Infinity is not the problem

An article published in May in Quanta Magazine had the following remark as its lead:

A surprising new proof is helping to connect the mathematics of infinity to the physical world.

My first thought was that the mathematics of infinity is already connected to the physical world. But Natalie Wolchover’s opening few paragraphs were inviting:

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The promise of uncomputability

I just listened to a talk given by Virginia Chaitin that can be found on academia.edu.   The title of the talk is A philosophical perspective on a metatheory of biological evolution.   In it she outlines Gregory Chaitin’s work on metabiology, which has been the subject of some of my previous posts – here,  here, and […]

“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. […]

Continuity, randomness and the Oracle

Flipping through some New Scientist issues from this past year, I was reminded of an article in their July 19 issue that brought together a discussion of the brain and mathematics with particular emphasis on the effectiveness of employing the sometimes counter-intuitive notion of the infinity of the real numbers. The content of the article, […]

Structure, structure and more structure

I was expecting to write about a paper I found recently by Oran Magal, a post doc at McGill University, On the mathematical nature of logic. I was attracted to the paper because the title was followed by the phrase Featuring P. Bernays and K. Gödel

I’m often intrigued […]