I didn’t know anything about topology before I entered graduate school, but I continue to see it as one of the more provocative specialties in mathematics and an important transition of thought. Most definitions of the subject describe it as the study of the properties of objects that are preserved through deformations like stretching and […]
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I was struck today by the title of an article in Science News that read, Before his early death, Riemann freed geometry from Euclidean prejudices. The piece, by science writer Tom Siegfried, was no doubt inspired by the recent claim from award-winning mathematician Michael Atiyah that he has proved the long standing Riemann hypothesis, one […] I’m not completely sure I understand where my desire to grasp the value of abstractions is taking me, but as I think about mathematics, and more recent trends in the sciences, I keep wanting to get further and further behind what our symbolic reasoning is actually doing, and how it’s doing it. I have this […] We all generally know the meaning of abstraction. We all have some opinion, for example, about the value of abstract painting. And I’ve heard from many that mathematics is too abstract to be understood or even interesting. (But I must admit, it is exactly this about mathematics that keeps me so captivated). An abstraction is […] A recent post on scientificamerican.com got my attention – no surprise given its title, Could Multiple Personality Disorder Explain Life, the Universe, and Everything. It was coauthored by three individuals: computer scientist Bernardo Kastrup, Psychotherapist Adam Crabtree, and cognitive scientist Edward F. Kelly. The article’s major source is a paper written by Kastrup, published this […] Earlier this month, Nature reported on Artificial Intelligence (AI) research, where deep learning networks (an AI strategy) spontaneously generated patterns of computations that bore a striking resemblance to the activity generated by our own grey matter – namely by the neurons called grid cells in the mammalian brain. The patterned firing of grid cells enable […] My thoughts started jumping around today, trying to land on what it was that I found so fascinating about a recent article in Quanta Magazine. This is one of the statements that got me going: …Numbers emerging from one kind of geometric world matched exactly with very different kinds of numbers from a very different […] A recent article in Quanta Magazine anticipates the publication of the 6th edition of Proofs from The Book, collected by Martin Aigner and Günter Ziegler. The original volume was inspired by the well-known and prolific mathematician Paul Erdős, who traveled the world, participating in countless collaborative efforts, and who would say of proofs that he […] My attention was just recently brought to the work of philosopher and poet Emily Grosholz. It’s rare to find an individual so steeped in the ways of poetry and mathematics, and the desire to explore how and what they express about us. What I would like to consider here, in this particular post, is really […] I have been particularly concentrated on whether mathematics can tell us something about the nature of thought, something that we have not yet understood about what thought is made from, how it happens, how it is connected to everything else in the universe. These questions inevitably point me in the direction of research in cognitive […] |
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