Written Work

Monographs (0+1)

To appear (2024+)

(with K. Heuer) Forschend Mathematik erleben: Zehn mathematische Entdeckungsreisen. Springer Spektrum, Springer-Verlag, Heidelberg. In preparation, contract signed. (In German; title translated to English: "Experiencing Mathematics via research: ten mathematical journeys of discovery".)

Articles in major journals with peer-review. (12+1)

Accepted / forthcoming

• (with J. Fairhurst and J. A. Pérez-Escobar) Against a Global Conception of Mathematical Hinges. The Philosophical Quarterly (2024+). DOI: 10.1093/pq/pqae090. (Open Access)

Published

• (with B. Fisseni and B. Schröder) How to annotate a corpus for research on frames in the language of mathematics. Kalbotyra 78, pp. 111–137. (2025) DOI: 10.15388/Kalbotyra.2025.78.5.
• (with J. A. Pérez-Escobar and K. Heuer) The making of a mathematical notion by analogy: The case of Hamiltonicity of (locally finite) infinite graph theory. European Journal of Philosophy of Science 15. A.73 (2025). DOI: 10.1007/s13194-025-00695-9.
• (with J. A. Pérez-Escobar and C. J. Rittberg) Petrification in Contemporary Set Theory: The Multiverse and the Later Wittgenstein. KRITERION – Journal of Philosophy 39(1–2) (2025). DOI: 10.1515/krt-2023-0016. (Open Access)
• (with J. A. Pérez-Escobar) Philosophical Investigations into AI Alignment: A Wittgensteinian Framework. Philosophy and Technology, 37, A.80 (2024). DOI: 10.1007/s13347-024-00761-9. (Open Access)
• (with B. Fisseni and B. Schröder) How to frame innovation in mathematics. Synthese, 202, A.108 (2023). DOI: 10.1007/s11229-023-04310-3. (Open Access)
• (with K. Heuer) Paving the cowpath in research within pure mathematics – a medium level model based on text driven variations. Studies in History and Philosophy of Science, Volume 100, pages: 39–46 (2023). DOI: 10.1016/j.shpsa.2023.05.006. (Open Access)
• (with K. Heuer) Forcing hamiltonicity in locally finite graphs via forbidden induced subgraphs I: nets and bulls. Journal of Graph Theory. Volume 103: 23–47 (2023). DOI: 10.1002/jgt.22902. (2023) (Open Access)
• (with S. Blessenohl) Science Advice: Making Credences Accurate. Synthese. Volume 200, Article 174 (2022). DOI: 10.1007/s11229-022-03620-2. (Open Access)
• (with J. A. Pérez-Escobar) Purifying applied mathematics and applying pure mathematics: How a late Wittgensteinian perspective sheds light onto the dichotomy. European Journal of Philosophy of Science volume 12, Article 1 (2022). DOI: 10.1007/s13194-021-00435-9. (Open Access)
• (with D. Kant and J. A. Pérez-Escobar) Three Roles of Empirical Information in Philosophy: Intuitions on Mathematics do not Come for Free. KRITERION — Journal of Philosophy. volume 35(3), pages: 247–278 (2021) DOI: 10.1515/krt-2021-0025. (Open Access)
• (with M. Carl, M. Cramer, B. Fisseni and B. Schröder) How to Frame Understanding in Mathematics: A Case Study Using Extremal Proofs. Axiomathes volume 31, pages 649–676 (2021). DOI: 10.1007/s10516-021-09552-9. (Open Access)
• (with D. Kant) A virtue-theoretic narrative of mathematical practice: Different narratives and their consequences for mathematics education and society. Synthese volume 199, pages 3405–3429 (2021). DOI: 10.1007/s11229-020-02939-y. (Open Access)

Articles in Books, Conference Proceedings and smaller journal articles, peer-reviewed (11+1)

Accepted

• (with J. A. Pérez-Escobar) AI tools and the skill of integrating and “denoising” information: A potential pitfall in education. To appear in Strahovnik, V. (Ed.): Exploring Identity and Virtue in the Context of Human-AI Interaction.

