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The Evolution of the Physicist’s Picture of Nature

Reading this Nautilus article about Julian Barbour led me recently to something I don’t think I’ve ever read before, Dirac’s 1963 Scientific American article The Evolution of the Physicist’s Picture of Nature. There is a very famous quote from this article that I’ve often seen: It is more important to have beauty in one’s equations than to have them fit experiment but I was unaware of the context of that quote, in which the...

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Some History

I’m heading out soon for a 10 day vacation in the Rocky Mountains, blogging likely to change from sparse to non-existent for the next couple weeks. I’ve come across the following things that people with an interest in the recent history of mathematics may find worthwhile: S. T. Yau over the past year has organized a series of talks on the recent history of mathematics, featuring prominent people in the subject giving expository...

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Hawking Hawking

There’s a very good new book about Stephen Hawking that just came out, Charles Seife’s Hawking Hawking. Some detailed reviews can be found at Prospect Magazine (Philip Ball) and the New York Review of Books (James Gleick). Seife has chosen to write the story of Hawking’s life starting at the end and ending at the beginning, which takes some getting used to, but provides a different perspective. Hawking was a huge world-wide...

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The God Equation

When I was out for a bike ride yesterday I stopped by a large book store and looked to see if they had a copy of Michio Kaku’s new book The God Equation. They didn’t, but did have plenty of copies for sale of his various previous efforts to promote string theory, such as 1987’s Beyond Einstein, 1994’s Hyperspace and 2005’s Parallel Worlds. If someone interested in fundamental physics walks into a bookstore, and looks in the...

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Twistor Unification

I’ve finally finished writing up a new version of some ideas that I first wrote about here last summer. The latest draft is here, I may set up a web page with more info here. Several people had very helpful comments on what I wrote last summer, especially in pointing out that I wasn’t providing sufficient justification for the most radical claim I was making, that the problems with analytic continuation of spinor fields indicated...

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New Spaces in Mathematics and Physics

Available online today (if your institution is paying…) from Cambridge University Press are two volumes well-worth spending some time with: New Spaces in Mathematics and New Spaces in Physics. These contain write-ups based on a workshop organized back in 2015 by Mathieu Anel and Gabriel Catren, the videos of which are available here. It would be hard to write in any detail about the wealth of material in these volumes, so I’ll...

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ABC is Still a Conjecture

Just a reminder that the abc conjecture is still a conjecture, there is no known valid proof (don’t believe what you might read in an EMS journal). For more about why one attempted proof doesn’t work, see here and here. For extensive background on this, you could start at this blog posting and work backwards, to the first announcement of a claimed proof back in 2012. By 2018 Scholze and Stix had shown that the claimed argument was...

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Yet More Geometric Langlands News

It has only been a couple weeks since my last posting on this topic, but there’s quite a bit of new news on the geometric Langlands front. One of the great goals of the subject has always been to bring together the arithmetic Langlands conjectures of number theory with the geometric Langlands conjectures, which involved curves over function fields or over the complex numbers. Fargues and Scholze for quite a few years now have been...

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What is a Spinor?

Recently Jean-Pierre Bourguignon recently gave the Inaugural Atiyah Lecture, with the title What is a Spinor? The title was a reference to a 2013 talk by Atiyah at the IHES with the same title. Bourguignon’s lecture is not yet online, but I realized there are lectures explaining what a spinor is that I can highly recommend: my own, in this semester’s course on the mathemematics of quantum mechanics. I’m closely following the...