Introduction.- Hardy, Littlewood, and polymath, (Martin and Pease).- Experimental Computation as an Ontological Game Changer: The Impact of Modern Mathematical Computation Tools on the Ontology of Mathematics (Bailey and Borwein).- Mathematical Products (Davis).-How Should Robots Think about Space? (Azzouni).- Mathematics and its Applications (Berlinski).- Nominalism: The Nonexistence of Mathematical Objects (Azzouni).- An Aristotelian Approach to Mathematical Ontology (Gillies).- Let G be a Group (Lützen).- From the Continuum to Large Cardinals (Stillwell).- Mathematics at Infinity (Gray).- Mathematics and Language (Avigad).- Mathematics as Language (Ross).- Mathematics as Multimodal Semiotics (O'Halloran).- Problems in Philosophy of Mathematics: A View from Cognitive Science (Piantadosi).- Beliefs about the Nature of Numbers (Rips).- What Kind of Thing Might Number Become? (Sinclair).- Enumerated Entities in Public Policy and Governance (Verran).
