Short proofs

August 2018 was this blog’s busiest month in two years.  Practically all the visits came in the first two weeks, with much of the traffic arriving from Germany (1788 of 5574 views).  The explanation, apparently, is that Peter Scholze’s Fields Medal was announced the first day of the month, and the Hausdorff Institute of Mathematics in Bonn chose my blog post  as one of three “interesting and popular articles” on his work, along with the article Erica Klarreich published in Quanta two years ago, and my chapter in the book What is a Mathematical Concept? edited by de Freitas, Sinclair, and Coles.  Quanta‘s articles on mathematics are notoriously interesting and popular; my chapter on the “perfectoid concept” may or may not be interesting, but I can’t imagine why anyone would consider it “popular”; and the blog post — which, as you may remember, is a text that did not qualify for publication in The New Scientist, is somewhere in between.

Anyway, my WordPress dashboard informs me that the Hausdorff Institute’s recommendations were picked up by (Frankfurter Allgemeine Zeitung) as well as  These two sites, together with the Hausdorff Institute, my indefatigable colleague Peter Woit’s blog, and the inevitable Google and Facebook, accounted for most of August’s referrals.

This year’s Fields Medals were widely covered by the international press, with Scholze’s story featured most consistently, along with the unexpected drama of the theft of Birkar’s medal.  Apart from Ulf von Rauchhaupt’s rather insightful article (visibly influenced by my blog post, not always with full attribution), coverage was mainly as approximate as one might expect, and was more informative about the current state of science reporting than about the priorities of contemporary mathematics.  Most entertaining for me was the article on the French website, which included this surprising bit of news:

Scholze a donc incontestablement la bosse des maths, mais il ne s’agit pas de son seul talent. En effet, il faisait partie d’un groupe de rock à 17 ans, puis a été professeur d’histoire allemande à 24 ans.

Rough translation:  “Scholze unquestionably has the math bump [a French expression that derives from phrenological notions popular in the 19th century — apparently there really is such a cranial bump, though its connection to mathematics is dubious] but it’s not his only talent: he played in a rock band at age 17, then at age 24 became professor of German history [sic!]”  Instead of a byline the article refers to three sources:  DW, El País, and Quanta.  I strongly suspect the sources were consulted and consolidated by a robot reporter which offered its own intrinsically logical interpretation of the sentence that opens the El Pais article:

Con 17 años tocaba el bajo en un grupo de rock, con 24 se convirtió en el catedrático más joven de la historia de Alemania.

The news coverage also revealed something of the network of journalists’ local contacts.  Thus the New York Times consulted Jordan Ellenberg, while El País quoted José Ignacio Burgos; Le Monde went to the trouble of finding four different mathematicians to contribute sentences about each of the four medalists:  Laurent Fargues (for Scholze), Philippe Michel (for Venkatesh), Jean-Pierre Démailly (for Birkar), and, inevitably, Cédric Villani (for Figalli).

Practically every article alluded to Scholze’s refusal of the New Horizons Prize, already discussed on this blog in 2015.   This came as no surprise to me; in fact, I had already anticipated the hypothetical reader’s fascination with this telling detail in the article I had prepared for The New Scientist, with the following sentence about his motivations:

My guess — but it’s no better than anyone else’s — is that he decided that the priorities of Silicon Valley are just not compatible with those of the mathematical community, as he sees it.

This means something very specific to me, and it may mean something to mathematicians reading this post, but to the hypothetical New Scientist reader it means exactly that Scholze refused the prize because he refused the prize, a vacuous observation embellished with the enigmatic expressions “mathematical community” and priorities.”  As we already know, this sentence never made it into the pages of The New Scientist; but, much to my surprise, it was translated into Spanish, at least twice, and at least once into German.  In each case my sentence was promoted to the status of a “speculation,” although the journalists had absolutely no reason to treat me as an authority on the matter, and besides which, as, I already explained, in the context of a newspaper article my sentence was totally devoid of content.  (Though one could always hope that a particularly attentive reader will find it surprising that not only is these such a thing as a “mathematical community” – though the word “community” disappeared from the German version — but that it even has “priorities”.   The reader may be sufficiently intrigued to wish to learn more about this, in which case:  good luck!)

Apparently Scholze’s refusal of the $100,000 prize cried out so desperately for explanation that the journalists grabbed at the only straw they found.  If they had been a little more patient, though they could have waited until August 6, when Scholze’s own answer to the question appeared in his interview with Helena Borges in O Globo:

O que posso dizer é que aquele era um prêmio e que este é outro. E é tudo que vou comentar sobre.

Rough translation, which curious readers are invited to ponder:  “What I can say is that that [the New Horizons Prize] was one prize, and that this [the Fields Medal] is a different one.  And that’s the only comment I’m going to make about that.”

The other item mentioned in practically all the press coverage recalled how Scholze distinguished himself already at age 22 when (quoting O Globo again) he “transformou uma teoria de 266 páginas em um texto sucinto de 37 folhas” — “transformed a 266-page theory into a succinct text of 37 sheets.”  Most of the other sources, starting with Erica Klarreich’s article in Quanta in 2016, identified the overstuffed “266-page theory” as none other than my book with Richard Taylor.  There is an interesting lesson hidden in that story about radical abbreviation, but that’s a silly (as well as misleading) way of putting it.  I was hoping to explain why that’s the case before I present an overview of the proof of the local Langlands conjecture to the graduate reading group that meets at Columbia tomorrow afternoon, but unfortunately I have run out of time, and I’ll have to return to the question later.

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