Gowers's Weblog (original) (raw)
Announcing an automatic theorem proving project
April 28, 2022
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 to take on up to about three PhD students and two postdocs over the next couple of years. I am imagining that two of the PhD students will start next October and that at least one of the postdocs will start as soon as is convenient for them. Before any of these positions are advertised, I welcome any informal expressions of interest: in the first instance you should email me, and maybe I will set up Zoom meetings. (I have no idea what the level of demand is likely to be, so exactly how I respond to emails of this kind will depend on how many of them there are.)
I have privately let a few people know about this, and as a result I know of a handful of people who are already in Cambridge and are keen to participate. So I am expecting the core team working on the project to consist of 6-10 people. But I also plan to work in as open a way as possible, in the hope that people who want to can participate in the project remotely even if they are not part of the group that is based physically in Cambridge. Thus, part of the plan is to report regularly and publicly on what we are thinking about, what problems, both technical and more fundamental, are holding us up, and what progress we make. Also, my plan at this stage is that any software associated with the project will be open source, and that if people want to use ideas generated by the project to incorporate into their own theorem-proving programs, I will very much welcome that.
Posted in complexity, Computing, Demystifying proofs, News, polymath | 57 Comments »
Leicester mathematics under threat again
January 30, 2021
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 the previous debacle. This time, the plan, known by the nice fluffy name Shaping for Excellence, is to get rid of research in certain subjects of which pure mathematics is one (and medieval literature another). This would mean making all eight pure mathematicians at Leicester redundant. The story is spreading rapidly on social media (it’s attracted quite a bit of attention on Twitter, Reddit and Hacker News, for example), so I won’t write a long post. But just in case you haven’t heard about it, here’s a link to a petition you can sign if, like a lot of other people, you feel strongly that this is a bad decision. (At the time of writing, it has been signed by about 2,500 people, many of them very well known academics in the areas that Leicester University claims to be intending to promote, in well under 24 hours.)
Posted in Uncategorized | 12 Comments »
Mathematical Research Reports: a “new” mathematics journal is launched
May 20, 2020
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 and collective memory of the original journal, and the other keeping the name and the publisher. Which is the “true” successor? In practice it tends to be the one with the editors, with its sibling surviving as a zombie journal that is the successor in name only. Perhaps there are examples that go the other way, and there may be examples where both journals go on to thrive, but I have not looked closely at the examples I know about.
I’m mentioning this because recently I have been involved in a rather unusual example of this phenomenon. Most cases I know of are the result either of frustration with the practices of the big commercial publishers or of malpractice by an editor-in-chief. But this was an open access journal with no publication charges, and with an extremely efficient and impeccably behaved editor-in-chief. So what was the problem?
The journal started out in 1995 as Electronic Research Announcements of the AMS, or ERA-AMS for short. It was still called that when I first joined the editorial board. Its editor-in-chief was Svetlana Katok, who did a great job, and there was a high-powered editorial board. As its name suggests, it specialized in shortish papers announcing results that would then appear with more details in significantly longer papers, so it was a little like Comptes Rendus in its aim. It would also accept short articles of a more traditional kind.
It never published all that many papers, and in 2007, I think for that reason (but don’t remember for sure), the AMS decided to discontinue it. But Svetlana Katok had put a lot into the journal and managed to find another publisher, the American Institute of Mathematical Sciences, and the editorial board agreed to continue serving. The name of the journal was changed to Electronic Research Announcements in the Mathematical Sciences, and its abbreviation was slightly abbreviated from ERA-AMS to ERA-MS.
In 2016, after 22 years, Svetlana Katok decided to step down, and Boris Hasselblatt took over. It was a good moment to try to revitalize the journal, so measures were taken such as designing a new and better website and making more effort to publicize the journal, in the hope of attracting more submissions (or more precisely, more submissions of a high enough quality that we would want to publish them).
However, despite these measures, the numbers remained fairly low — around ten a year (with quite a bit of variation), and this, indirectly, caused the problem that led to the split. The editors would have liked to see more papers published, but were not worried about it to the point where we would have been prepared to sacrifice quality to achieve it: we were ready to accept that this was, at least for now, a small journal. But AIMS was not so happy. In an effort to remedy (as they saw it) the situation, they appointed a co-editor-in-chief, who in turn appointed a number of new editors, with a more applied focus, with the idea that by broadening the scope of the journal they would increase the number of papers published.
That did not precipitate the resignations, but at that stage most of us did not know that the new editors had been appointed without any consultation even with Boris Hasselblatt. But then AIMS took things a step further. Until that point, the journal had adopted a practice that I strongly approve of, which was for the editor who handled a paper to make a recommendation to the rest of the editorial board, with other editors encouraged to comment on that recommendation. This practice helps to guard against “rogue” editors and against abuse of the system in general. It also helps to maintain consistent standards, and provides a gentle pressure on editors to do their job conscientiously — there’s nothing like knowing that you’re going to have to justify your decision to a bunch of mathematicians.
