## The most expensive french integer is 1

March 15, 2015

The first ever domain name was recorded in 1985 (see this very nice infographics for a timeline from then to 2015).

Until recently, the historical TLDs (whether gTLDs like .com .org .net, or ccTLDs like .fr .co.uk) did not offer single character names : most single characters names of gTLDs were reserved in 1993 by IANA, and all 1 & 2 characters names of ccTLDs were too by their respective operators.

But in 2008 ICANN initiated a program to allow new TLDs, and 1930 applications met a 2011 deadline, which resulted in the approval of several hunded ones.

This meant that new money was about to pour in from investors vying for marketable names, especially short ones.  Perhaps as a result, in october 2009 single-characters names of .de  were made available, and snapped-up.

The period 2014-2015 sees many of the aforementioned new TLDs start selling domains in the usual three phases (sunrise, landrush, public), and some of them (a minority thought) are allowing single-characters names.

With the renewed interest in domain names, in 2014 the .fr operator afnic opened a similar procedure to sell 1 and 2 character names (with proceeds going to some public funds to reduce inequalities in France).  Afnic decided to price the 4 weeks of the landrush phase in a degressive manner : the first week each domain cost 15,000€ excluding VAT, the second they cost 10,000€, the third they were set at 5,000€, and the final week at 100€ (the next phae being at the public price, a few euros).  Of course, most people buy their domain name through a registrar, which means some extra costs.

I was obviously interested in buying a number like 11.fr or name like pi.fr and set my sight on the last week of landrush, which opened march, 9 at 12:00 Paris time.  The only number to have gone in a previous week was 1.fr, for 5,000€, making it the most expensive french number.

When the moment arrived,  I was all set, and made my first order at 12:00:05. Already bought! Wow, tried several other numbers, all already gone!  Some controversy quickly erupted on twitter, with several users noticing that some registrars (specialized in the resale of domain names) had placed orders up to a full 30 minutes before the deadline.  Not fair indeed, and to the credit of Afnic these orders were swiftly canceled with the 311 corresponding names back for sale on the wednesday (and the culprits blacklisted)…only for other similar registars to buy them all within a few seconds after the start time. Lots of ordinary people interested in simply getting their initials or a number got disapointed.

So, except for 1.fr, all domains from 0.fr to 99.fr will have their price set up on the secondary market, but I doubt they’ll top 1.fr :-)

## Forthcoming epijournals

March 7, 2015

Six months ago, I was wondering whether epijournals might be just around the corner, when in restrospect that wasn’t the case…

But very recently, the episciences.org website has listed the titles (and titles only for now) of three new journals, among which two seem to focus on mathematics : the Hardy-Ramanujan Journal, and Mathematica Universalis.

Obviously several people are hard at work on this, and probably doing things very carefully to ensure a smooth launch.

Flower 6.6.6 Work in progress, by Ella T. on flickr,

whose great gallery is not to be missed !

## Girard’s Transcendental Syntax

March 1, 2015

Jean-Yves Girard has recently put online his two papers on Transcendental Syntax.   As of early march 2015, part I is now said to be in final state while part II is still a blueprint (“This part is so new, the notions are so fresh, that can hardly be more than a blueprint; I am not yet familiar with the notions introduced, which may account for the sloppiness of notations. Hence the inclusion of this section in annex. I beg for the leniency of the reader in view of the absolute novelty of the ideas.“)

The aim is apprently a “fully independent approach to logic: no syntax, no semantics, i.e., no prejudice.

As usual with Girard, the papers introduce new terminology that probably requires a fair amount of time to grasp, but at the same time are written in appealing semi-discursive style, with motivations fully apparent.

## Cédric Villani’s book tour

February 21, 2015

Cédric Villani, who is running an undergraduate MOOC with Diaraf Seck on evolution equations, is apparently about to tour the english-speaking world, now that his essay has been translated to english and is about to hit the stores (I did enjoy the original french version).

Some people from the book publishing world have started talking about it on twitter (e.g. here or there), while a review in The Times has just appeared (behind a paywall).

