**Published Papers:**

(2021). “Impurity in Contemporary Mathematics”.

Notre Dame Journal of Formal Logic.(preprint : official version)62(1): 67-82(2021) “Induction and explanatory definitions in mathematics”.

Synthese198,1161–1175. (preprint : official version)

**Mathematics Publication:**

Forthcoming. “Reidemeister moves in Gauss diagrams

“. Involve.(co-written with S. Ganzell, C. Lopez, G. Magallon, and A. Thompson.)

**Papers in Preparation:**

“Exemplification as a Means to Understanding in Mathematics”

“The Abstract Subject Matter of Mathematics: Virtual Knot Theory”

“Understanding as the Aim of Mathematics”

**Talks:**

February 2021: “Visualizing Mathematics”, at Conjunto No Vacio Semillero, Universidad de los Andes, invited speaker.

December 2019: “Mathematical Explanation as a Means to Understanding”, at Explanation and Understanding within Mathematics Workshop, hosted by Vrije Universiteit Brussel. (abstract : event)

November 2019: “Understanding as the Aim of Mathematics”, University of Notre Dame Colloquium Series, elected graduate student speaker.

November 2019: “The Explanatory Value of Category Theory”, at Midwest Philosophy of Mathematics Workshop, University of Notre Dame. (abstract : event)

November 2019: “Understanding as the Aim of Mathematics”, at Novembertagung on the History and Philosophy of Mathematics. (abstract : event)

October 2019: “The Explanatory Value of Category Theory”, Category Theory OctoberFest 2019, Johns Hopkins University. (abstract : event)

October 2019: “The Explanatory Value of Category Theory”, UConn Logic Colloquium, invited speaker. (abstract : event)

March 2019: “Impurity in Contemporary Mathematics”, at Mathematics in Philosophy: Purity and Idealization, hosted by University of Notre Dame. (event)

May 2018: “Rigor and Intuition in Topology: The Development of the Poincaré Conjecture”, at the Masterclass in the Philosophy of Mathematical Practice (2018), hosted by Vrije Universiteit Brussel. (abstract)