But suddenly the publishers told us that this system had to change, and that from now on the editorial board would not have the opportunity to vet papers, and would continue to have no say in new editorial appointments. (Various justifications were given for this, including that it would make it harder to recruit editors if they thought they had to make judgments about papers not in their immediate area.) At that point, it was clear that the soul of the journal was about to be destroyed, so over a few days the entire board (from before the start of the changes) resigned, resolving to start afresh with a new name.
That new name is Mathematical Research Reports. We will continue to accept reports on longer work, as well as short articles. In addition we welcome short survey articles. We regard it as the continuation in spirit of ERA-MS. Another unusual feature of this particular split is that the other half, still published by AIMS, has also changed its name and is now called Electronic Research Archive.
If, like me, you are always on the lookout for high-quality “ethical” journals (which I loosely define as free to read, free to publish in, and adopting high standards of editorial practice), then please add Mathematical Research Reports to your list. Have a look at the back catalogue of ERA-MS and ERA-AMS and you will get an idea of our standards. It would be wonderful if the unfortunate events of the last year or so were to be the catalyst that led to the journal finally becoming established in the way that it has deserved to be for a long time.
Posted in News | 12 Comments »
How long should a lockdown-relaxation cycle last?
March 28, 2020
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 serious enough to cause the number of cases to decline, and more relaxed measures that allow it to grow again. They call this adaptive triggering: when the number of cases needing intensive care reaches a certain level per week, the stronger measures are triggered, and when it declines to some other level (the numbers they give are 100 and 50, respectively), they are lifted.
If such a policy were ever to be enacted, a very important question would be how to optimize the choice of the two triggers. I’ve tried to work this out, subject to certain simplifying assumptions (and it’s important to stress right at the outset that these assumptions are questionable, and therefore that any conclusion I come to should be treated with great caution). This post is to show the calculation I did. It leads to slightly counterintuitive results, so part of my reason for posting it publicly is as a sanity check: I know that if I post it here, then any flaws in my reasoning will be quickly picked up. And the contrapositive of that statement is that if the reasoning survives the harsh scrutiny of a typical reader of this blog, then I can feel fairly confident about it. Of course, it may also be that I have failed to model some aspect of the situation that would make a material difference to the conclusions I draw. I would be very interested in criticisms of that kind too. (Indeed, I make some myself in the post.)
Before I get on to what the model is, I would like to make clear that I am not advocating this adaptive-triggering policy. Personally, what I would like to see is something more like what Tomas Pueyo calls The Hammer and the Dance: roughly speaking, you get the cases down to a trickle, and then you stop that trickle turning back into a flood by stamping down hard on local outbreaks using a lot of testing, contact tracing, isolation of potential infected people, etc. (This would need to be combined with other measures such as quarantine for people arriving from more affected countries etc.) But it still seems worth thinking about the adaptive-triggering policy, in case the hammer-and-dance policy doesn’t work (which could be for the simple reason that a government decides not to implement it).
Read the rest of this entry »
Posted in News | 55 Comments »
Advances in Combinatorics fully launched
October 30, 2019
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, which is that its very small running costs (like Discrete Analysis, it uses the Scholastica platform, which charges 10persubmission,aswellasafixedannualchargeof10 per submission, as well as a fixed annual charge of 10persubmission,aswellasafixedannualchargeof250, and there are a few other costs such as archiving articles with CLOCKSS and having DOIs) are being met, for the next five years in the first instance, by the library of Queens University in Kingston Ontario, who are also providing us with very useful administrative support. My dream would be for other libraries to have the foresight to support similar ventures, since the potential for savings if the stranglehold of the big commercial publishers is broken is huge. I do not underestimate the obstacles, but for a long time I have felt that what we are waiting for is a tipping point, and even quite a small venture can in principle have a significant effect on when that tipping point occurs.
The aim of Advances in Combinatorics is to be a top specialist combinatorics journal. Information about the editorial board, the submission process, and of course the articles themselves, can all be found on the website. Like Discrete Analysis, the journal has Editorial Introductions to each article, with the aim of making the webpage informative and fun to browse. We will be grateful for any feedback, and even more grateful for support in the form of excellent combinatorics papers while we are still getting established.
A final remark is that although I have reached the limit of the number of journals of this type that I can be closely involved in, I would be delighted to hear from anybody who thinks that they can put together a high-quality editorial board in an area that does not have a suitable journal for people who want to publish good papers without supporting the big commercial publishers. I know people who can offer advice about suitable platforms, funding, and similar matters. It would be great if free-to-read free-to-publish journals could cover all of mathematics, but we are still a long way from that at the moment.
