It happens many times in class that I say, “in mathematics when you see something you don’t know, you try to figure it out using something you do know. And, recently, in the context of thinking about the generalizations that blossomed in late 19th and early 20th century mathematics, I’ve also wondered how it is […]
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For me, one of the more intriguing things that happened in mathematics is what is called the arithmetization of the Calculus. This is not because it contributes to my understanding of fundamental concepts (because it doesn’t). Nor is it because the ideas are exotic (they’re not). I’m captivated, instead, by what it may demonstrate about […] 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 […] The first page of text in Morris Kline’s Mathematics and Western Culture quotes Descartes: …..I was not surprised that many people, even of talent and scholarship, after glancing at these sciences, have either given them up as being empty and childish or, taking them to be very difficult and intricate, been deterred at the very […] |
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