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.


  • Carol Hutchins, 2012/01/29 An important point you are making is the differential between “breakthroughs” and what one might call the Big Middle. Let’s set aside that there is some tail of really really awful contributions at the other end. Think of the frogs and birds, per F. Dyson.
    • Peter 2012/01/29 Thank you, Carol. I’m sure there’s a tail of awful contributions. That’s why I’m speaking of an attention economy instead of a production economy. We need to share what we think about each others work. On the other hand, I think if we had activities other than writing papers which we could still put in the research section of our CV (such as open reviewing, helping other people make progress in their work), then the pressure to write as many papers as possible could be reduced, leading to fewer awful papers. But nobody can do that if we do not experiment more in this respect. By the way, I’ve sometimes seen the argument “but then the cranks take over” which I find hilarious since I’ve yet to meet a mathematician who cannot spot a crank from a mile away.
  • Micheal Pawliuk 2012/02/01 I get the impression from your posts Peter that all mathematicians are terrible presenters and writers. :) The problem I suppose is that good presentation skills are (unfortunately) often orthogonal to good research skills. I have even heard that some people with particularly strong teaching backgrounds actually have a harder time getting an academic job. (sigh)
    • Peter 2012/02/03 Mike, unfortunately, I think your observations are on point. The reason why mathematicians are bad speakers actually has a simple answer — we receive no training and there’s no active discussion in the community on how to present well (just check out the Journal of Number Theory’s youtube channel…). There’s also no feedback for speaker, i.e., nobody tells you what went badly in your talk or how to improve, even if you ask arond. Giving productive feedback is, of course, also a skill to be trained. The trouble is that most people think you cannot learn this — which is plain wrong. To be a good speaker can be trained, just like anything else. The observation regarding the job market is, I think, also correct, but for entirely different reasons. This is quite simply a (poor) decision of our community to actively favor the wrong set of skills (or rather, focus on one skill exclusively “paper writing”). If you look around, the truly great mathematicians (Tim Gowers being a formidable example) are very good teachers and speakers. I think it is a misconception in our community that this skill is not important to further mathematical research; a misconception most likely originating from the fact that such skills could not be documented/evaluated until very, very recently.
      • Izabella Laba 2012/02/07 There are truly great mathematicians who are not good expositors at all. I’m not sure that it would serve anyone’s interests to post names on a public blog, but they’re in Gowers’s league, research-wise. I’ve come to think that there might just be no correlation at all. I’m all for recognizing a wider range of skills and contributions. I just don’t think that we should expect everyone to have every skill and make every type of contribution in the book. We have to wear a lot of hats already as it is.
        • Peter 2012/02/07 I don’t know if there’s no correlation. I’d like to think that the very best, the extraordinary mathematicians are good expositors but I have no data to support this. Ultimately, I think, it comes down to values of the community – I would call someone with a lesser “new results” record the greater mathematician if they are a great expositor. What good are results if nobody can understand them (and why we don’t value people who make them understandable)? For example, I find it hard to call Perelman anything near great; his results, yes, but the mathematician, the member of our community? Another example would be Grothendieck, thanks to this letter. I also fully agree with you that nobody should have to make every type of contribution. In fact, I hope for the exact opposite! People should contribute the best way they can. However, they can’t as long as the community does not value all types of contributions. I see a monoculture where only people who can produce the right kind of “new results” papers will get into the “right” journals and, ultimately, get the jobs. And I worry that it is not a sustainable culture.
          • Izabella Laba 2012/02/07 I’m thinking of someone in particular who, research-wise, is at the absolute top of several fields of mathematics. I do wish that his papers were easier to read. But we still read them (even if it takes an effort) and use his ideas (and there’s an abundance of them, and they’re often unexpected and have far-reaching consequences, so it’s all worth the time we invest in it). He has been incredibly influential in many areas and has developed a huge following. To me, there’s no question about either his greatness or being a valuable member of the community. Sometimes you can’t have it all. On the other hand, I really would like to see expository work better valued. Right now, if someone writes an article making X’s unreadable but important work accessible to the community, this is dismissed as “just expository” and therefore lesser work, unless the author manages to attach some minor new result to it whereupon the paper gets upgraded immediately to the “research” category. I don’t think that this is right.
            • Peter 2012/02/07 I see your point. What might help is a culture of seeking co-authors to remedy such deficits (if I was daring, I’d suggest this as referee of such a paper but that’s most likely too late in the game). In set theory, Saharon Shelah seems similar to the researcher you describe. Reading a Shelah paper can be very painful, but reading a Shelah-Goldstern or Shelah-Blass paper usually isn’t (of course, with 1000+(!) papers Shelah has many, many co-authors for other practical reasons). Oh, and I wholeheartedly agree with you that we should value expository work seriously!
  • Joel David Hankins 2012/02/02 Peter, I’m unsure whether to take your remark in the second comment as criticism or as joking praise… I would think that vigorous participation on MO by a logic user such as myself or Andreas Blass (or Emil, Carl, Francois, etc. etc.) would be seen as fundamentally encouraging of a vigorous logic activity there.
    • Peter 2012/02/03 Joel, I mean it as both criticism and praise. Praise, obviously, for giving fantastic answers. But it is also criticism. I see mathoverflow activity as something that adds to the research reputation of, in particular, untenured faculty. In fact, I sincerely hope that activities such as mathoverflow will soon find their rightful place in the research section of people’s CV. (And I’m baffled that not even Anton is getting the recognition he deserves — mathoverflow has probably created more impact than an entire year of Inventiones papers.) The problem I see is that nobody else has a chance of building a reputation by answering questions because of power users such as yourself. This is not a specific logic/set theory problem, since I’ve seen colleagues in other fields make the same observation. It’s probably easier to spot in a small field such as set theory. I think it would help if there was a culture of less hurry on MO. Why not leave a question unanswered for a day or two even if you have an answer? The question is hardly life-and-death… But younger people (such as graduate students, postdocs) might get a chance to take a first step into the community. I’m not saying that there is a solution — there might very well not be. In fact, when I say that MO deserves to be in the research section of a CV, I don’t mean that it should be the only thing there. We need many, many more platforms to allow researchers to contribute in other forms than old-fashioned papers. I should add, this isn’t about me. There are other reasons why I don’t participate on MO anymore (though I like reading it).
      • Joel David Hamkins 2012/02/04 But surely a major part of the attraction of MO is its vitality, the energetic participation by knowledgeable users. My view is that its mildly competitive nature, from a sociological design perspective, is absolutely key to its success.
      • Peter 202/02/04 I wasn’t trying to describe why MO is attractive to some of its users. I was trying to describe why it isn’t attractive to others. Izabella Laba had a discussion with yet different reasons a while ago. But yes, I disagree with your view that the competitive nature is key to MO’s success. It may have been in the past, but I think it can become damaging in the future.
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