My CV may be found here.

Voici mon CV français.

I am the co-PI, with Heather Burnett, of the ANR project MATHY, on mathematical hygiene, funded from 2024 to 2028.

• Elements of Purity, Cambridge University Press (2024).

Here are some books I've edited.

• Idéaux de preuve. Œuvres choisies de Michael Detlefsen, Vol I. (edited with Emmylou Haffner and David Rabouin), Vrin (2024).
• Précis de philosophie de la logique et des mathématiques, Volume 2, philosophie des mathématiques (edited with Marco Panza), Éditions de la Sorbonne (2022).

Here are some articles I've written.

• “Mathematical Hygiene” (with Heather Burnett). Synthese 202:4 (2023), 1-28.
• “On the difficulty of discovering mathematical proofs” (with Will Stafford). Synthese 202:2 (2023), 1-29.
• “Purity and Explanation: Essentially Linked?”. In Mathematical Knowledge, Objects and Applications: Essays in Memory of Mark Steiner, edited by Carl Posy and Yemima Ben-Menahem, Springer (2023), 25-39.
• “Idéaux de preuve : explication et pureté”. In Précis de philosophie de la logique et des mathématiques, Volume 2, philosophie des mathématiques, edited by Andrew Arana and Marco Panza, Éditions de la Sorbonne (2022), 387-425.
• “Takeuti's well-ordering proofs revisited” (with Ryota Akiyoshi). Mita Philosophy Review 146 (2021), 83-110.
• “Takeuti's proof theory in the context of the Kyoto School” (with Ryota Akiyoshi). Jahrbuch für Philosophie das Tetsugaku-Ronso 46 (2019), 1-17.
• “On the alleged simplicity of impure proof”. In Simplicity: Ideals of Practice in Mathematics and the Arts, edited by Roman Kossak and Philip Ording, Springer (2017), 207-226.
• “Imagination in mathematics”. In The Routledge Handbook of the Philosophy of Imagination, edited by Amy Kind, Routledge (2016), 463-477
• “On the depth of Szemerédi's theorem”. Philosophia Mathematica 23:2 (2015), 163-176. This article is part of a special issue on mathematical depth.
• “Plane and solid geometry: a note on purity of methods” (with Paolo Mancosu). In From Logic to Practice : Italian Studies in the Philosophy of Mathematics, edited by Gabriele Lolli, Marco Panza, and Giorgio Venturi, Springer (2015), 23-31.
• “Purity in arithmetic: some formal and informal issues.” In Formalism and Beyond. On the Nature of Mathematical Discourse, edited by Godehard Link, De Gruyter (2014), 315-336.
• “On the relationship between plane and solid geometry” (with Paolo Mancosu). Review of Symbolic Logic 5:2 (2012), 294-353.
• “Geometria piana e solida: una nota sulla purezza del metodo” (with Paolo Mancosu). Notae Philosophicae Scientiae Formalis 1:1 (2012), 89-102.
• “L'infinité des numbers premiers : une étude de cas de la pureté des méthodes”. Les études philosophiques 2:97 (2011).
• “Purity of methods” (with Mic Detlefsen). Philosophers' Imprint 11:2 (2011).
• “Descartes and the cylindrical helix” (with Paolo Mancosu). Historia Mathematica 37:3 (2010), 403-427.
• “Proof theory in philosophy of mathematics”. Philosophy Compass 5:4 (2010), 336-347.
• “On formally measuring and eliminating extraneous notions in proofs”. Philosophia Mathematica 17 (2009), 189–207.
• “Logical and semantic purity”. Protosociology vol. 25 (2008), 36-48; reprinted in Philosophy of Mathematics: Set Theory, Measuring Theories, and Nominalism, Gerhard Preyer and Georg Peter (eds.), Ontos (2008).
• “Possible m-diagrams of models of arithmetic”. In Reverse Mathematics 2001, edited by Stephen Simpson, Lecture Notes in Logic 21, A.K. Peters Publishers / Association for Symbolic Logic (2005) 27-41.
• “Arithmetical independence results using higher recursion theory”. The Journal of Symbolic Logic 69:1 (2004) 1-9.
• “Solovay's Theorem Cannot Be Simplified”. Annals of Pure and Applied Logic 112 (2001), 27-41.

Here are some book reviews I've written.

• Review of Reactionary Mathematics. A Genealogy of Purity by Massimo Mazzotti, University of Chicago Press (2023). Physis LIX:2 (2024), 614-618.
• Review of Model theory and philosophy by Tim Button and Sean Walsh, Oxford University Press (2018). Bulletin of Symbolic Logic 26:3-4 (2020), 287-292.
• “The changing practices of proof in mathematics”. Review of Computation, proof, machine by Gilles Dowek, Metascience, 26:1 (2017), 131-135.
• Review of Computability: Turing, Gödel, Church, and Beyond, edited by B. Jack Copeland, Carl J. Posy, and Oron Shagrir. Notre Dame Philosophical Reviews 3:20 (2015).
• Review of Plato's Ghost by Jeremy Gray. Philosophia Mathematica 20:2 (2012), 252–255.
• Review of Visual Thinking in Mathematics by Marcus Giaquinto. Analysis 69 (2009), pp. 401–403.
• Review of The Architecture of Modern Mathematics, edited by José Ferreirós and Jeremy Gray. Mathematical Intelligencer 30:4 (2008), 57–61.
• Review of Toward a philosophy of real mathematics by David Corfield. Mathematical Intelligencer 29:2 (2007), 80–83.
• Review of In the Light of Logic by Solomon Feferman. Mathematical Intelligencer, 27:4 (2005), 38–40.

andrew.arana at univ-lorraine.fr

Department of Philosophy
Université de Lorraine
Archives Poincaré (CNRS UMR 7117)
Nancy
France