Published

• (with J. A. Pérez-Escobar) On AI Alignment and the Later Wittgenstein: a Response To Sorin Bangu. Philosophy and Technology 38. A.138 (2025). DOI: 10.1007/s13347-025-00993-3.
• A Plea for Research-Based Teaching in Mathematics Education (Due to Ethical Reasons). In: Ernest, P. (Ed.) Ethics and Mathematics Education. Advances in Mathematics Education. Springer, Cham. (2025), DOI: 10.1007/978-3-031-58683-5_23.
• (with J. A. Pérez-Escobar) The post-COVID-19 era, chatbots, and the homogenization of education: Pluralism as an epistemic virtue exemplified by mathematics education. Philosophy of Mathematics Education Journal, 41. (2024)
• (with K. Heuer) Brainteasers vs. offene Problemfelder. In: N. Sturm, L. Baumanns & B. Rott (Eds.), Wenn es sein muss, dann halt in Distanz: Online-Herbsttagung 2021 des GDM-Arbeitskreises Problemlösen. (2023) Ars Inveniendi et Dejudicandi (19). DOI: 10.37626/GA9783959872706.0.07. (pp. 87–98)
• (with K. Heuer and B. Rott) Das Polymath-Format: Online kollaborativ arbeiten am NIM-Spiel. Mathematik Lehren, 235 (2022)
• (with K. Heuer and B. Rott) Diagnostik mathematischer Begabung. MU, Der Mathematikunterricht, 4/2021 (pp. 11–18).
• (with K. Heuer and B. Rott) Eine Adaption von Polymath für mathematisch begabte Schüler:innen: Ein Vorschlag (auch) für Distanzphasen. (pp. 81–95) In: L. Baumanns, B. Rott & N. Sturm: Mit Abstand die beste Tagung. Tagungsband der Herbsttagung des GDM-Arbeitskreises Problemlösen online 2020 (2021). Ars Inveniendi et Dejudicandi (17). DOI: 10.37626/GA9783959871945.0.06.
• (with K. Heuer) On the interplay of intuitions and formalism: modelling the transgression from school to student to researcher. In: B. Pieronkiewicz (Ed.), Different perspectives on transgressions in mathematics and its education (pp. 105–127). Cracow, Poland: Scientific Publishing House of the Pedagogical University of Cracow. (2020). (Full text freely available via ResearchGate)
• (with B. Fisseni, B. Schröder and M. Schmitt) How to frame a mathematician. Modelling the cognitive background of proofs. In: S. Centrone, D. Kant and D. Sarikaya (Eds.): Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts. Synthese Library, Springer, Berlin. (2019) DOI: 10.1007/978-3-030-15655-8_19.
• (with K. Heuer) Group theory via symmetries for enrichment classes for gifted youth. In: M. Nolte (Ed.): Including the Highly Gifted and Creative Students – Current Ideas and Future Directions Proceedings of the 11th International Conference on Mathematical Creativity and Giftedness (MCG 11). p. 257–263. (2015) (Open Access)
• (with B. Fisseni, A. Kurji and M. Viehstädt) Story Comparisons: Evidence from Film Reviews. In: M. A. Finlayson, B. Fisseni, B. Löwe and J. C. Meister (Ed.): 2013 Workshop on Computational Models of Narrative, Bd. 32. Dagstuhl, Germany: Schloss Dagstuhl-Leibniz-Zentrum für Informatik (Open Access Series in Informatics) p. 94–99. 2013. DOI: 10.4230/OASIcs.CMN.2013.94. (Open Access)

