Mathematics as Mathematicians’ Practice

The philosophy of mathematical practice attempts to give the philosophy of mathematics a new beginning. Essential for this beginning is to acknowledge that mathematics is constructed by humans. Hence, as with any other kind of human knowledge construction, mathematics is fallible, corrigible, tentative, and evolving. According to the philosophy of mathematical practice, mathematics can be defined simply as the mathematicians’ practice—it is what mathematicians do. For a philosophy of mathematical practice, it is important to address features of this practice instead of being preoccupied with problems defined through philosophic traditions. It is important to explore the concept of proof, not by embracing any specific ideals, but by considering the variety of ways proof is accomplished in practice. As with logicism, formalism, and intuitionism, so also the philosophy of mathematic practice operates in an ethical vacuum by not considering what might be the social impact of bringing mathematics into action.