As pointed out by Philippe, this abstruse goose cartoon shows that analytic number theory is now part of the *Zeitgeist*.

# Category: Literature

## Is the Kierkegaardian idea true? and other queries

In February, I was invited to give talks in Bristol and Oxford, and I spent the night after the second talk in a guest room of Worcester College. While looking at the brochure explaining the history of this college, I noticed that a previous guest had left a cryptic inscription, which I took a photograph of:

Can anybody make a guess of what is the first line? It is

What is the **** historical perspective?

but I can’t read the missing fourth word!

And what is the Kierkergaardian idea, really?

## On diplomats

Quizz: who wrote

Il a publié il y a deux ans (…) un ouvrage relatif au sentiment de l’Infini sur la rive occidentale du lac Victoria-Nyanza et cette année un opuscule moins important, mais conduit d’une plume alerte, parfois même acérée, sur le fusil à répétition dans l’armée bulgare, qui l’ont mis tout à fait hors de pair.

or, in translation:

He has published two years ago (…) a book concerning the feeling of Infinity on the occidental shore of the Victoria-Nyanza lake, and this year another booklet, less important but written with a lively, and even piercing, pen, on the repeating rifle in the bulgarian army, which have made him rather peerless.

This reminds of the curiously little-known hilarious “Antrobus stories” of diplomatic mishaps:

It was during one of those long unaccountable huffs between ourselves and the Italians. You know the obscure vendettas which break out between Missions? Often they linger on long after the people who threw the first knife have been posted away. I have no idea how this huff arose. I simply inherited it from bygone dips whose bones were now dust. It was in full swing when I arrived — everyone applying freezing-mixture to the Italians and getting the Retort Direct in exchange. (…) So while bows were still exchanged for protocol reasons they were only, so to speak, from above the waist. A mere contortion of the dickey, if you take me, as a tribute to manners. A slight Inclination, accompanied by a

moue. Savage work, old lad, savage work!

(from “The game’s the thing”, where a soccer game between the English and Italian embassies rather degenerates.)

## More things of the day(s)

(1) Today’s Word of The Day in the OED: *afanc*, which we learn is

In Welsh mythology: an aquatic monster. Also: an otter or beaver identified as such a monster.

Maybe the Welsh otters, like their rugbymen, are particularly fierce?

(2) Yesterday’s Google doodle, in Switzerland at least, celebrated the 57th birthday of Gaston Lagaffe

I’ve heard that Gaston

is mostly unknown to the US or English, leaving many people with no reaction to the mention of the *contrats de Mesmaeker*

or to the interjection *Rogntudju!*.

This lack of enlightenment is a clear illustration of the superiority of the continental mind.

## James Maynard, auteur du théorème de l’année

How many times in a year is an analytic number theorist supposed to faint from admiration? We’ve learnt of the full three prime Vinogradov Theorem by Helfgott, then of Zhang’s proof of the bounded gap property for primes. Now, from Oberwolfach, comes the equally (or even more) amazing news that James Maynard has announced a proof of the bounded gap property that manages not only to ask merely for the Bombieri-Vinogradov theorem in terms of information concerning the distribution of primes in arithmetic progressions, but also obtains a gap smaller than 700 (in fact, even better when using optimal narrow *k*-tuples), where the efforts of the Polymath8 project only lead to 4680, using quite a bit of machinery.

(The preprint should be available soon, from what I understand, and thus a full independent verification of these results.)

Two remarks, one serious, one not (the reader can guess which is which):

(1) Again, from friends in Oberwolfach (teaching kept me, alas, from being able to attend the conference), I heard that Maynard’s method leads to the bounded gap property (with increasing bounds on the gaps) using as input any *positive* exponent of distribution for primes in arithmetic progressions (where Bombieri-Vinogradov means exponent 1/2; incidentally, this also means that the Generalized Riemann Hypothesis is strong enough to get bounded gaps, which did not follow from Zhang’s work). From the point of view of modern proofs, there is essentially no difference between positive exponent of distribution and exponent *1/2*, since either property would be proved using the large sieve inequality and the Siegel-Walfisz theorem, and it makes little sense to prove a weaker large sieve inequality than the one that gives exponent 1/2. **Question**: could one conceivably even dispense with the large sieve inequality, i.e., prove the bounded gap property only using the Siegel-Walfisz theorem? This is a bit a rhetorical question, since the large sieve is nowadays rather easy, but maybe the following formulation is of some interest: do we know an example of an increasing sequence of integers , not sparse, not weird, that satisfies the Siegel-Walfisz property, but has unbounded gaps, i.e.,

(2) There are still a bit more than two months to go before the end of the year; will a bright PhD student rise to the challenge, and prove the twin prime conjecture?

[P.S. Borgesian readers will understand the title of this post, although a spanish version might have been more appropriate…]