 Hi, this is Drew Sutherland. We are here at Innova-Wolfach conference, and I thought I'd ask him to explain to us the polymath project. Sure. So what is it? Well, so the very first polymath project, Polymath 1, was started by Tim Gower's, I don't remember exactly when, some years ago now. There was, and it was an experiment in massive open collaboration between mathematicians to solve a problem of common interest. So the first problem was known as the density-hills-Jewitt theorem, which is a celebrated theorem in extremal combinatorics, and it had been proven, but the proof was very long and involved, and they were looking for a more elegant proof. And this project was created initially by Tim Gower's with a blog post and a place where people from all walks of life didn't necessarily have to be a professional mathematician, anyone who wants to participate. And eventually they found a very nice, beautiful, elegant proof of this theorem. It was published, and the results were written up in a paper and published in the Annals of Mathematics. And the publication was under what kind of authorship? So it was under a pseudonym. They chose the initials DHJ polymath. So DHJ stands for density-hills-Jewitt, which was the name of the first problem they worked on. And then, following that, there were a number of other polymath projects on different topics, and not all of them were somewhere more successful than others, but there have been several papers published under the same pseudonym, like DHJ Polymath. If you go into Maths Signet, you can look up papers written by DHJ Polymath. And so you participate in some of them. What do you think? How is it working? How do you see this project? Well, so I can only speak of the project that I participated in directly, which was the eighth polymath project, on polymath 8, on prime gaps. Not long after Yutang Zhang's breakthrough result, where he proved that there were infinitely many pairs of prime separated by a gap of at most 70 million, which came out in May of 2013. In his paper, Zhang's effort was very much focused on the very difficult technical details of his formal theorem. He consciously decided not to put a lot of effort in trying to make the number as small as possible. I mean, the major breakthrough was that you could prove a finite bound of any size. So getting from infinity down to 70 million was already a huge progress, and he left it to others to try and refine, further refine the results. And then there was some discussion on some popular mathematical blogs, including Scott Morrison's blog, where people started talking about some easy ways one could go about improving this bound of 70 million. And as people started to look at it, they found more and more ways that they might be able to make improvements. And then I think it was June 4th, 2013, Terry Tao, Fields Medalist, and someone who has a very large presence on the internet. He has a very popular blog that he runs and posts on many different topics, and a lot of people follow his blog. He suggested that we start an official polymath project with the intention, really with two goals. One was to really try to better understand Zhang's proof, which was quite new at the time. Not everyone really understood all the details. So he hosted sort of an online reading seminar where he went through different parts of Zhang's paper. And then the other part was to try and optimize Zhang's result to the extent possible. And so first of all, as you said already, but just to emphasize, this is something that is completely open to absolutely anybody. Absolutely. And so how do you think, in your opinion, this, in a way, changing the way mathematics is being done? Well, I think it's done two things. One, it's opened it up to a lot of people who might not have otherwise gotten engaged in this particular case. There were, I know, at least three people who were active participants in the project who would not call themselves professional mathematicians. One of them is a biologist, another one works on robotics. But they had some really good ideas, asked a lot of interesting questions, and made strong contributions to the project. And it also served to bring together mathematicians from very different fields who might not otherwise have been likely to talk to each other unless they happen to work at the same university. So I think it really does help to foster a lot of communication between mathematicians both within the field and even outside the field that might not otherwise occur. And the people that are participating, and say particularly the young people that maybe need to prove that their career is in track and so on, is participating in something like this, something that they can get the right recognition, do you think? Yeah, that's a very good question. I think it's something that we think about a lot. I mean, I think as the Polymath projects are becoming more well-known, I think it's more and more likely that being able to talk about the contributions that you made to a project like this would impress people. Certainly, I know it's kind of funny even within my own department. I mean, I'm well-known among the other number theorists now that you raised my group. But working on the Polymath project actually brought me to the attention of other people in the department who perhaps the only thing they know about me is that I happen to have worked on this project. So it has been actually even more positive than the other way around? Absolutely. It's definitely been a positive. I was invited to speak at one of the colloquium on this particular topic just because the Polymath problems tend to be well-known problems that are of interest to large numbers of people. So working on one of these problems can bring you to the attention of a broader community. And does the system kind of self-policies itself? I mean, how does it have issues with people doing inappropriate things or how does that work? It has really at least, again, I can only speak about the project I worked on. It has absolutely not been a problem. I mean, the results of the project are written up on a Wiki page. Everybody who's participating has access to the Wiki and can make changes. Anybody who wants to can comment on any of the blog posts and make suggestions. It really hasn't been a problem. I will say it has certainly helped that in this particular project we had somebody helping to organize and lead the whole effort in Terry Tao who is extremely capable and very highly respected, obviously. So I think that probably helps to keep everybody on their best behavior. But I think in general, you know, mathematicians are nice people. They like to work together. They like to work together on problems and are happy to exchange ideas freely. So no, it really hasn't been a problem. Great. Well, it's great to hear. So thanks very much, Drew, and I hope things keep going well for you. Thank you. Bye.