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 […]

Self-organizing, art, and mathematical mutants

Deciphering the principles of self-organizing systems is often at the heart of new ideas in biology, including neurobiology. A complex, self-organizing system contains a large

number of elements that have predictable, local interactions with each other, but these local interactions create global properties that cannot be predicted from even the most well-understood local events. This […]

Mathematical behavior without a brain?

I have made the argument on more than one occasion that a refreshed look at mathematics may help illuminate the relationship between our experience of the physical and our experience of the thoughtful. Mathematics is a discipline characterized by complex relations among abstract things but, as has been explored from many directions, the action of […]

The plasticity of grids, in our heads and otherwise

Familiar mathematical structure is found in the neural activity that governs how the body orients itself and navigates its environment. Grid cells are neurons, found in areas neighboring the hippocampus, whose individual firings line up in a coordinate-like pattern according to an animal’s movement across the full extent of its environment. Their grid pattern acts […]

The Mind of Arithmetic

I like finding what I believe are productive generalizations, or some sameness across apparently diverse events.  Often the subject of Mathematics Rising are things like the observation that we seem to search for words in patterns that resemble the trajectories of a rat foraging for food, or the possibility that natural language can be described […]

Number, insight, and the Riemann Hypothesis

The Riemann Hypothesis came to my attention again recently. More specifically I read a bit about the possibility that quantum mechanical measurements may provide a proof of a centuries-old hypothesis and one of mathematics’ most famous enigmas.

Within mathematics itself, without any reference to its physical meaning, the Riemann Hypothesis highlights the kind of […]

The difference between dreaming and being awake

I could go on for quite some time about the difference between dreaming and being awake.  I could see myself picking carefully through every thought I have ever had about the significance of dreams, and I know I would end up with a proliferation of questions, rather than a clarification of anything.  But I think […]