small orders n the num...

Just like any other cultural group, mathematicians like to tell stories. We tell heroic stories about famous mathematicians, to inspire or reinforce our cultural values, and we encase our results in narratives to explain how they are interesting and how they relate to other results. We also tell stories to convince others that our results are valid...

In this paper, the recent emergence of a professed “experimental” culture in mathematics during the past three decades is analysed based on an adaptation of Hans-Jörg Rheinberger’s notion of “experimental systems” that mesh into experimental cultures. In so doing, I approach the question of how distinct mathematical cultures can coexist and blend i...

Laura Søvsø Thomasen & Henrik Kragh Sørensen: “All in. Gambling in Literature From Lessing to the Financial Crisis”For centuries, gambling has been a recurring theme in fiction. Since the recent credit crunch of 2008, gambling has attained a partly new role in the emerging genre of “crunch fiction”. It can now be connected to financial speculation...

As a reaction to the changed political landscape in Scandinavia following the dissolution of the union between Norway and Sweden in 1905, the prominent Swedish mathematician Gösta Mittag-Leffler extended ‘a brotherly hand,’ calling for Scandinavian colleagues to meet for a congress of mathematicians in Stockholm in 1909. This event became the first...

The association of names to mathematical concepts and results (the creation of eponyms) is often a curious process. For the case of abelian groups, we will be taken on a quick, guided tour of the life of Niels Henrik Abel, elliptic functions, a curve called the lemniscate, the construction of the regular 17-gon, and a particular class of solvable e...

Resumé
Efter nazisternes magtovertagelse i 1933 måtte en række tyske matematikere emigrere, og nogle af dem kom til Danmark for kortere eller længere tid. Denne artikel analyserer de danske matematikeres og de tyske emigranters samspillende agendaer, som formede dansk matematik, især i København, i løbet af 1930ʼerne. Først gives et vue over de ini...

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,...

An efficient algorithm is presented for calculating higher weight enumerators of linear codes given generator matrices. By this algorithm, the higher weight enumerators of the unique doubly-even, self-dual code are calculated. The algorithm is based on a previously shown relationship between Tutte polynomials and higher weight enumerators.

Arbejdsgruppen giver nogle konkrete eksempler på målbeskrivelser og medfølgende faglige kriterier for karaktergivning efter den nye karakterbekendtgørelse. De er tænkt som oplæg til en diskussion og bør læses som sådan. Sådanne beskrivelser kan komme til veje på flere måder. Men inden procestiltag foreslås, følger en kort introduktion til arbejdsgr...

Abstract During the first 3 years of the existence of the Journal für die reine und angewandte Mathematik (1826–1828), a now unknown mathematician named Louis Olivier contributed 12 articles covering a broad range of contemporary mathematics. Apart from a single ‘faulty’ result, none of these works have received much interest from historians of mat...