OTHER

Other Papers (11+0) not peer reviewed

• (with W. Bedenknecht and K. Heuer) Förderung mathematisch begabter Jugendlicher innerhalb des Klassenverbandes am Beispielaufgabenfeld der Parkettierung der Ebene. Mitteilungen der Mathematischen Gesellschaft in Hamburg 45 (2025), 36pp. Preprint online via: https://karlheuer.files.wordpress.com/2023/01/parkett_wbkhds.pdf.
• Die Frage nach der Willensfreiheit: Emergenz, ein Gefängnis auf dem Campus Stanfords, Nudges und nur noch ein Video! To appear in: Latif, M. (Ed.), Facetten der Freiheit. Perspektiven auf ein Grundrecht. (pp. 43–53) Herder Verlag.
• (with B. Löwe) Die ersten hundert Jahre Mathematik an der Hamburger Universität. In: Nicolaysen, R., Krause, E., Zimmermann, G. B. (eds.), 100 Jahre Universität Hamburg. Studien zur Hamburger Universitäts- und Wissenschaftsgeschichte in vier Bänden. Band 4. Mathematik, Informatik, Naturwissenschaften, Medizin. (pp. 29–58.) Wallstein Verlag. (2024)
• (with B. Löwe) Vorwort. In: Löwe, B.; Sarikaya, D. (Eds.) 60 Jahre DVMLG (2022). (pp. vii–xiii.) College Publications. (2022) (Open Access, slightly corrected version)
• (with D. Kant) Gespräch mit Arnold Oberschelp, dem Vorsitzenden der DVMLG von 1970 bis 1976. In: Löwe, B.; Sarikaya, D. (Eds.) 60 Jahre DVMLG. (pp. 121–126.) College Publications. (2022) (Open Access)
• (with B. Löwe) Satzungen der DVMLG durch die Jahrzehnte. In: Löwe, B.; Sarikaya, D. (Eds.) 60 Jahre DVMLG. (pp. 203–224.) College Publications. (2022) (Open Access)
• (with S. Nagler and H. Pillin) Introduction to the Special Issue on Lakatos’ Undone Work. KRITERION - Journal for Philosophy (pp. 1–10). (2022) DOI: 10.1515/krt-2022-0008. (Open Access)
• (with S. Centrone and D. Kant) Introduction. In: S. Centrone, D. Kant and D. Sarikaya (Eds.) Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts. Synthese Library, Springer, Berlin (2019).
• Gibt es Revolutionen in der Mathematik? [Do revolutions occur in mathematics?]. In Cog!to, the independent journal of the philosophy students of the Ludwig-Maximilians-Universität München 5, p. 54–56. (2015).
• (with K. Heuer) Variations in open problem fields as a tool for mathematical education: from basics to open questions in 90 minutes. In: M. Nolte (Ed.): Including the Highly Gifted and Creative Students – Current Ideas and Future Directions Proceedings of the 11th International Conference on Mathematical Creativity and Giftedness (MCG 11). p. 340–342. (2015). (Extended Abstract, Open Access)
• (with A. Block, R. Bod, B. Fisseni, A. Kurji, C. León and B. Löwe) Objectivity and reproducibility of formal narrative representations or annotations: Propp’s functions & narrative summarization. In: ILLC Prepublications Series PP-2012-10 (2012). (Preprint server, Open Access)

Submitted / in RnR (10) Titles will be announced after acceptance in case of blind review

• Die Weisheit der Vielen und Vielfalt der Weißheit. Submitted to Latif, M. (Ed.), Book Project on Plurality
• On Philosophical Methodology
• (with L. Bellmann) TBA. On Data-driven Philosophy of Logic.
• (with J. Fairhurst and J. A. Pérez-Escobar) On Longtermism.
• (with J. Fairhurst and J. A. Pérez-Escobar) On PMP and Hinge Epistemology. (2)
• (with Chr. Herzog) On AI and Practices
• (with K. Heuer) Forcing hamiltonicity in locally finite graphs via forbidden induced subgraphs II: paws. Submitted to: Journal of Graph Theory
• (with J. A. Pérez-Escobar) On Philosophy of Mathematics: Explanations.
• (with J. Raab) On Mathematics and Concept Development.
• (with C. Rittberg) On historicity of mathematical knowledge.

In Prep (8)

• On AI and education
• (with Chr. Herzog) On AI and Practices (2)
• (with Chr. Herzog and Robin Preiß) On AI and Education
• (with J. A. Pérez-Escobar) On AI and Alignment (3).
• (with J. A. Pérez-Escobar and Mira Sarikaya) On Wittgenstein and planned languages.
• (with M. Sarikaya) TBA. On the Philosophy of AI
• (with TBA) Opinion Piece on Digitalization
• (with TBA) White Paper on Education

Reports (2)

• (with B. Grabmayr, R. Krapf and A. Njegomir) Ouroboros: Workshop on formal criteria of self-reference in Mathematics and Philosophy, co-sponsored by the Association for Symbolic Logic (Bonn, Germany, February 16–18, 2018). The Bulletin of Symbolic Logic, 24(4), 544–545. (2018)
• (with B. Grabmayr, D. Kant and L. Kühne) Workshop on the Foundation of Mathematics: Univalent Foundation and Set Theory (FOMUS 2016), co-sponsored by the Association for Symbolic Logic (Bielefeld, Germany, July 18–23, 2016). The Bulletin of Symbolic Logic, 23(2), p. 267–268. (2017)

Scientific Qualification Work (4)

• Master’s thesis in philosophy: Automatische Theorembeweiser. Eine kuhnsche Revolution in der Mathematik? [Automatic theorem proving: A Kuhnian revolution in mathematics?].
• Bachelor’s thesis in philosophy: Aspekte der Methode der Widerlegungsbäume für die modalen Aussagenlogiken [Aspects of the method of prefixed tableaux for modal propositional logic].
• Master’s thesis in mathematics: Topological Infinite Graph Theory: Hamiltonicity results by compactness and transfinite construction for locally finite, claw-free graphs.
• Bachelor’s thesis in mathematics: Matchings in hypergraphs. On (nearly) perfect matchings in large k-uniform (k-partite) hypergraphs.