Tag Archives: polymath

Waiting for the Polymath revolution — thoughts from a bystander

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Tim Gowers has hinted at a revival of the fifth Polymath project. Which brings something back from the bottom of my draft folder.

Let’s talk about Polymath

If you haven’t heard of the Polymath project, then, hm, well… anyway, here’s the beginning of its Wikipedia entry:

The Polymath Project is a collaboration among mathematicians to solve important and difficult mathematical problems by coordinating many mathematicians to communicate with each other on finding the best route to the solution. The project began in January 2009 on Tim Gowers’ blog when he posted a problem and asked his readers to post partial ideas and partial progress toward a solution. This experiment resulted in a new answer to a difficult problem, and since then the Polymath Project has grown to describe a particular process of using an online collaboration to solve any math problem.

(If you’ve really never heard of the Polymath project, then you might want to go through the references on Wikipedia.)

I think nobody who stumbled upon Polymath in 2009 and 2010 could escape the deep fascination and exhilaration of its early successes and the positive spirit it created in the online math community. It was an exciting time. Personally, I was not actively involved in any Polymath project, have neither contributed nor seriously tried to follow the intricate but vast amount of information that Polymath projects have left in their wake — it was simply too far from my own research interests. Like many mathematicians, however, I have followed it as an interested party.

I write, therefore, as a bystander, a simple mathematician who has an ongoing interested in the future of the field and its community. And as such, I’ve begun to worry about the impact of the Polymath project.

To return to the above quote, what continues to bug me is the last half-sentence.

[...] since then the Polymath Project has grown to describe a particular process of using an online collaboration to solve any math problem.

O RLY?

Isn’t Polymath dead?

Now that’s just silly, of course it isn’t. I just told you Tim Gowers will have another one, didn’t I? In fact, I’m quite certain that a revival led by Tim Gowers will get another paper out of it (I mean, he got the dHJ paper into Annals for crying out loud).

But that doesn’t change my feeling that Polymath is dead — or rather, that it is a mirage.

What is Polymath, actually?

Polymath is certainly not dead if you think of it as a research project of Tim Gowers, Terry Tao, Michael Nielsen and some of their friends. However, this is not how most people think about it. Instead, Polymath has left a much larger impression in- and outside the mathematical community thanks to numerous mentions on all kinds of news outlets. And then there’s the position Polymath takes in Michael Nielsen’s writing, in particular in Reinventing Discovery which has lead to every science journalist hearing about this “great revolution” of how we do (mathematical) research.

If you think that that’s what Polymath is — a revolutionary new way of doing research — then, unfortunately, Polymath is either dead or, more appropriately, has never existed in the first place, has only been an illusion.

Would the real revolutionary please stand up?

Wikipedia tells us

A revolution (from the Latin revolutio, “a turn around”) is a fundamental change in power or organizational structures that takes place in a relatively short period of time.

Hm…

Maybe it’s still too early. It’s only been three years.

Maybe it isn’t and instead it’s time to think about what’s keeping this revolution from happening.

  • Polymath aims to proof theorems to publish as papers in journals.

Compared to open notebook science, citizen science, tricki.org or Wikipedia, Polymath fails to be revolutionary in its output. It does not add to the accepted notions of “research activity”. It produces more papers, in traditional journals. Perfectly fine mathematics, just not exactly revolutionary.

  • Polymath cannot be reproduced by people other than Gowers and Tao.

Six Polymath projects have been formally started so far. Only two seem to have come to the desired conclusion. These two were headed by Gowers and Tao. Two Fields Medalists leading a research project, even a cool one like Polymath, well, it’s not “fundamental change in power or organizational structures”.

  • Polymath has not become a model of research activity, i.e., nobody else is doing it.

