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.

My CV may be found here.

Here are some articles I've written.

- “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). - “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. (Reviewed here, here, and here) - “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). (Reviewed here)

A few years back I gave a talk at a conference in honor of Harvey Friedman's 60th birthday. Here you can find streaming videos of the talks at the conference, including mine.

Here are some book reviews I've written.

- 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 Jose 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, epistemology, and the philosophy of religion.

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