My research begins with a question: what does it mean to think in mathematics? It is primarily philosophical and seeks to characterize the distinctive forms of mathematical thinking, the powers it brings into play, and the conditions of its development.
Abstraction, generality, structures, and invariants are approached as modes of mathematical thinking. The inquiry draws on mathematical work as it is actually carried out, especially in modern and contemporary mathematics—from Fréchet and Banach to Grothendieck and Gowers.
It also examines the emergence of artificial forms of mathematical thinking and, more recently, mathematics as an “ortho…
My research begins with a question: what does it mean to think in mathematics? It is primarily philosophical and seeks to characterize the distinctive forms of mathematical thinking, the powers it brings into play, and the conditions of its development.
Abstraction, generality, structures, and invariants are approached as modes of mathematical thinking. The inquiry draws on mathematical work as it is actually carried out, especially in modern and contemporary mathematics—from Fréchet and Banach to Grothendieck and Gowers.
It also examines the emergence of artificial forms of mathematical thinking and, more recently, mathematics as an “orthoepy of being”: a mathematically regulated articulation of thought’s relation to being.
