Peter Krautzberger on the web

A comment on Tim Gowers's blog

I just left an awfully long comment on Tim Gowers’s blog. Thanks, François for mentioning the new post on twitter! Incidentally, it seems that my email is considered spam by Akismet these days, so it will most likely never show up on Gowers’s blog. Tim Gowers was very kind and took the trouble of going through his blog’s spam folder to retrieve my comment. On top of that he explained what I did wrong – I had too many links in my piece, silly me. Thank you! I’ve also added another comment from there where somebody asked me to clarify a few points. I wished there was a system for collecting my comments…

First comment

Thank you for continuing this discussion. I had feared it would stop after the pledge worked so well.

I must admit that I find myself wondering if the points you raise are going in the right direction.

I got rather uncomfortable when you described the idea of “Breakthroughs in Mathematics”. I don’t think that breakthrough papers are the problem – with your support, such a journal would likely be an instant success.

The problem is rather with average papers. The kind of papers that more and more young researchers find themselves writing not because they want to write them but because they must publish to find a job, to survive an evaluation etc. And of course, these papers must end up at reasonably high impact factor journals because that is what we are reduced to in job applications.

This, I think, is the main problem why the journal system appears broken – an inflation of papers that has devalued the concept of papers and hence of the only thing we consider in the research section of a mathematician’s CV.

I seems that the problem of scientific and mathematical research is not the production of results anymore. Your generation has done a great job at creating more and more PhDs that can write papers a plenty.

Instead of production, the problem is now attention, i.e., identifying the better papers amid the flood of average papers that nobody has time to read. As you described yourself, you were surprised that the Electronic Journal of Combinatorics actually contained a lot of interesting material that you didn’t even know about. Have you ever considered writing about interesting papers? And maybe even use to make this known? Or perhaps use to rate the paper? (You could also do this anonymously.)

Instead of more papers (and hence more journals), I strongly believe that we need to focus on new ways of finding good research results and value this as research activity. In fact, after your suggestion for a MathOverflow+ArXiv publishing system, Claire Mathieu had suggested to only publish other people’s work – taking the idea of valuing the identification of good research to a wonderful extreme. There’s of course also the much larger debate going on regarding post-publication peer-review (such as f1000) which is precisely about this issue.

The second problem I see is what Michael Nielsen raises in Reinventing Discovery: the modularization of research. The sciences have already experimented very successfully with ways to modularize research from by now classic examples like Galaxy Zoo to more recent ideas and

We mathematicians have nothing to offer in this respect.

As you wrote yourself a while ago, the wonderful tricki has failed much like other wikis outside of Wikipedia (whereas other research areas have begun to value Wikipedia contributions as research).

I would even go as far as say that Polymath has failed (even though it was all about publishing papers and not disruptive in that sense). However, there still might be a chance to salvage it if we find a way to scale it away from top research to more average level research, more realistic problems or simply open-notebook science.

At the same time, a lot of young mathematicians “grow up” online. But they are still strongly discouraged not to experiment with communicating their mathematics online. Having attended Science Online 2012 last week, I was again shocked by the positive community the scientific online community offers.

The scientific online community embraces the younger generation. (Did you know that young graduate students write at the Scientific American’s blog network as equals of experienced scientists and professional science journalists?.) In mathematics, e.g., the MathOverflow community has worked very hard at discouraging even experienced graduate students from contributing (just ask some average graduate student). The scientific online community also offers protection and support by encouraging and developing safe systems for pseudonymous online activities.

As some comments have already indicated, we mathematicians are significantly behind in founding an online community that deserves the name. In particular, our academic societies do not take the online community seriously – which is somewhat bizarre given the current count of roughly 350 blogs in the research category on

Can we find a way to raise awareness of the potential for our community? Can we get to a culture where we value more and more experiments like the tricki, Polymath, mathoverflow until we find enough systems that actually work and everyone can participate meaningfully?

Finally, in a most likely vain attempt at getting back on topic: Can we find a way to use online journals in new ways, to modularize the mathematical research process instead of just copying a 300 year old idea to the web?

Oh dear, this has gotten far too long. I apologize.

Second comment

@Marcin Kotowski.

My wording regarding MO was unfortunate. I did not mean to imply graduate students are actively discouraged by the community. However, almost all graduate students I have talked to about this (here at Michigan but also at conferences and workshops) have given me precisely this impression – they do feel discouraged to participate. This has many reasons and for privacy reasons I don’t want to describe individual stories. There’s also the “problem” of MO having extraordinary users in some areas (such as my own), making it impossible to participate much (have you ever tried answering a question that Joel Hamkins knows the answer to?). Finally, there are those fields which are not well represented on MO in general, another hindrance for younger researchers.

I do think that MO is an amazing community in many, many ways and something where we are truly ahead of everybody else, really. But that doesn’t mean it’s without flaws.

The second part you quoted was much more general in nature, not just about MO but also other activities such as blogging, wikipedia, tricki, expository writing, reviewing other people’s papers, engaging with your community through social media etc.. From my own experience but also from conversations with other postdocs, it is clear that non-tenured folk are discouraged to do anything online – if you’re very good, then it is non-negative for your career.

I’ve personally heard the advice to “definitely not mention this on your CV”. It boils down to the old “you could have written a paper instead”-argument, really, and it is not going away while hiring committees effectively reduce applicants to impact factors of the journals they publish in. Again, as I said before, this is not about breakthrough mathematics but about “average” research.

Finally, here’s a link to a video from Science Online 2011 on “blogging in the academy” starting with an introduction from the perspective of MIT. It’s quite sobering even if it is only about blogging.