Mathematics related discussions
For the sake of anyone who might read this blog post in the distant future (a month from now, say), let me mention that I am writing it a few days after OpenAI announced that it had solved ten major problems in mathematics and theoretical computer science, including the first construction of a non-sofic group, [ ]
Last September I went to a workshop at the Lorentz Centre in Leiden to discuss mathematics and AI with historians, philosophers, computer scientists, AI researchers, and mathematicians of several different flavours (though there was a surprising preponderance of algebraic geometers). The whole event was extremely stimulating, with some talks but also a lot of time [ ]
We are all having to keep revising upwards our assessments of the mathematical capabilities of large language models. I have just made a fairly large revision as a result of ChatGPT 5.5 Pro, to which I am fortunate to have been given access, producing a piece of PhD-level research in an hour or so, with [ ]
An Artin-Tits group is a group with a finite set of generators in which every relation is of the form or for some positive integer , where and are two of the generators. In particular, the commutation relation is allowed (it is the case of the first type of relation) and so is the braid [ ]
It s been over three years since my last post on this blog and I have sometimes been asked, understandably, whether the project I announced in my previous post was actually happening. The answer is yes the grant I received from the Astera Institute has funded several PhD students and a couple of postdocs, and [ ]
I am very happy to say that I have recently received a generous grant from the Astera Institute to set up a small group to work on automatic theorem proving, in the first instance for about three years after which we will take stock and see whether it is worth continuing. This will enable me [ ]
Four years ago I wrote a post about an awful plan by Leicester University to sack its entire mathematics department, invite them to reapply for their jobs, and rehire all but six lowest performers . Fortunately, after an outcry, the university backed down. Alas, now there s a new vice-chancellor who appears to have learned nothing from [ ]
From time to time academic journals undergo an interesting process of fission. Typically as a result of some serious dissatisfaction, the editorial board resigns en masse to set up a new journal, the publishers of the original journal build a new editorial board from scratch, and the result is two journals, one inheriting the editors [ ]
The adaptive-triggering policy. On page 12 of a document put out by Imperial College London, which has been very widely read and commented on, and which has had a significant influence on UK policy concerning the coronavirus, there is a diagram that shows the possible impact of a strategy of alternating between measures that are [ ]
It s taken longer than we originally intended, but I am very happy to report that Advances in Combinatorics, a new arXiv overlay journal that is run along similar lines to Discrete Analysis, has just published its first five articles, with plenty more in the pipeline. I am excited by the business model of the journal, [ ]
I have just received an email from Sergey Kitaev, one of the three combinatorialists at Strathclyde. As in many universities, they belong not to the mathematics department but to the computer science department. Kitaev informs me that the administrators of that department, in their infinite wisdom, have decided that the future of the department is [ ]
This post is addressed at anyone who is voting in Great Britain in the forthcoming elections to the European Parliament and whose principal aim is to maximize the number of MEPs from Remain-supporting parties, where those are deemed to be the Liberal Democrats, the Greens, Change UK, Plaid Cymru and the Scottish National Party. If [ ]
A couple of months ago, I can t remember precisely how, I became aware of a book called How I Wish I d Taught Maths, by Craig Barton, that seemed to be highly thought of. The basic idea was that Craig Barton is an experienced, and by the sound of things very good, maths teacher who used [ ]
The following story arrived in my email inbox (and those of many others) this morning. Apparently a paper was submitted to the Taylor and Francis journal Dynamical Systems, and was accepted. The published version was prepared, and it had got to the stage where a DOI had been assigned. Then the authorS received a letter [ ]
One should of course be concerned when anybody is detained for spurious reasons, but when that person is a noted mathematician, the shock is greater. Six academics have recently been detained in Turkey, of whom one, Betül Tanbay, is due to become vice president of the European Mathematical Society in January. I do not know [ ]
This is a bit of a niche post, since its target audience is people who are familiar with quasirandom graphs and like proofs of an analytic flavour. Very roughly, a quasirandom graph is one that behaves like a random graph of the same density. It turns out that there are many ways that one can [ ]
First, I d like to thank the large number of commenters on my previous post for keeping the discussion surprisingly calm and respectful given the topic discussed. In that spirit, and to try to practise the scientific integrity that I claimed to care about, I want to acknowledge that my views about the paper have changed [ ]
Update to post, added 11th September. As expected, there is another side to the story discussed below. See this statement about the decision by the Mathematical Intelligencer and this one about the decision taken by the New York Journal of Mathematics. Further update, added 15th September. The author has also made a statement. I was [ ]
This post is to announce that a new journal, Advances in Combinatorics, has just opened for submissions. I shall also say a little about the journal, about other new journals, about my own experiences of finding journals I am happy to submit to, and about whether we are any nearer a change to more sensible [ ]
It has been in the news recently or rather, the small corner of the news that is of particular interest to mathematicians that Maryanthe Malliaris and Saharon Shelah recently had an unexpected breakthrough when they stumbled on a proof that two infinities were equal that had been conjectured, and widely believed, to be [ ]
While Polymath13 has (barring a mistake that we have not noticed) led to an interesting and clearly publishable result, there are some obvious follow-up questions that we would be wrong not to try to answer before finishing the project, especially as some of them seem to be either essentially solved or promisingly close to a [ ]
There is widespread (even if not universal) agreement that something is deeply wrong with the current system of academic publishing. The basic point, which has been made innumerable times by innumerable people, is that the really hard parts the writing of papers, and the peer review and selection of the ones to publish [ ]
I have now completed a draft of a write-up of a proof of the following statement. Recall that a random -sided die (in the balanced-sequences model) is a sequence of length of integers between 1 and that add up to , chosen uniformly from all such sequences. A die beats a die if the number [ ]
It has become clear that what we need in order to finish off one of the problems about intransitive dice is a suitable version of the local central limit theorem. Roughly speaking, we need a version that is two-dimensional that is, concerning a random walk on and completely explicit that is, giving [ ]
I hope, but am not yet sure, that this post is a counterexample to Betteridge s law of headlines. To back up that hope, let me sketch an argument that has arisen from the discussion so far, which appears to get us close to showing that if and are three -sided dice chosen independently at random [ ]