Mathematics Rising

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 by disputes over whether mathematics can [...]

I’d like today to stay on the topic of mathematics from the cognitive science perspective, and in particular, to make available another set of interesting studies summarized by C. R. Gallistel, Rochel Gelman and Sara Cordes. The studies are described in their contribution to the book Evolution and Culture (edited by Stephen C. Levinson and [...]

I saw an opinion piece by Stephen Ornes, in the March 16 issue of New Scientist which ties the ongoing debate about the nature of mathematical ideas, to a modern one about money and ownership.  Ornes argues that patentability is one of the most hotly contested issues in software development.  The problem, as many see [...]

I’m intrigued by Max Tegmark’s conviction that the universe is, itself, a mathematical structure.  He presented his ideas, again, on February 15 at the recent annual meeting of AAAS, in a symposium called Is Beauty Truth? He said that he has just completed a book on the same topic.  I listened to the entire session [...]

I have always been intrigued by the extraordinary insights of the self-taught mathematician Srinivasa Ramanujan.  He worked in almost complete isolation from the mathematical community, and independently rediscovered many existing results while also making his own unique contributions.   He didn’t even share notation with the rest of the community, somehow finding his way without being [...]

I have recently spent some time sorting out the points Arkady Plotnitsky makes about the significance of Riemann’s notion of manifold (or manifoldness) in his paper which appeared in the journal Configurations in 2009.  The paper has the title Bernhard Riemann’s Conceptual Mathematics, and the Idea of Space.  It is refreshing in that it considers [...]

Julian Barbour is a theoretical physicist with a clear interest in tackling foundational issues and the errors of judgment that can lead physics theories astray.  One of these candidates for a mistaken judgment is time itself, and in 1999  Barbour authored the book The End of Time published by the Oxford University Press. He wrote [...]

Leibniz disassociated ‘substance’ from ‘material’ and reasoned that the world was not fundamentally built from material.  His is not simple or familiar reasoning but it was clear to Leibniz that for a substance to be real, it had to be indivisible and since matter was infinitely divisible, the true nature of reality could not be [...]

Yesterday I happened upon a Huffington Post blog from Mario Livio. For anyone who has been following my blog, it will come as no surprise that this piece, about the surprising similarity between spider webs and computer generated cosmic webs, caught my attention.  After showing us a few, Livio says: For an astrophysicist, perhaps the [...]

Three things I read today converged in a way I had not anticipated and they all had something to do with truth.  First, there was the announcement of the Foundational Questions Institute’s 4th essay contest.  Entrants are invited to address this topic: Which of Our Basic Physical Assumptions Are Wrong?  Scientific American is a cosponsor [...]