I started today by taking a look at what might be the latest on what cognitive scientists were saying about mathematics. The broad scope of cognitive science includes the investigation of what Mark Turner calls (in the title of one of his books) “the riddle of human creativity.” When exploring the origins of conceptual systems, […]
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I just flipped back and forth between reading about 18th and 19th century developments in mathematics (analysis in particular) and 18th and 19th century transitions in art. The language of art history and the language of math history is very different. It does feel a little like going from color to black and white, or […] Many of this week’s circumstances are limiting the time I have to write but I would like to point to a few sources that contain very nice accounts of what is known as the foundational crisis in mathematics. One of them was written by Paul Bernays in 1935. Understanding the nature of some of the […] Let’s ask again, “What is the nature of the bridge between sense perceptions and concepts? It’s a simple question to ask, but a fairly difficult one to answer. Raphael Nunez contributed a chapter to the Springer book, Recasting Reality: Wolfgang Pauli’s Philosophical Ideas and Contemporary Science. A pdf of the chapter can be found here. […] Cantor once remarked that the essence of mathematics lies entirely in its freedom. And it is this about mathematics that consistently inspires me. But understanding how it finds that freedom, and the relevance or meaning of what it accomplishes with it, is a deep and complex question. And so I would like to go back […] It’s easy to neglect the detail of one person’s, now historic, philosophical discussion of math and science. But there is a moment, in Henri Poincare’s well known text Science and Hypothesis, that I would like to shine a light on today. The first English translation of the book was published in 1905. Chapter IV is […] In the first half of the twentieth century, physicists and mathematicians began to raise questions about what they could say about what they were actually doing. The ‘truth’ of things was beginning to elude the seekers of that truth. Both the validity of mathematical ideas and the objectivity of physics came under scrutiny. Questions about […] I’ve become a bit preoccupied recently with the world of early 20th century mathematicians, partly because of a book I’m working on, but also because of how late 19th and early 20th century thinking largely defines the mathematics students learn today. In this light I found a book of selected writings of Hermann Weyl, a […] Even students of mathematics rarely have the opportunity to explore the kind of thinking that leads to ground-breaking achievements in their discipline. I was struck, very recently, by how students in my calculus class would not likely reflect on how it was possible that the tedious arithmetic they were doing (solving equations involving clumsy fractions […] It isn’t often that the human experience of mathematics is explored in the arts, but it does happen. A Beautiful Mind and Proof are two recent examples of math-related dramas. But it seems that, by many accounts, A Disappearing Number has succeeded in weaving mathematics itself into the mystery of human lives. The play premiered […] |
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