Besides the fact that only Gowers and Tao seem to be able to bring a Polymath project to a conclusion, there’s a much bigger issue: Nobody else is even trying. The projects can be traced back to a close circle of bloggers around Gowers, Nielsen and Tao — Kalai, Lipton, Ellenberg etc. Here’s an (unfair) comparison: the arXiv did not revolutionize the dissemination of preprints because Paul Ginsparg put his own and his bff’s papers up on the web. Instead, a continued effort reached more and more of the community and established the arXiv as the standard for pre-print releases and self-archival, making it a corner stone of many scientific communities today. (Fun fact: according to Michael Nielsen in Reinventing Discovery, a physicist once described Ginsparg as wasting his talents, collecting “garbage”. Would anybody say anything like this about Polymath? In other words, is a Polymath project in any sense risky?)

  • Polymath does not seem to scale in terms of difficulty.

The few Polymath projects that have been attempted have all had a reasonably high level of complexity. Additionally, the tendency seems to be towards more complicated research questions rather than simpler ones. Maybe this is MathOverflow’s fault for taking care of so many “easy” questions, i.e., questions somebody else simply seems to have the answer to. Additionally, people on MO often spend a considerable amount of work on solving questions — an effort that could just easily be considered a micro-contribution if we had a platform for these.

  • The Polymath projects are not understood.

There’s a lot of talk about how awesomesauce !eleventy!1! Polymath projects are but there seems to be no effort towards understanding the successes and failures. Of course, this is not surprising since there aren’t that many examples to consider. But there is nevertheless a lot of data. Analyzing the available data, the process, what works and what doesn’t could help immensely. In particular, if the “failed” projects could be turned into productive contributions, we might actually get a new form of research activity that benefits the greater part of the community. Failed atttempts are the mathematical analogue of negative data in the sciences and there’s similar lack of dissemination.

Evolution or how could Polymath become something meaningful for the entire community?

It may seem that I have some kind of beef with Polymath, but that’s not the case at all. Polymath was quite simply amazing. I did wish, however, it (or something like it) would work for more people and would actually turn into a (much needed) revolution.

Mathematics has the greatest potential for “doing research online”. There’s no physical entity needed and our primary standard of scientific communication is the written word. There’s nothing in mathematical research that cannot be digitalized. We will never face the problem that somebody on the other side on the net would have to actually look at our specimen, our antibody staining, our test subjects. The web works perfectly for us.

Hence, mathematicians could be at the forefront of experimenting with new research activities that use the connectivity the web can offer in new and imaginative ways. Polymath was one experiment and it worked to a certain point. Even if Polymath5 can be revived in its current form, this most likely won’t help the community as a whole (except in lazy bragging rights). Just like anywhere else on the web, the experiments continue — 20 years into the invention of this mind boggling creation, we don’t have a clue what the future has in store for us.

The goal could be to find a way to do Polymath-esque research on a large scale, involving large parts of the mathematical community (or at least, the online community). But maybe we need something completely different. It would simply be a shame if the Polymath projects ended up “a fun project for a few top mathematicians”. Maybe we need another Ginsparg, ready to endure the ridicule of “wasting” a research career. But I don’t like heroic sacrifice.

I would rather hope for a group effort, maybe led by an innovative department or a group of college faculties coming together or some grant agency or academice society supporting a significant grant for the development of new ideas, looking to other successful projects like MathOverflow, wikipedia, the n-lab, blogs, activity on social networks etc. But more likely we simply need a crazy group of young researchers fighting to revolutionize the community regardless of the consequences for themselves, ready to kick the hornets’ nest of old white dudes established researchers.

Just keep experimenting. Polymath doesn’t work for most people, that’s ok, let’s try something else, change it, revamp it, do the complete opposite.

But, please, for a change, let’s not ask Tim Gowers to do everything for us!

Aufklärung ist der Ausgang des Menschen aus seiner selbstverschuldeten Unmündigkeit.

Coda.

Do you expect a project led by Fields Medalists to create a revolution? Overthrowing what exactly?

But there might be a more fundamental problem: do we have the right people in the first place? Michael Nielsen wrote in WSJ:

The tools are a way of connecting the right people to the right problems at the right time, activating what would otherwise be latent expertise.

