“The future of mathematics is more a spiritual discipline…”

I did some following up on the work of Vladimir Voevodsky and for anyone who might ask, “what’s actually going on in mathematics,” Voevodsky’s work adds, perhaps, even more to the mystery. Not that I mind. The mystery emerges from the limitless depths (or heights) of thought that are revealed in mathematical ideas or objects. […]

Finding hidden structure by way of computers

An article in a recent issue of New Scientist highlights the potential partnership between computers and mathematicians. It begins with an account of the use of computers in a proof that would do little, it seems, to provide greater understanding, or greater insight into the content of the idea the proof explores. The computer program […]

Collective behavior: flocks, magnets, neurons and mathematics

The analysis of collective behavior is quickly becoming cross-disciplinary.  I wrote a few years ago about a study that analyzed the coordination of starling flocks. That post was based on the work of Thierry Mora and William Bialek, presented in their paper Are Biological Systems Poised at Criticality. The paper was published in the Journal […]

Architecture, orientation and mathematics

Recently, I became intrigued with the discussions of topology that I found among architects and historians of architecture. I saw a few familiar threads running through these discussions – like the emergence and self-organizing principles of biology, together with the view that mathematics was not, primarily, a tool but more a point of view.

I […]

Embodiment and a Philosophy of Mathematics

Yesterday I gave a talk at a symposium at the 36th annual Cognitive Science Conference. The content of the talk was described this way in our symposium proposal:

Mathematics has been the subject of experimental studies in cognitive science that explore the sensory grounding of number and magnitude. But mathematics also provides conceptual schemes that […]

Dante, art, vision, and mathematics

We adopted a dog a couple of months ago, and there have been moments when I have watched a change in his attention or a change in his behavior, and wondered how his awareness might be structured.   When we drive with him, he usually sits in front of the back seats of our Honda Element, […]

Archimedes, particle accelerators and being visual

I feel like I was pulled into a little whirlpool of interesting bits of info this morning.  I was attracted to the title of David Castelvecchi’s blog: Archimedes and Euclid?  Like String Theory versus Freshman Calculus.   The blog reports the opening of an exhibition at the Walters Art Museum in Baltimore, showcasing one of three […]

Knotted DNA

I recently read the announcement of a National Science Foundation Career Award  given to Mariel Vazquez (Associate Professor at San Francisco State University) for the work she does in mathematics and biology.  Vazquez has been involved for some time in the application of knot theory to the analysis of DNA.

Knot Theory is one of […]