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## Full-Text Articles in Philosophy

Maths Living In Social Arenas, From Practice To Foundations, Nigel Vinckier

#### Maths Living In Social Arenas, From Practice To Foundations, Nigel Vinckier

*Journal of Humanistic Mathematics*

Maths comes to life in human interaction. This has consequences for the mathematics itself. This paper discusses how this ``coming to life'' of mathematics in different social arenas influences the foundations of maths. We will argue that this influence is profound, to the extent that it is hard to upkeep the idea that there is or should be one foundation on which all mathematics can be built.

Mathematicians Versus Philosophers In Recent Work On Mathematical Beauty, Viktor Blåsjö

#### Mathematicians Versus Philosophers In Recent Work On Mathematical Beauty, Viktor Blåsjö

*Journal of Humanistic Mathematics*

Recent attempts at defining mathematical beauty fall roughly into two schools of thought. One takes its starting point in the subjective experience of the mathematician and characterises mathematical beauty in cognitive terms. The other seeks to reduce beauty to objective notions such as truth, symmetry, or simplicity. This second approach is popular among analytic philosophers, who are committed to seeing mathematics and science as prototypically rational enterprises. I criticise this stance on the grounds that this commitment makes its supporters approach beauty in mathematics not with a genuine desire to sympathetically understand it, but with the preconceived goal of explaining ...

Explanatory Proofs And Beautiful Proofs, Marc Lange

#### Explanatory Proofs And Beautiful Proofs, Marc Lange

*Journal of Humanistic Mathematics*

This paper concerns the relation between a proof’s beauty and its explanatory power – that is, its capacity to go beyond proving a given theorem to explaining why that theorem holds. Explanatory power and beauty are among the many virtues that mathematicians value and seek in various proofs, and it is important to come to a better understanding of the relations among these virtues. Mathematical practice has long recognized that certain proofs but not others have explanatory power, and this paper offers an account of what makes a proof explanatory. This account is motivated by a wide range of examples ...

Teaching The Complex Numbers: What History And Philosophy Of Mathematics Suggest, Emily R. Grosholz

#### Teaching The Complex Numbers: What History And Philosophy Of Mathematics Suggest, Emily R. Grosholz

*Journal of Humanistic Mathematics*

The narrative about the nineteenth century favored by many philosophers of mathematics strongly influenced by either logic or algebra, is that geometric intuition led real and complex analysis astray until Cauchy and Kronecker in one sense and Dedekind in another guided mathematicians out of the labyrinth through the arithmetization of analysis. Yet the use of geometry in most cases in nineteenth century mathematics was *not* misleading and was often key to important developments. Thus the geometrization of complex numbers was essential to their acceptance and to the development of complex analysis; geometry provided the canonical examples that led to the ...

The Mathematical Cultures Network Project, Brendan P. Larvor

#### The Mathematical Cultures Network Project, Brendan P. Larvor

*Journal of Humanistic Mathematics*

The UK Arts and Humanities Research Council has agreed to fund a series of three meetings with associated publications on mathematical cultures. This note describes the project.