Throughout Reinventing Discovery, there’s something that Michael Nielsen does not discuss: the social impact. New ways of doing research will have a huge impact on the actual people involved and will require them to be willing and able incorporate these changes. The “right people” does not just mean “the researchers who know the right thing” but also “the researchers who can work with these tools”.

It could be that the groups of mathematicians that influence the conversations and developments within the mathematical community, e.g., tenured faculty at the top math departments, consist entirely of the “wrong” people, unable to be in the right place at the right time. Simply because it’s not why they got the job — they are where they are because they are excellent at doing research in the current model, the steampunk approach of “papers in journals”.

Prelude to a small experiment

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I haven’t posted anything in almost two months — life happened. It’s still a bit chaotic and maybe I’ll write about it when things calm down. For now, I’m back from a productive trip to Toronto where, among other things, I had the pleasure to reconnect with Sam, Assaf and Mike.

Meanwhile back at the ranch

In the mean time, Felix Breuer scooped me and wrote a great piece (better than anything I would have written) entitled “Not only beyond Journals, not only beyond papers, but beyond Theorems”. You absolutely must read it. He takes a point I made in several discussions with him and just nails it. So go and read his piece — don’t worry, I’ll wait.

You’re back? Excellent! Reading Felix’s piece, I thought I should try something I’ve been thinking about for a while. Though I’m arguing (as does Felix) that mathematicians need to move beyond “new result”-papers, I’m not advocating the end of new results. (Or the end of review by peers.) The bane is rather that we write too many papers. I think, paradoxically enough, that we can only overcome this inflation of papers (and its damaging monoculture) by reducing the “least publishable unit” further. We must develop new ways of sharing mathematics that are better adapted to the effective dissemination of research — while allowing researchers to build a track record.

Science Online 2012 revisited

This brought back an idea that I returned with after talking to the altmetrics folks at ScienceOnline2012, in particular totalimpact‘s Jason Priem and Figshare‘s Mark Hahnel.

Figshare is a platform to make all kinds of research results public and, importantly, citeable. They started with scientific figures (duh) but since it’s official launch earlier this year went on to more general data (they have a few of the big citizen science projects onboard now), and is really open to everything — from grant proposals to short research notes to anything. (Figshare also has very interesting financial backing.) Getting to know figshare made me wonder what mathematical content could be suitable for it.

There’s obviously stuff that works: data in applied mathematics and also visualizations and mathematical software packages fit the bill. But for logicians and set theorists none of these are usual. What would fit? The first thing that came to mind was the mathematical analogue of negative experimental data (which figshare is eager to host) — in other words, counterexamples. What else?

For my second idea, I need to return to Science Online where I had a wonderful long conversation with Jason about the invisible college, new measures for research and other ideas (which I will try to write about in the future). In that conversation, we also discussed the idea of micro-contributions, contributions much smaller than a small paper. At first, this seems more important to the sciences — publishing your data in real time seems a natural progression there and open notebook science is already a development in that direction. I think this is also a natural step for mathematicians — share your research as soon as it’s done — don’t worry about the great result but help by making things public. As a mathematical example of open notebook science, you might consider Polymath, but Dror Bar-Natan’s pensieve is probably a better comparison. You might be afraid to do this, worrying about being scooped or not being able to publish afterwards. But we need to experiment and create more examples that work.

Polymath was wonderful, but has only worked twice so far, once led by Tim Gowers, once led by Terry Tao. It might turn out that Polymath simply does not scale to the “average” researcher. But in any case, there’s every reason to continue experimenting on the web. I read a great comparison recently: the state of the 20-year-old web is roughly that of the printing press 100 years after its invention — that’s 1540, mind you, when almost all prints were illegal copies of short pamphlets. Which reminds me of this:

So what’s this about then?

Well, this post is supposed to be the prelude to an upcoming double-post which is precisely this — a micro-contribution, a small result, far smaller than the least publishable unit, nothing big, but at the same time a curious observation which is, I believe, worth recording (if only because it made me question a certain intuition of mine).

