I work in logic and the philosophy of mathematics. I am an associate professor of philosophy and mathematics at the University of Illinois at Urbana-Champaign.

During the 2014-15 academic year I am a EURIAS fellow at the Mediterranean Institute of Advanced Research (IMéRA) in Marseille, France.

I am also an editor of the Review of Symbolic Logic.

My CV may be found here.

Voici mon CV français.

Here are some articles I've written.

- “On the depth of Szemerédi's theorem”.
*Philosophia Mathematica*23:2 (2015), pp. 163-176. This article is part of a special issue on mathematical depth, all of whose articles plus forward and afterward are free to access here. - “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), pp. 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), pp. 315-336.
- “On the relationship between plane and solid geometry” (with Paolo Mancosu).
*Review of Symbolic Logic*5:2 (2012), 294-353. Preprint here. - “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. Preprint here. - “On formally measuring and eliminating extraneous notions in proofs”.
*Philosophia Mathematica*17 (2009). - “Logical and semantic purity”.
*Protosociology*vol. 25 (2008), pp. 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, pp. 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).

Here are some videos of talks I've given.

- “Grumeaux d'ordre dans une pate informe: on the depth of Szemerédi's Theorem”, at a conference on mathematical depth at UC Irvine in 2014.
- “Simplicity and the interface of algebra and geometry”, at a conference on simplicity in mathematics and the arts at the CUNY Graduate Center in 2013.
- “On Purity of Methods”, at a conference in honor of Harvey Friedman's 60th birthday at Ohio State in 2009.

Here are some book reviews I've written.

- Review of B. Jack Copeland, Carl J. Posy, And Oron Shagrir's
*Computability: Turing, Gödel, Church, and Beyond*, Notre Dame Philosophical Reviews 3:20 (2015). - Review of Jeremy Gray's
*Plato's Ghost: The Modernist Transformation of Mathematics*,*Philosophia Mathematica*20:2 (2012). - Review of Marcus Giaquinto's
*Visual Thinking In Mathematics*,*Analysis*69 (2009), pp. 401-403. - Review of José Ferreiros and Jeremy Gray's
*The Architecture of Modern Mathematics*,*Mathematical Intelligencer*30:4 (2008). - Review of David Corfield's
*Toward a Philosophy of Real Mathematics*,*Mathematical Intelligencer*29:2 (2007). - Review of Solomon Feferman's
*In The Light of Logic*,*Mathematical Intelligencer*27:4 (2005).

In recent years I've taught courses in logic, the history of modern philosophy, the philosophy of mathematics, and the theory of knowledge.

Department of Philosophy

University of Illinois at Urbana-Champaign

810 S. Wright Street

105 Gregory Hall, MC-468

Urbana, IL 61801

(217) 333-2889

aarana@illinois.edu