First some mathematics items:

- Igor Shafarevich, one of the great figures of twentieth century algebraic geometry and algebraic number theory, died this past weekend at the age of 93. Besides his many contributions to mathematics research, he was also a remarkably lucid expositor. His two volume Basic Algebraic Geometry is a wonderful introduction to that subject, his survey volume Basic Notions of Algebra emphasizes the connections to geometry, and his volume on number theory (with Borevich) struck the AMS reviewer as “delectable”.
Shafarevich was also known for his religiously-motivated nationalistic views which to many were distressingly anti-Semitic. In the spirit of respect for the recently deceased, I’ll just link to a quite interesting recent discussion (very sympathetic to Shafarevich) of the issue by David Mumford here (and ruthlessly delete attempts to argue about this in the comment section).

- The AMS Notices has a set of articles in honor of Andrew Wiles and his work, which include some great explanations of the mathematics, as well as a long in-depth interview.
- For another detailed interview with a mathematician, see Quanta magazine for a piece by Siobhan Roberts about Sylvia Serfaty of the Courant Institute.

On the physics front, there’s:

- For his contribution to the Why Trust a Theory? conference (see here and here), Helge Kragh has a new paper which examines the question of whether history of science can help evaluate recent claims about the need to change the way theories are assessed. He sees in the unsuccessful “vortex theory” of the late nineteenth century an analog of string theory, with many of the same claims and justifications for lack of success. He quotes as a typical example of the enthusiasm of the time:

I feel that we are so close with vortex theory that – in my moments of greatest optimism – I imagine that any day, the final form of the theory might drop out of the sky and land in someone’s lap. But more realistically, I feel that we are now in the process of constructing a much deeper theory of anything we have had before and that … when I am too old to have any useful thoughts on the subject, younger physicists will have to decide whether we have in fact found the final theory!

but then explains that this is actually a quote from Witten, with “string” replaced by “vortex”.

- Scientific American this month has an article (also available here) about the problems with the theory of inflation. The authors end by pointing out the dangers to science of multiverse inflationary scenarios (which they call the “multimess”):

Some scientists accept that inflation is untestable but refuse to abandon it. They have proposed that, instead, science must change by discarding one of its defining properties: empirical testability. This notion has triggered a roller coaster of discussions about the nature of science and its possible redefinition, promoting the idea of some kind of nonempirical science.

A common misconception is that experiments can be used to

*falsify*a theory. In practice, a failing theory gets increasingly immunized against experiment by attempts to patch it. The theory becomes more highly tuned and arcane to fit new observations until it reaches a state where its explanatory power diminishes to the point that it is no longer pursued. The explanatory power of a theory is measured by the set of possibilities it excludes. More immunization means less exclusion and less power. A theory like the multimess does not exclude anything and, hence, has zero power. Declaring an empty theory as the unquestioned standard view requires some sort of assurance outside of science. Short of a professed oracle, the only alternative is to invoke authorities. History teaches us that this is the wrong road to take. - Nautilus has an article by Juan Collar about the increasing skepticism about Wimps as dark matter candidates, and the interest in alternatives.

**Update**: With results from the full 13 TeV dataset just a few weeks away, SUSY enthusiasts have given up hope for the LHC. A new paper just out argues that pre-LHC claims that naturalness + SUSY implied a gluino mass upper bound of 350 GeV (the latest LHC limits are more like 1900 GeV, likely to go up next month) were misguided. According to these authors, the right number for the upper bound is 5200 GeV and the “HE-LHC with [cm energy] 33 TeV is required to either discover or falsify natural SUSY”. So, claims that the LHC could falsify natural SUSY are no longer operative now that it has done so by earlier metrics, and such discovery or falsification is still just around the corner. All that’s needed is to rebuild the LHC into a higher energy version (that’s what the HE-LHC proposal is, may take a while…).

**Update**: Another excellent article by Natalie Wolchover at Quanta, this time about progress in studying conformal quantum field theories in higher dimensions (above 2). Definitely one of the more interesting things going on in theory at the moment. The reference in the subtitle to “geometry underlying all quantum theories” I don’t think though is really justified, this is really just about conformal field theories.

There’s probably lots more to be learned about these, with this conformal symmetry still not fully exploited. I’m somewhat fond of the point of view that you really shouldn’t try and think of QFTs just as effective theories for some different physics at short distances. Rather, what might be going on at short distances is not some new kind of theory at the cutoff scale, but a conformal theory valid at all scales.

**Update**: From the comments, unfortunately two other deaths to report, those of Bert Kostant (I’ve written something here) and Ludwig Faddeev.