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 […]
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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 […] The extent to which an idea in mathematics creates an idea in science is largely underappreciated. It is common to think of mathematics as the tool that one needs to describe the reality explored by physics, as if the mathematics is secondary, or a purely linguistic consideration. But it should be clear that this is […] When I first became interested in studying mathematics an artist friend of mine expressed his disapproval by characterizing mathematicians as people who made bombs. Although I didn’t know very much mathematics at the time, I knew enough to know that he was wrong. But I was reminded today of one of the ways his mistake […] I listened to three short talks today and found that they had something nice in common – they each show us how sensory experience (often vision) gives rise to mathematics that provides access to what cannot be seen, and clarifies what is seen. The first of these talks was called Symmetry, reality’s riddle presented by […] Unfortunately for us, philosophies of science and mathematics are rarely brought to the attention of individuals who are not engaged in these efforts. Yet, while difficult to access, the views of the world provided by mathematics and science are pregnant with meaningful implications for all of us. I have always been struck by the depth […] |
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