Author: Jim Turner

Mathematical Understanding as Seen Within a Framework of Beauty (part 4)

Following upon my previous posts, where I began to explore the possibility of framing mathematical understanding within the Thomistic modes of beauty proportio and claritas, I now consider the third mode of beauty, that of integritas. This mode brings beauty in mathematical understanding to its fulfillment and serves to complete and unite the other two […]

Mathematical Understanding as Seen Within a Framework of Beauty (part 3)

In the first two parts of this series, I began outlining how mathematics and mathematical understanding can be framed within the Thomistic modes of beauty: proportio, claritas, and integritas. In particular, I defined mathematics as the science whose subject-matter is measurable orders: objects understood as parts united into whole, having a distinction of same or […]

Mathematical Understanding as Seen Within a Framework of Beauty (part 2)

In part 1 of this series, I began to explore how mathematical reasoning can be understood within a Thomistic framework of beauty as expressed in the modes proportio, claritas, and integritas. In that post, I arrived at an initial description of the subject-matter of mathematics as pertaining to quantitative being understood as parts ordered into […]

Mathematical Understanding as Seen Within a Framework of Beauty (part 1)

In a previous series of posts (part 1 being here:  https://thinkingbeautifully.org/form-beauty-and-euclids-elements-part-1/) I began to describe how mathematics could be understood as an endeavor of human discovery and invention by showing how form and the pursuit of beauty underlies successes in such efforts. In particular, I focused on the opening of Book I of Euclid’s Elements […]

Beauty, Form, and Euclid’s Elements Part 3

In the previous posts to this series, https://thinkingbeautifully.org/form-beauty-and-euclids-elements-part-2/ I set out to articulate a perspective on the opening of Euclid’s Elements as arising by abstraction of forms that arise from sensible perceptions of things experienced in the real world. I aimed to make the case that certain ones of his Definitions and the forms his Postulates […]

Form, Beauty, and Euclid’s Elements (part 2)

In the previous installment https://thinkingbeautifully.org/form-beauty-and-euclids-elements-part-1/ (upon which this part depends), I gave what I feel is the correct beginning in how to arrive at and understand basic notions in mathematics. In doing so, I attempted to re-appropriate medieval concepts of matter, form, and abstraction in order to understand what constitutes the objects and subject-matter of […]

Form, Beauty, and Euclid’s Elements (part 1)

I want to begin exploring, or perhaps recovering, a way of understanding the discipline of mathematics as one that integrally involves a perspective of beauty, not a “beauty cold and austere, like that of a sculpture,” (Bertrand Russell) but a beauty that irradiates from the form of anything that can be understood as having being. […]