A little more than a month ago, we started this blog. It has grown a lot faster than we could have ever anticipated. We are grateful to everyone for the trust they have put in this project and in us. We are amazed by the engagement and the interest we have witnessed here, both through contributing posts and participating in the comments.
We would like to take this opportunity to open a direct discussion with anyone who reads this blog. We’ll share first what we have learned, what we still have to figure out, and what we are hoping to see in the future. But this is mainly an excuse to hear your thoughts and feedback! Feel free to comment on any of the topics mentioned below, as well as anything we might have forgotten to include.
Why we started this blog
For most of us, AI became a central conversation topic months before we started this blog. We all talked about it with colleagues and peers, be it at conferences, over lunch, or in common rooms. Some of us experimented with it, and some of us were watching from the sidelines. But eventually, we all had our moment of realisation: be it Navier-Stokes, the 10 open problems, the unit distance conjecture, or successfully counting how many Rs are in strawberry (3).
It was evident that everyone had thoughts about AI in mathematics and many were not afraid to voice strong opinions. These conversations remained limited in their reach though, as most mathematicians do not have a natural platform. Some may have their own blogs, sometimes with massive visibility and with takes we agreed with wholeheartedly. But we felt there was a risk in letting the discourse in the community be held exclusively by ‘the loudest in the room’. In addition, the mathematical community is, often surprisingly to outsiders, not very present on social media.
A platform for everyone
We thus made this blog in an attempt to create a natural place for people to speak, exchange and start conversations. We are grateful to the many who submitted a contribution, commented, and kept the conversation going. Here is an excerpt from a submission email we received early on:
I have been feeling the need to express my views on large language models in mathematics for the past few weeks, but never started writing as I did not know what to do with whatever I would write. Your initiative gives me exactly the right kind of venue and has helped me finally turn my ideas into words.
We are incredibly happy to see that this has been successful. We have had submissions from undergraduate students to Fields medallists: in this forum, everyone is on equal footing.
But we would be deluding ourselves thinking we have achieved everything we set out for. Even at the scale of the mathematical community, our blog has mostly posted contributions from academics in the US and western Europe. Similarly, out of the 40 posts, only a handful are authored by women. We would like to hear from, and to record the opinions of, everyone!
A plurality of ideas
As some of you might have noticed, disagreements are common here. Many posts have given rise to heated debates and fierce responses in the comment section (and sometimes in our inbox). Some of these discussions outgrew the comment section and gave rise to responses, additional posts, which in turn generated more debates.
We hoped Proofs and Prompts could become a venue recording and displaying the plurality of ideas in our community. We believe this has been, to some extent, successful: we have had posts proposing a general moratorium on AI, posts suggesting that AI is not playing enough of a role in mathematics, some claiming that nothing is new, and some rejecting it altogether. The Mathathon discussion on this blog featured both a critical open letter and a response from the organisers, at the same time.
We are in awe of the diversity of the community that expresses itself here. This is precisely what we were looking for and we are hoping to see the breadth of ideas expand further. On many of the issues discussed in this blog, there is even disagreement among the hosts.
Newsfeed
Of course it is impossible for one forum to contain the whole kaleidoscope of points of view on this topic. We were wary of this from the beginning, and so we had a Links page, containing relevant links to other blogs, articles, videos, and personal statements. We then realised that these become out of date very quickly. So we now have a new feature in the blog, for which we brought one extra person on board: a newsfeed. The links are still available there, but now there is also a newsfeed about relevant recent events, and interesting posts on maths and AI appearing elsewhere online. Please email us if you have suggestions of things to add in there.
Moderation
We really value the diversity of opinion, and the discussions that have appeared in the comments. However, some people disagree with posts, and instead of starting a constructive discussion in the comments, they write lengthy emails about why a certain post is bad and should not have been published in the first place.
It is impossible to make everybody happy. If we start picking sides, and refusing certain posts because we don’t like them, that sets a bad precedent, and infringes on the social contract we have with the audience, that we are a neutral ground where everyone is safe to share their opinions on maths and AI, whatever they might be.
A main reason for complaint has been that people don’t want to see AI-generated posts. We ask authors to only use LLMs for small things to preserve the authenticity of this project, but we don’t have the authority, the time, or the energy, to police this.
Anonymous posts
We recognise that this topic is very divisive, and some people might want to express strong views without running the risk of being judged harshly by their colleagues. Because of this, it is important that we give the opportunity to publish anonymously. But so far no anonymous post has appeared. We strongly encourage anyone that has thoughts which they regard as controversial to share them anonymously with us.
However, we still need posters to follow the usual process of writing us with a homepage and an institutional address that allows us to verify their identity. If the anonymity were full, and we allowed posts where not even we know who is writing, then that would open up further problems, where people could push a specific point of view by flooding us with tons of anonymous posts. If the poster does not want their identity known to all hosts, they can also write directly to one of us, who will not disclose it to the rest of the hosts.
Schedule of posting
This is perhaps the topic on which we have had the most back and forth. After an intense first week, we settled on one a day Monday – Friday. We started on a first-come-first-served basis, sometimes shuffling for thematic diversity. As a month-long backlog accumulated, we increased the rate to 7 a week.
One important exception is that some of the submissions we get are time sensitive or particularly topical. In these situations, we will add these special posts on top of the usual schedule: they “skip the line”, but do not delay the posts that have already been scheduled for weeks.
We understand that some posters have been frustrated with having to wait a few weeks between the first submission and the posting date. Here are two ways we’ll try to ease this frustration:
- You can send us small changes to your post even after you have submitted the first version. (Please try to be reasonable and only send small changes, otherwise we have to reformat the whole thing again.)
- You can book a slot for a post. To do that, send us an email with a short abstract for what you plan to write about. We will then put you in the line, and ask you to submit the text about a week before the proposed publishing date.
Mathstodon
As some comments point out, centralization and commercialization may be part of the problems with AI. . On the decentralized social media Mastodon, Terrence Tao regularly posts, and more recently, Tristan Buckmaster posted his statement about Navier-Stokes.
Proofs & Prompts is now also on Mathstodon (an instance of Mastodon for people who love maths). For now we will just announce every new post through this account. But if you want to interact more with us there, it can become something more active!
What we would like to see in the future
At the risk of sounding like a broken record, we have no editorial line, and will publish any post we receive (except for spam, trolls, and off-topic posts). That being said, we are not just hosting, we are also among the only people that read every single post, and so we sometimes notice arguments being repeated, and certain points of view being overlooked.
Along these lines, let us make a plea, we want to hear from:
- Journal editors. They have a pivotal role right now, and it would be great to hear what they are thinking (anonymously or not);
- Mathematicians from all over the world. How cultural differences and experiences impact viewpoints and adoption of AI, and also access discrepancies;
- People who work in AI. Those working on LLMs or other classes of models, AI safety, open source and open weight models, and so on;
- Mathematicians who have incorporated AI extensively. How their research is evolving, but also technicalities such as harnesses;
- Those involved with formalisation;
- Those involved in institutional responses and new initiatives.
This is not an exhaustive list. Let us reiterate that we want to hear from everyone. If you feel like you are not being represented enough, you should consider writing something yourself, and invite people around you to do the same.
This is a communal project. It will only be as good, as varied, and as honest as the people who write for it.
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