This micro-result has been lying around in my notes for almost two years now. At first I thought it might be incorporated into something else, but as it turns out, this never happened. And yet, I’m sitting on it. Sure, the people involved in it know about it, but since it’s so small, it would never be published as a paper and thus never appear. I think that’s really unnecessary — I want to make my work public, that’s kind of the point, isn’t it? And I don’t want to be pretentious and waste time finding a way to blow this up into yet another paper that nobody reads. Thus, this experiment.

A question on the side. Could we have a “journal” for micro-contributions? What would that even look like? Would we need peer-review? What would peer-review look like? Could it simply be done in the comments of a blog or by short “replies” on (a common or different) platforms such as arXiv or figshare?

Besides making this micro-contribution public I would like to give you the story behind the result. You see, the result is really “micro”. So if I only gave you the proof, we’d be done in a minute. And then you’d have 1-2 pages tops, in the usual brutally short mathematical paper-style writing (only expanded by my silly habit of writing proofs as lists). I mean, don’t worry, that version will be there, too, in the end, much like my dream of one day having papers with computer checkable proofs in the appendix. But while I’m trying something new why not try some mathematical storytelling simultaneously?

So before I reach those bare bones of proof, I will take the time to tell you the story of how the result came to be. Not because it is an especially important or impressive story — neither is the case. In fact, it’s rather ordinary and I’m sure every mathematician will have experienced this, probably on a much more significant level than I did. Yet I’d like to try writing about it and it will take me a double post to do so.

Reversely, I hope you, my two readers, will be kind enough to provide some feedback. I could imagine this being in three ways:

  • the mathematical side: is the result correct?
  • the lyrical side: is the result well written?
  • the experimental side: is this a concept you could see yourself employing?

Finally, I do plan to post the result of all this properly somewhere; you know, as a research note of sorts, with a proper bibliography and so forth. Maybe on figshare, maybe on the arXiv, maybe on github, not sure yet (any thoughts?). In any case, stay tuned for the first post — the rough drafts are finished, but some fine tuning is still missing.

Tools for your online collaboration

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So the winter school in Hejnice ended two weeks ago is long past — and despite my intentions I did not find the time to blog. This is primarily a sign of the quality of the winter school, both scientifically and socially. I do admit I spent the lunch breaks walking in the beautiful surrounding mountains instead of blogging…

Anyway, on the last evening of the winter school a couple of people gathered together to exchange tools for collaborating via the intertubes. I volunteered — also with the upcoming third Young Set Theorists meeting in mind — to make the discussion available online. Of course, the title refers to this wonderful paper by Goldstern and Judah which taught me the little bit of iterated forcing that I know.

For now I will restrict myself to freemium services. Of course, this is an open list — drop me a comment to add to this list (hm, a google wave would be better, right?).

Phones

A much better tool than a phone is? A videophone! (especially for handwaving arguments). Namely, skype comes to mind, but there are alternatives like tokbox or google talk which are web based. With possibly lower video quality they offer other useful things like actual video conferences (whereas skype restricts you afaik to 1-1 video calls) and invitation by link. There are also numerous true VoIP/SIP clients like Ekiga. But they may have the need for some firewall configuring. For more general information, check out wikipedia.

Whiteboards

But what good is a (video)phone if you cannot write on a blackboard together? In any serious mathematical discussion, notation will become an issue sooner or later. A simple, but bandwidth friendly and flash based whiteboard is scriblink — just go to the site and give your partner the invitation link. An alternative is dabbleboard which offers some shape recognition and also allows multiple pages in the free version and — most importantly — PDFs as background images. However, it is a little heavy on the bandwidth, especially latency which often annoys my voip connection.

Of course, if you want to use an online whiteboard efficiently you need some kind of tablet to write with. I personally have been very happy with a graphics tablet, a Wacom Bamboo to be exact. You can get tablets for 40€ and lower in Germany, but prices will differ regionally. Of course, I also use my Gigabyte M1028T tablet pc — although its tablet functionality is basic (no pressure sensitivity, only moving by clicking) making writing with it less suitable for real note taking — see the PDF section below.

