
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 […]
The idea that geometry in Gothic architecture was used to structure ideas, rather than the edifice itself, has come up before here at Mathematics Rising. But I would like to focus a bit more on this today because it illustrates something about mathematics, and mathematics’ potential, that the modern proliferation of information may be obscuring. […]
Roger Antonsen came to my attention with a TED talk recorded in 2015 that was posted in November. Characterized by the statement, “Math is the hidden secret to understanding the world,” it piqued my curiosity. Antonsen is an associate professor in the Department of Informatics at the University of Oslo. Informatics has been […]
First, I would like to apologize for posting so infrequently these past few months. I have been working hard to flesh out a book proposal closely related to the perspective of this blog, and I will be focused on this project for a bit longer.
However, a TED talk filmed in Paris in May came […]
I think often about the continuity of things – about the smooth progression of structure, that is the stuff of life, from the microscopic to the macrocosmic. I was reminded, again, of how often I see things in terms of continuums when I listened online to a lecture given by Gregory Chaitin in 2008. In […]
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. […]
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 […]
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 preverbal humans and nonverbal animals, cells in the brain that abstract visual attributes (like verticality), the algebraic forms in […]
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, […]
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 […]


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