White smoke over Oxford?


I looked for tweets from the events of the first day of the Clay Mathematics Institute Workshop on Mochizuki’s inter-universal Teichmüller theory, especially from the discussions scheduled to end at 18:00 GMT.  No tweets, but I did find an exceptionally thorough 3200-word article by Agnes Handwerk, published last June on the website of Deutschlandradio Kultur, entitled Wann ist ein Beweis richtig? [When is a proof correct?].   If you listen to the 30-minute broadcast you will recognize the voices of Gerd Faltings, Norbert Schappacher, Minhyong Kim (under a German voiceover), and Samuel Patterson, among other mathematicians — and sociologists.   Mochizuki’s proof is treated alongside Heegner’s solution of the class number one problem as examples of proposed solutions to important problems that were not immediately recognized as such.  It takes an unusually theoretically-oriented radio audience to appreciate the aim of Handwerk’s explicitly sociological account of Wahrheitsfindung in der Mathematik.

Back in 2008, Handwerk wrote (and broadcast) a no less densely extraordinary piece on the occasion of Grothendieck’s 80th birthday, entitled Geometry and Revolt; for this she won the Journalism Prize of the Deutsche Mathematiker-Vereinigung.  (With Harrie Willems, Handwerk also produced a biographical video of Yuri I. Manin and another one about Wolfgang Doeblin.)  While waiting for the white smoke of Wahrheitsfindung to float (or not) above Oxford you can do worse than read Handwerk’s articles.


Update:  When I posted this yesterday I was unable to retrieve the one-line summary of Handwerk’s sociological thesis.   Here it is:

Und es besteht ein Gegensatz zwischen dem Kreativen, dem freien ungebundenen Denken, und dem Normativen, den Regeln der Community.

which means (roughly) “there is a conflict between the Creative — free unbound thinking — and the Normative, the rules of the community.”  Handwerk’s sociological reference is Pierre Bourdieu, as read by the contemporary Berlin sociologist Christian Schneikert.  That’s a somewhat strange choice; Bourdieu didn’t focus on consensus formation in the sciences.

A first tweet by math_jin reports that Felipe Voloch is reporting on the conference from Google+.  Voloch’s feed is being followed actively.  Journalists take note!

Update:  Der Spiegel published a 300-word piece on the Oxford conference entitled Todeszone der Mathematik.

 In die­sen Hö­hen ist die Luft der Abs­trak­ti­on so dünn, dass Hal­lu­zi­na­tio­nen auf­tre­ten.

The journalist compares attempting to follow the explanations of Mochizuki’s work to the consequences of reading Monty Python’s Funniest Joke in the World.  (Update of update:  I have just been reminded that there was already a Monty Python comment in Davide Castelvecchi’s Nature article, the subject of this earlier post.)  There’s a sensible discussion of what’s behind the Spiegel article on scienceblogs.de.

I’d be curious to know what the internet is saying in Japanese and Chinese.  There’s quite a lot of material and I would be grateful for translations.


17 thoughts on “White smoke over Oxford?

  1. Voynich

    Handwerk’s article is really nice. Not sure if this was an idiosyncrasy of Google Translate or some characteristic of the German language (or both), but some of the sentences struck me as especially interesting and provocative in their wording, for example: “He calls on his colleagues to abandon previous certainties.” A native English speaker formulating a similar thought would almost certainly have said ideas/assumptions instead of certainties. Food for thought?


    1. mathematicswithoutapologies Post author

      The word is “Gewissheiten” and I don’t think any other translation is natural. This is Handwerk’s reading and not a quotation from Mochizuki. I don’t believe he has called on his colleagues to abandon ALL previous certainties; that would be a most peculiar way to advance mathematics.

      On the other hand, Google Translate renders “fordern” as “to call upon” whereas I had read it as “demand.” I note that an alternative translation is “challenge.” A native German speaker is needed to sort these out.


  2. Gerd

    Assuming you are referring to this sentence (I am native German but consider my command of English rudimentary):
    “Er fordert von seinen Kollegen, bisherige Gewissheiten aufzugeben.” I would loosely translate it like: He demands (with a touch of “requires”) to abandon things hitherto taken for granted.


    1. mathematicswithoutapologies Post author

      This is very helpful. I checked the Wikipedia entry on Gewissheit, which treats the word as a philosophical term, with a brief discussion of the meaning in probability theory. On the one hand, Wikipedia gives certainty as the English equivalent; on the other hand, the German article says Gewissheit in everyday language is a kind of subjective Sicherheit whose English equivalent is security, which is what you get from a Sicherheitsgürtel or seatbelt. So Handwerk says Mochizuki is demanding that his colleagues unfasten their seatbelts.


      1. Gerd

        Out of context and on demand of a one-word translation, I would translate “Gewissheit” also with “certainty”. But then in this context and especially with the predicate “bisherig” (until now/hitherto) it makes more sense to weaken it. Its a paradox “bisherige Gewissheit” but then its also quite much of a standing expression, implying that later it will turn out that in fact it was not really a certainty, but just appeared like that.
        I read her like Mochizuki says you should forget what you always took for granted (in order to be able to digest his theory). Its a bit like the in the Kung-Fu movies “forget everything you have learned before it is of no use”.


  3. elbert

    Wow, I think I’m starting to see the problem here. This man is trying to reinvent the Yin and the Yang of Principia Mathematica and this blog is hanging on the translation of one word from an unrelated writer…


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  6. dalawat

    Felipe Voloch is blogging about the goings on in Oxford on his Google+ page :


    Sample quote :

    Yamashita’s talks were very much like his online notes. So there we are. Yamashita (and later Mochizuki on Skype) referred to previous talks for answers to some questions. Readers may recall that earlier some questions were answered by saying that answers would come later. This subject may be locally trivial, but it seems to have infinite monodromy.

    Liked by 1 person

    1. mathematicswithoutapologies Post author

      I have been following Voloch’s comments, and so has everyone else in my department. Interestingly, his Google+ page seems to have been created specifically in order to trash my book. My March post “How to Read a Bad Review” has been seeing a lot of action over the last few days, a byproduct of the inconclusive Oxford events.


      1. voloch

        One does not create a Google+ page, one creates a Google+ account and the (initially empty) page gets created automatically. I’ve had the account for quite a while. I usually don’t find reasons to post but I read Google+ (and comment occasionally on other people’s posts) using that account. Your book, which I admittedly really dislike, indeed motivated my first post there. I thought Google+ would be a good platform for my ABC posts. The juxtaposition with my criticism of your book was an unfortunate accident, I am sorry if it brought unwanted attention. I will be willing to delete my post on MWA if it bothers you so much. Let me know.


      2. David Roberts

        Honest question: who are the “right sort” of people? Presumably not just average Jane mathematician…?

        As to Google+, a reasonable number of mathematicians were early adopters for one reason or another, so it became a reasonable source of interesting posts and discussions. One can read it without an account, but not comment (account is automatic for all with a gmail address).


      3. mathematicswithoutapologies Post author

        Thanks for the explanation regarding Google+. I have a gmail address that I avoid using unless absolutely necessary, so I could undoubtedly join if I saw the need.

        The comment about “the right sort of people” was meant to be ambiguous, but it’s to be expected that some people who adhere to positions that the book questions will not like it. I can think of other categories of people who might not like it (CDO managers, ministers under Sarkozy, militant platonists…)


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