Eierlegende Wollmilchsau Swiss Army Knives

There are of course those services which offer all of the above at once. A prime example would be dimdim which offers a nice, unified service including video conferencing, instant messaging, whiteboard, pdf viewing and collaborative websurfing — all of this available with a free account which is limited only in the number of participants (and there are premium services available, of course).  Additionally dimdim’s server technology is mostly open source, so you can set up your own server if you have the means. Unfortunately, I never got the video conference system to work correctly under linux. Although not quite with collaboration in mind there is also the awesome TeamViewer. It is a great remote assistance tool designed for efficient access to another computer screen. In that sense you could use it to access your home or office machine from anywhere — if your department allows that. But in the latest version (although windows only) Teamviewer also offers Video chat and a whiteboard to communicate. For further tools look here.

Instant Chat, Online Docs and Google Wave

Personally, I have not used instant messaging for mathematics so far — video phones seem better. However, Pidgin has a LaTeX plugin to display basic TeX code. This is of course a useful feature. I’ll come back to the general problem of displaying mathematics on the web later.

I feel I must also mention Google Wave and its competitors. These are powerful tool mixing mail, chat, wikis and collaborative document editing. I have not tried any of these yet but if there’s someone to collaborate with it’s worth a try.

PDFs I — what you can do with them

PDFs is the somewhat dominant standard for (compiled) TeX documents (sorry, dvi and ps fans). Besides the next section there is another aspect which makes them worthwhile — PDF annotation. If you are like me and like to take your notes with you (for all those typos and indices that drive you mad in some papers) there is nothing better than annotating a PDF directly — especially if you invested in a (graphics) tablet.

My favourite is the open source Xournal with excellent tablet support on both linux and windows. Alternatives are Jarnal (which also works as real time whiteboard) and (for Mac users) Skim.

Although it does not quite fit in here (or anywhere): if you feel that PDFs are inadequate to present mathematics, why don’t you take a look at prezi? It offers a different angle on presentations altogether. I sometimes dream of having a prezi like ability to zoom into papers or rather proofs giving me details where I want them and letting me quickly browse through the main ideas dynamically whenever I choose to…

PDFs II — Personal online libraries

It is convenient to store papers and other materials online. If you cannot set up a decent sftp or a version control system on your university’s server, you might want to try dropbox or teamdrive. If you frequently use public computers you might want to use something more web based like google documents or the very pretty isssu that I use from time to time on this blog.

Community Sites

Of course, all science is community driven but I think (pure) mathematics could profit more from an online community than any other science or (liberal) art. The biggest player is certainly facebook — which already has a group for, of course, the winterschool itself. Facebook attracts academia (as opposed to myspace), hence it is the more obvious place to connect — this does not mean that you shouldn’t worry about its privacy settings or rather the partial lack thereof.

On the other hand, there are a couple of science focused community sites, among them researchgate which offer science specific tools like (p)reprint lists, online references, database searches etc. This might be better for purely professional intent but I have no experience using it.

A young and incredibly successful new site is mathoverflow — a mathematical version of the great stackoverflow. You can ask and answer questions of all sorts in a very efficient manner — just don’t get lost in all the fun.

Databases

Of course the mother of all things is the arXiv — do I need to explain it? And then there are Google’s products scholar and book search. A somewhat different database is gigapedia where you can easily search for books and find free ones. In all things beware of legal issues though.

LaTeX or displaying mathematics on the web

Of course mathematicians are used to LaTeX. On the web the best way for displaying mathematics is (from a web standards point of view) mathml. The problem is that mathml is a) too difficult to write as code directly, b) difficult to view since not all browsers view them correctly and from a visually impaired point of view it seems to be a disaster, too (see the discussion on Terry Tao’s blog) and c) it is difficult to convert back to LaTeX.

There are numerous workarounds. On the one hand you can (as I do) use tex4ht to convert LaTeX to mathml. Of course, as my blog shows this is a rather tedious thing if you do not have (or want to have) control over the webserver. Alternatives are jsMath which might be superseded by mathjax. If you have a wordpress blog you can (even on your free account on wordpress.com) use this plugin — which converts basic LaTeX commands into (rather ugly) PNGs.