Posted in News | 15 Comments »
The fate of combinatorics at Strathclyde
June 19, 2019
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 best served by axing discrete mathematics. I won’t write a long post about this, but instead refer you to a post by Peter Cameron that says everything I would want to say about the decision, and does so extremely cogently. I recommend that you read it if this kind of decision worries you.
Posted in News | 7 Comments »
Voting tactically in the EU elections
May 21, 2019
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 you have other priorities, then the general principles laid out here may be helpful, but the examples of how to apply them will not necessarily be appropriate to your particular concerns.
What is the voting system?
The system used is called the d’Hondt system. The country is divided into a number of regions, and from each region several MEPs will be elected. You get one vote, and it is for a party rather than a single candidate. Once the votes are in, there are a couple of ways of thinking about how they translate into results. One that I like is to imagine that the parties have the option of assigning their votes to their candidates as they wish, and once the assignments have been made, the 
For example, if there are three parties for four places, and their vote shares are 50%, 30% and 20%, then the first party will give 25% to two candidates and both will be elected. If the second party tries a similar trick, it will only get one candidate through because the 20% that goes to the third party is greater than the 15% going to the two candidates from the second party. So the result is two candidates for the first party, one for the second and one for the third.
If the vote shares had been 60%, 25% and 15%, then the first party could afford to split three ways and the result would be three seats for the first party and one for the second.
Read the rest of this entry »
Posted in News | 17 Comments »
How Craig Barton wishes he’d taught maths
December 22, 2018
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 to take a number of aspects of teaching for granted, until he looked into the mathematics-education literature and came to realize that many of his cherished beliefs were completely wrong. Since I’ve always been interested in the question of how best to teach mathematics, both because of my own university teaching and because from time to time I like to pontificate about school-level teaching, I decided to order the book. More surprisingly, given my past history of buying books that I felt I ought to read, I read it from cover to cover, all 450 pages of it.
As it happens, the book is ideally designed for people who don’t necessarily want to read it from cover to cover, because it is arranged as follows. At the top level it is divided into chapters. Each chapter starts with a small introduction and thereafter is divided into sections. And each section has precisely the same organization: it is divided into subsections entitled, “What I used to believe”, “Sources of inspiration”, “My takeaway”, and “What I do now”. These are reasonably self-explanatory, but just to spell it out, the first subsection sets out a plausible belief that Craig Barton used to have about good teaching practice, often ending with a rhetorical question such as “What could possibly be wrong with that?”, the second is a list of references (none of which I have yet followed up, but some of them look very interesting), the third is a discussion of what he learned from the references, and the last one is about how he put that into practice. Also, each chapter ends with a short subsection entitled “If I only remember three things …”, where he gives three sentences that sum up what he thinks is most important in the chapter.
Read the rest of this entry »
Posted in Mathematical pedagogy | 23 Comments »
Taylor and Francis doing Trump’s dirty work for him
December 9, 2018
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 explaining that “following internal sanctions process checks” the article could not after all be published because one of them was based in Iran.
I don’t know what the legal consequences would have been if Taylor and Francis had simply gone ahead and published, but my hunch is that they are being unduly cautious. I wonder if they turned down any papers by Russian authors after the invasion of Ukraine.
This is not an isolated incident. An Iranian PhD student who applied for funding to go to a mathematics conference in Rome was told that “we are unable to provide financial support for Iranians due to administrative difficulties”.
I’m not sure what one can do about this, but at the very least it should be generally known that it is happening.
Update. Taylor and Francis have now reversed their decision.
Posted in News | 45 Comments »
Worrying news from Turkey
November 16, 2018
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 of any petitions for their release, but if they are not released very quickly I hope that there will be a strong reaction. The EMS has issued the following statement.
The European Mathematical Society is outraged at the news that the Turkish police have detained, in Istanbul on the morning of 16th November 2018, Professor Betül Tanbay, a member of the EMS Executive Committee. We are incredulous at the subsequent press release from the Istanbul Security Directorate accusing her of links to organized crime and attempts to topple the Turkish government.
Professor Tanbay is a distinguished mathematician and a Vice President Elect of the European Mathematical Society, due to assume that role from January 2019. We have known her for many years as a talented scientist and teacher, a former President of the Turkish Mathematical Society, an open-minded citizen, and a true democrat. She may not hesitate to exercise her freedom of speech, a lawful right that any decent country guarantees its citizens, but it is preposterous to suggest that she could be involved in violent or criminal activities.
We demand that Professor Tanbay is immediately freed from detention, and we call on the whole European research community to raise its voice against this shameful mistreatment of our colleague, so frighteningly reminiscent of our continent’s darkest times.
Update. I have just seen this on Twitter:
Police freed 8 people, incl. professors Turgut Tarhanli and Betul Tanbay, while barring them from overseas travel, & is still questioning 6 others
Posted in News | 7 Comments »