The fluency of geometry

My thoughts started jumping around today, trying to land on what it was that I found so fascinating about a recent article in Quanta Magazine.  This is one of the statements that got me going:

…Numbers emerging from one kind of geometric world matched exactly with very different kinds of numbers from a very different […]

Proofs, the mind, and mathematics

A recent article in Quanta Magazine anticipates the publication of the 6th edition of Proofs from The Book, collected by Martin Aigner and Günter Ziegler.  The original volume was inspired by the well-known and prolific mathematician Paul Erdős, who traveled the world, participating in countless collaborative efforts, and who would say of proofs that he […]

Mathematical hybrids and the like

My attention was just recently brought to the work of philosopher and poet Emily Grosholz.  It’s rare to find an individual so steeped in the ways of poetry and mathematics, and the desire to explore how and what they express about us.  What I would like to consider here, in this particular post, is really […]

I spy the confluence of mathematics, psychology, and physics

I find the relationship between mathematics and vision fascinating.   Even within mathematics itself, seeing how the geometric expression of ideas can clarify or further develop countless mathematical thoughts is always worth noting – like the graphs of functions, or the projections of figures.  I’ve written before about the relationship between the brain’s visual processes and […]

Spaces

I read about the sad passing of Maryam Mirzakhani in July, and the extraordinary trajectory of her career in mathematics. But I did not know much about what she was actually doing. A recent post in Quanta Magazine, with the title: Why Mathematicians Like to Classify Things, caught my attention because the title suggested that […]

Random Geometry

Random is often the word chosen to describe something that has no order. But randomness has become an increasingly useful tool in mathematics, a discipline whose meaningfulness relies, primarily, on order.

In statistics, randomness as a measure of uncertainty, makes possible the identification of events, whether sociopolitical or physical, with the use of probability distributions. […]