When writing the last column I expected that the topic of this one would be the relaunch of the New Zealand Journal of Mathematics, but unusual circumstances have delayed the relaunch, which is still expected to happen by the end of 2019. The NZJM is a classic example of a scholar-run journal with almost zero budget, subsidised easily by universities and the NZMS because its costs are so low. An argument often made by vested interests in the publishing industry is that high quality journals are expensive (many journals make income of thousands of dollars per published paper). A recent study (fittingly published as a PeerJ preprint) shows that US$200 per paper should be an upper bound.

I have spent some time on Twitter recently, but not for mathematical purposes (I run the accounts @oa_math and @freejournalnet). A substantial number of mathematicians have Twitter accounts, although many seem to use them more for political purposes than to discuss mathematics (for example, Ian Stewart (@JoatStewart) and even Timothy Gowers (@wtgowers) who has been using it for less than a year, after the demise of Google+ necessitated another forum.) This list of mathematicians on Twitter is a useful starting point.

Of course there is a large representation of experts in public outreach, such as Steven Strogatz (@stevenstrogatz), Hannah Fry (@FryRsquared), Marcus du Sautoy (@marcusdusautoy). Interesting feeds relating to the politics of academia include those by Izabella Laba @ilaba.

Some other accounts that caught my eye and focus more on mathematics include: Numberphile (@numberphile) from MSRI (there is also a Youtube channel and other resources at https://www.numberphile.com/) and Fermat’s Library (@fermatslibrary). These channels are focused more at the undergraduate level. Research-level mathematics is not as well represented. The first mathematical blogger John Carlos Baez has a nice feed at @johncarlosbaez.

The American Mathematical Society (and also London Mathematical Society @LondMathSoc and Australian Mathematical Society @AustMS) are there, but not the New Zealand Mathematical Society yet. The University of Auckland Department of Mathematics is there: @mathsmatter – are any other departments? Antipodean mathematicians I found include Nalini Joshi (@monsoon0) and our own Steven Galbraith (@EllipticKiwi).

Twitter of course has its downsides. The pace at which tweets appear requires a lot of discipline in whom to follow and how to read – at times it is like looking at a library of newspapers but only reading the headlines. This goes against the traditions of mathematics. The 140 (now 280) character limit favours concision. LaTeX is not yet supported; mathematical formulae can be embedded as pictures if necessary. Perhaps the medium is simply not (yet) well adapted for mathematicians. Will we ever see Terence Tao on Twitter? Somehow I doubt it. But overall I think it is worth exploring, and I welcome feedback from readers (if I have any – at least on Twitter I can get some idea about that).

We finish with some brief notes that may help to feed your procrastination.

- Youtube has a lot of mathematically related content which I may survey in future. I have dipped my toes in by recording some (I claim) high-quality lectures at Stage 2 level: https://www.youtube.com/c/MarkCWilson
- Proof assistants are not just useful for proving things we already believe to be obvious: “Sébastien Gouëzel, when formalising Vladimir Shchur’s work on bounds for the Morse Lemma for Gromov-hyperbolic spaces, found an actual inequality which was transposed at some point causing the proof (which had been published in 2013 in J. Funct. Anal., a good journal) to collapse. Gouëzel then worked with Shchur to find a new and correct (and in places far more complex) argument, which they wrote up as a joint paper.”

https://mathoverflow.net/questions/291158/proofs-shown-to-be-wrong-after-formalization-with-proof-assistant/312661#312661 - Karen Uhlenbeck became the first female winner (out of 20 so far) of the Abel Prize. https://www.quantamagazine.org/karen-uhlenbeck-uniter-of-geometry-and-analysis-wins-abel-prize-20190319/
- If you are interested in showing the human diversity of mathematicians, the Instagram account https://www.instagram.com/_forall/ may be useful.
- I found the reminiscences by a student (Thomas Hales) of Langlands https://arxiv.org/pdf/1906.11358.pdf very interesting.