Peter Krautzberger on the web

Prelude to a small experiment

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 [Wayback Machine]. 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.


  • fbreuer, 2012/03/27 Thanks for the mention! I am looking forward to your double-post! I am all for micro-contributions! With their “open” nature they explore the territory “beyond theorems”, even if they are micro-theorems themselves. The main challenge I see is that of discoverability. How will we discover relevant micro-contributions if we are already flooded with macro-contributions? Dror Bar-Natan’s pensieve is an interesting example in this regard. On the one hand it is absolutely brilliant in its radicality! (Just the thought of putting all my xournal notes online is scary.) On the other hand, who is going to dig through all these notes to sift out the great ideas? I am sure, though, that in the case of your double-post, discoverability will not be much of an issue as your blog gets plenty of readers. (I can tell by the amount of traffic you have sent my way. 😉
    • Peter, 2012/03/29 Yes, discoverability is an issue (then again, googling or duckduckgoing for idempotent ultrafilters puts some of my stuff on the front page) . I think we’ll never get enough motivation for a good solution for this without creating and sharing the content that we want to be discovered. So I worry about that first while keeping an eye on the discoverability. Personally, I favor decentralized social networks via tools like wordpress to host the content as well as specialized search engines // aggregators to discover content and the people behind it.
  • Carl Mummer 2012/03/28 The “microresult” idea is very similar to the motivation I have for experimenting with online publishing. I agree with many of Felix Breuer’s comments in his blog post, that it is becoming increasingly impossible to keep up with the volume of mathematics (this has been a problem for several decades, of course). But at the same time I think that we don’t publish enough. There are many microresults that we discover, possibly write in a notebook, and then leave because there’s not a good way to fit them into a peer-reviewed paper. These often get passed around as folklore in larger departments, discussed over tea. After our discussion last night, I’ve started to think about a post for my blog to try to collect my ideas on this.
    • Peter 2012/03/29 Looking forward to your post on this!
  • David Roberts 2012/08/29 Hi Peter, thought I might drop in an example of a microcontribution of mine from a few years back: this is referenced at the nLab page This is a mechanism which overcomes to some extent the problem of discoverability. Wikipedia famously has a ‘no original research’ policy, but the nLab famously takes the opposite approach, and indeed was originally set up to capture what you are calling microcontributions that arose in discussion at the n-category cafe. As far as the microcontribution itself goes, it was a merely a shift in perspective on my part that made a number of things make sense, and unified a bunch of facts - something that doesn’t even deserve a blog post, and would probably fit into a tweet. In the discussions about moving MathOverflow onto the StackExchange platform (and hence move to currently maintained software!), a number of people were concerned about not losing Brian Conrad’s comments on questions. These comments were in fact complete, elegant solutions to problems in algebraic geometry. I would count these as microcontributions in the sense they may not solve a problem that hasn’t been solved before, but are approaching Book-status.
    • Peter 2012/09/24 Oops, I never replied?!? Thanks for the pointer, David!