The winner for best practices with mathml, I think, is the n-Category Cafe. Besides being a very active group blog they have developed impressive technologies such as mathml inclusion, the LaTeX dialect itex, the itex capable instiki with itex2mml to convert tex to mathml on the fly and all of this available in the comments, too.

Blogs, blogs, blogs

Almost last but in no way least, there are blogs.  This would be worth an independent post and there are plenty of examples for this, but here we go.

They come in all colours, for an impressive list go here. Also, go to any of those blogs and check their blogroll to find many more mathematics blogs. If you don’t understand what blogs are good for you might read John Baez’s article. To name a few contenders for ‘most influential mathematical blogs’: What’s new with Terence Tao, the most active single user blog I know, Timothy Gowers’s Weblog and Gil Kallai’s Combinatorics and more.

Of course, they are the ones that got me started with reading math blogs, but it’s the small blogs that got me hooked. The diversity is a challenge (I don’t understand half of what I read) but blogs form the best mathematics newspaper out there.

Polymath

At the moment the most hardcore project when it comes to online collaboration is clearly Polymath. With one paper on the arxiv, two projects finished and three projects going it is the perfect show case. Driven by the “big three” — Tao, Gowers, Kallai — one may argue that their power makes sure that it works (and is protected from theft). Polymath is an exemplary web project. It follows Jeff Jarvis’s rule and shows the synergetic behaviour of web projects — using multiple technologies at once: there’s the blog for the main discussion, but also the authors individual blogs used partly to organize. Finally there’s the wiki for fixing proper definitions and notational issues and finally they frequenly use mathoverflow to recruit new people by e.g. singling out distinct partial or dervitative questions.

But I believe it shows a glimpse of the future of mathematics. On the one hand, many problems have become too complex to be tackled by a single person or research group. On the other hand, although the techology might change considerably in the future, the idea of having researchers on all levels collaborate — with every contribution being valued — could be a prototype that values many soft skills, be it good writing, accessible presentation, social skills for bringing conversations to converge productively, taking a bird’s view of the process to assist or acquiring empirical experimentation and implementation. It is also a very flexible approach where people can help as much or as little as they find the time for while (with proper support like Gower’s current EDP posts) still being able to follow the flow and ideally being able to change their level of involvement as they please.\

That’s all for now. Let me know what I forgot.

Addenda

2010-02-15

Unicode characters

There was also a question regarding unicode characters and the like (instead of mathml). I just found this chart via mathoverflow — maybe it helps.

2010-02-17

Feeds and feed readers

Feeds in either Real simple syndication (RSS) or Atom from are worth mentioning on its own. As a tool for 1-to-infinity communication it’s an important technology for collaboration. You’ll find feeds for all kinds of newssites and blogs, but also for each section of the arxiv. To read feeds you can use lots of different programs and web based services.

Video sites

Videos of research level mathematics are pretty rare. There is the archive of the MSRI and singular popular mathematics gems like Gowers’s talk on multiplication. Also, you should check out MIT’s impressive youtube channel.

To put up a video you don’t need much these days, so it’s strange that there’s not more around — especially since (pure) mathematics seems easier to share than, say, complicated science experiments. There are too many free video sites out there. Next to the already mentioned youtube I would point out the science video site SciVee (with its strong, yet somewhat expensive premium service) and Vimeo with its focus on original content.

Reference management

Thanks to David for reminding me that I forgot one aspect of pdf management — reference management (see the list on wikipedia). Now there are many programs out there to get your citations, i.e., your BibTeX files organized. But there are also programs that connect the citations with the pdf, offer online database searches, tags, pdf annotation and social networking ideas.

A big list can (once again) be found on wikipedia. To present a few. I personally use referencer but David also mentioned Mendeley in his comment which has an impressive list of features including online access and social network aspects and I’ll probably try it out. To give credit where it is due a few of these programs name Papers as inspiration which unfortunately is Mac only. With a different flavour there are the web-only Zotero, a powerful Firefox addon, and I, Librarian, a groupware tool.