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Interesting Esoterica Summation, volume 5
Whoah there, traveller! Time for a break. Unhitch your wagon from the locomotive of Progress and roll into the railway siding of Idle Curiosity. I’ve got some more interesting esoterica for you.
In case you’re new to this: every now and then I encounter a paper or a book or an article that grabs my interest but isn’t directly useful for anything. It might be about some niche sub-sub-subtopic I’ve never heard of, or it might talk about something old from a new angle, or it might just have a funny title. I put these things in my Interesting Esoterica collection on Mendeley. And then when I’ve gathered up enough, I collect them here.
In this post the titles are links to the original sources, and I try to add some interpretation or explanation of why I think each thing is interesting below the abstract.
Some things might not be freely available, or even available for a reasonable price. Sorry.
Katie Steckles interviewed on mathblogging.org
Tip-top maths blog review site mathblogging.org has been running a series of interviews with maths bloggers. I think all three of the Aperiodical triumvirate have taken part, but Katie’s answers were published today. She said some things that made me feel unexpectedly positive about this site, so I’m happy.
I’m sure mine and Peter’s responses will appear in due course. Meanwhile, interviews with Igor Carron, Izabella Laba, Samuel Hansen, David Wees and Christian P. Robert are already online and worth reading.
Henry Segerman’s 30-cell puzzle
Henry Segerman is a mathematician at the University of Melbourne with a keen interest in 3d-printing mathematical shapes. He’s just uploaded a video showing off his latest creation, a 30-cell burr puzzle created in collaboration with Saul Schleimer:
[youtube url=https://www.youtube.com/watch?v=FJwqT_sbB_A]
Pretty cool, eh?
As well as providing a PDF describing the puzzle, Henry’s uploaded the design to Shapeways so you can have your very own copy to play with.
Earlier this year, Henry and Saul’s half 120- and 600-cells won the “Best Use of Mathematics” award at the 2012 Bridges Conference.
Probabilitelly
On the 18th of October BBC Four is going to broadcast a programme called Tails You Win: The Science of Chance, presented by Prof David Spiegelhalter, as part of its Big Science series.
Here’s the BBC’s description:
Smart and witty, jam-packed with augmented-reality graphics and fascinating history, this film, presented by Professor David Spiegelhalter, tries to pin down what chance is and how it works in the real world. For once this really is ‘risky’ television ((I’m going to guess this sentence is what clinched the commission – CP)).
The film follows in the footsteps of The Joy of Stats, which won the prestigious Grierson Award for Best Science/Natural History programme of 2011. Now the same blend of wit and wisdom, animation, graphics and gleeful nerdery is applied to the joys of chance and the mysteries of probability, the vital branch of mathematics that gives us a handle on what might happen in the future. Professor Spiegelhalter is ideally suited to that task, being Winton Professor of the Public Understanding of Risk at Cambridge University, as well as being a recent Winter Wipeout contestant on BBC TV.
Proof News
Here’s a little catch-up with the status of the claimed proofs of some big statements that were announced recently.
At the end of August, Shin Mochizuki released what he claims is a proof of the abc conjecture (link goes to a PDF). Barring someone spotting a huge error, it’s going to take a long time to verify. It’s mainly quiet at the moment, apart from a claimed set of counterexamples to one of Mochizuki’s intermediate theorems posted by Vesselin Dimitrov on MathOverflow, which was quickly shut down because the community there didn’t approve of MO being used to debate the validity of the proof. No doubt there are other niggles being worked out in private as well.
At the start of September, Justin Moore uploaded to the arXiv what he claimed was a proof that Thompson’s group F is amenable. Like Mochizuki’s abc proof, experts thought Moore’s proof was highly credible. We were waiting for my chum Nathan to write about it, since his PhD was all about Thompson’s groups F and V, but it turns out we don’t need to: at the start of this week, Justin retracted his paper because of an error which “appears to be both serious and irreparable”. The amenability of Thompson’s group F has been proven and disproven many times, so I still want Nathan to tell me (and you) all about it.
In lighter news, via Richard Green on Google+, recent uploads to the arXiv show that Goldbach’s conjecture and the Riemann hypothesis are true. I’d love to know how it feels to upload a six-page paper which you know proves something like the Riemann hypothesis. It must be a lovely state of mind. Certainly much better than what people like Moore and Mochizuki must go through, waiting for the first email to arrive telling them they’ve made a terrible mistake and their work is not yet complete.
If I’ve inspired you to have a go yourself, look at Wikipedia’s list of unsolved problems in mathematics and take a crack at one this weekend. Can’t hurt ((Disclaimer: depending on levels of ability, perseverance and agreement with consensus reality, attempts to solve these problems may well ruin your life)) to try!
Elsevier has made lots more maths articles free to access
Elsevier has just announced in its third open letter to the mathematics community (how much does that sound like a Papal Bull?) that all of the archived material from its “primary mathematics journals” is now free to access.
This completes the process begun in April, when they made everything published after 1995 and before 2008 free. From now on, all articles in the affected journals will be made free to access four years after publication ((Sadly, because this is Elsevier, the articles are only available through the user-contemptuous ScienceDirect, so the incidence of heads being banged on desks is likely to go up once people start trying to access it and encountering the site’s maddeningly hyperactive sliding toolbars)). The journals involved include Advances in Mathematics, Discrete Mathematics, and the Journal of Algebra. It looks like each journal now has a prominent “Open Archive” section on its homepage, containing a list of recently dispaywalled articles.