“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. […]

M.C. Escher’s visual inquiries

The Amazing World of MC Escher is a new exhibit at the Scottish National Gallery of Modern Art in Edinburgh. It will be there from June 27 to September 27. The exhibit prompted a nice piece on Escher in The Guardian. Author Steven Poole mentions, but does not much explore, the relationship between Escher’s work […]

Pattern, language and algebra

I’ve spent a good deal of time exploring how mathematics can be seen in how the body lives – the mental magnitudes that are our experience of time and space, the presence of arithmetic reasoning in pre-verbal humans and nonverbal animals, cells in the brain that abstract visual attributes (like verticality), the algebraic forms in […]

Orientation through words and notation

I thought recently, again, about the relationship between the written word and mathematical notation, both being systems of marks that carry meaning. Both systems grow with usage, and both provide some steady refinement of what we are able to see. I’m not so much interested, here, in the relationship between mathematical proficiency and language proficiency, […]

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 […]

Mathematics in the light of Maturana’s biology of cognition

As I have investigated all of the things in science and mathematics that get my attention, I have developed an impression of mathematics that, philosophically, seems most consistent with Humberto Maturana’s biology of language.  Maturana outlines his perspective in great detail in an essay by the same name that appeared in 1978 in the text […]

Where does mathematics live?

A Scientific American article brought mathematical knitting to my attention once again, and within the article was a link to Bridges, an organization which oversees the annual Bridges conference that explores the connections between art and mathematics.  Following the link to their 2013 Conference, I found their Short Movie Festival. I’ve watched a number of […]

What the experience of mathematical beauty could imply

Back in September, 1992 Semir Zeki wrote an article for what was then a special issue of Scientific American called Mind and Brain. In it he described what was known about how the brain produces visual images.  I have referred back to the article many times because it highlights the philosophical implications of our current […]

Numerosity, vision, language and mathematics

Understanding the neural functions that contribute to the birth of mathematical structure and meaning is an active subject of research in cognitive science.  A significant amount of work has been done to identify an innate ability we share with other creatures, namely the ability to perceive quantity.  This is sometimes called our approximate number sense.  […]

More on category theory and the brain

I’ve referred to category theory on more than one occasion (particularly with respect to physicist Bob Coecke’s graphical language).  Not too long ago, Ronald Brown, at Bangor University, brought my attention to the work that he and colleagues have been doing to investigate the kind of mathematics that could be used to model the complexity […]