A few recent items of interest:

- Martin Greiter has put together a written version of Sidney Coleman’s mid-1990s lecture Quantum Mechanics in Your Face, based on a recording of one version of the lecture and copies of Coleman’s slides.
It’s often claimed that leading physicists of Coleman’s generation were educated in and stuck throughout their careers to a “shut up and calculate” approach to the interpretation of quantum mechanics. Coleman’s lecture I believe gives a much better explanation of the way he and many others thought about the topic. In particular, Coleman makes the crucial point:

The problem is not the interpretation of quantum mechanics. That’s getting things just backwards. The problem is the interpretation of classical mechanics

He ends with the following approach to the measurement problem:

Now people say the reduction of the wave packet occurs because it looks like the reduction of the wave packet occurs, and that is indeed true. What I’m asking you in the second main part of this lecture is to consider seriously what it would look like if it were the other way around—if all that ever happened was causal evolution according to quantum mechanics. What I have tried to convince you is that what it looks like is ordinary everyday life.

While some might take this and claim Coleman as an Everettian, note that there’s zero mention anywhere of many-worlds. Likely he found that an empty idea that explains nothing, so not worth mentioning.

- For the past year the CMSA has been hosting a Math-Science Literature Lecture Series. The talks have typically been excellent surveys of areas of mathematics, given by leading figures in each field. To coordinate with Tsinghua, the talks have often been at 8am here in NYC, and several times the last couple months I’ve made sure to get up early enough to have breakfast while watching one of the talks. All of the ones I’ve seen were very much worth the time, they were the ones given by Edward Witten, Andrei Okounkov, Alain Connes, Arthur Jaffe and Nigel Hitchin. Jaffe’s covered some of the ideas on Euclidean field theory that I’ve been spending a lot of time thinking about. For a more detailed version of his talk I highly recommend this article.
- Peter Scholze has posted at the Xena blog a challenge to those interested in formalizing mathematics and automated theorem proving (or checking): formalize and check the proof of a foundational result in his work with Dustin Clausen on “condensed mathematics”. As part of the challenge, he provides an extensive discussion of the motivation and basic ideas of this subject, which attempts to provide a replacement (with better properties) for the conventional definition of a topological space.
Spending a little time reading this and some of the other expositions of the subject convinced me this is a really thorny business. Scholze explains in detail his motivation for making the challenge in part 6 of the posting. My suspicion has always been that most of the value of computer theorem checking lies in forcing a human to lay out clearly and unambiguously the details of an argument, with that effort likely to make clear if there’s a problem with the theorem. It will be fascinating to see what comes of this project.

I see there’s also a blog posting about this at the n-category cafe.

- On the topic of theorems that definitely don’t have a clear and unambiguous proof, supposedly PRIMS will be publishing Mochizuki’s IUT papers in 2021. Mochizuki and collaborators have a new paper claiming stronger versions of Mochizuki’s results.