I’ve seen that events are planned next march in London, in Bristol, and in Oxford. Also, a BBC radio 4 program is scheduled, and then in april an event in Seattle. And perhaps other things elsewhere that I didn’t spot.

Update: apparently there’s a second event in London. Also, the Guardian now has a review of the book, and so has the New Scientist.

Update 2: the reviews are now abundant so I won’t care to track them all. Just to mention two more,there’s one in The Spectator, and another in THES.  Some like the book while others virulently dislike it.

## Launch of the North-Western European Journal of Mathematics

February 20, 2015

As announced in the new issue of Gazette des Mathématiciens, a new (diamond-like) Open Access journal has been launched recently, the North-Western European Journal of Mathematics.

It is technically based in Lille and has support from the French Mathematical Society (SMF), the Dutch Mathematical Society (KWG), the Luxembourg Mathematical Society (SML) and the Fields Institute.

The editor-in-chief Serge Nicaise and technical director Nicolas Wicker say in the Gazette that :

Notre but est de mettre en place un journal académique de grande qualité en accès libre faisant concurrence aux trop nombreuses revues payantes détenues par les grandes maisons d’édition.

[…]

Évidemment, une telle initiative est un pari, et ne pourra être couronnée de succès qu’avec un mouvement d’ensemble de notre communauté vers les revues libres. Notre contribution à ce qui est une bataille contre les éditeurs privés est de joindre nos efforts
avec nos voisins du nord afin de faire déborder la lutte hors de la France, qui pour l’instant fait figure de pionnière.

Rough translation :

Our goal is to set up an academic open access journal of great quality to compete against the too vast number of non-free journals detained by the big publishing houses.

[…]

Of course, such an initiave is a bet, and can only become a success with a common movement of our community towards open access journals. Our contribution to what is a battle against the private publishers is to join our efforts with our northern neighbours to make this struggle develop beyond the boundaries of France, which for the moment acts as a pioneer.

So, that’s another journal added to the list of open access ones.

## Embedding a Turing Machine

February 17, 2015

The idea to embed a Turing Machine in famous problems seems to have popped up a lot in recent years, some examples I’ve noticed :

That last paper does mention Bjorn Poonen’s very interesting essay on the topic of undecidability.

## Recent efforts to understand Mochizuki’s work

February 15, 2015

As pointed out by Thomas Riepe on Mathoverflow, yesterday Ivan Fesenko released overview notes on Shinichi Mochizuki’s work, with lots of efforts to relate IUT to earlier “mainstream” knowledge. And several workshops are planned in Europe and Japan in the coming years.  To quote Fesenko:

The mathematical vision and perseverance of the author of IUT during 20 years of work on it is admirable.

A valuable addition to this is his investment of time and effort in answering questions about his work and explaining and discussing its parts, via email communication or skype talks and during numerous meetings and seminars at RIMS.

Given the number of upvotes for Minhyong Kim’s two recent open-ended questions What is a Frobenioid? and What is an étale theta function? it seems as though there’s definitely momentum building up.

## Auctions of mathematical texts

February 12, 2015

On saturday in Royan there will be on offer (for about €300/350) a handwritten set of lecture notes of Cauchy’s 1824 course on Calcul différentiel et intégral, taken by Lamoricière.  It may well beat that estimate by some margin.

Indeed, last december, the own annotated copy of Hugens’ Horologium Oscillatorium Sive de Motu Pendulorum ad Horologia Aptato Demonstrationes Geometricae (1673), went for \$965,000 after an estimate of 150,000/200,000.

A month earlier, a 1931 offprint of Gödel’s Über Formal Unentscheidbare Sätze der Principia Mathematica und verwandlter Systeme I, achieved £104,500 after an estimate of £12,000/£16,000.

So, there seems to be a market for the rare and historically important items, that’s not too surprising but the level is pretty high (I guess all it takes is just a couple of mathematically enclined high-ranking google executives, or the likes…). And it’s not only auctions, fixed price items exist too, like these 3 manuscript pages by Gauss available for €65,000.

Update: the aforementioned sale has been broadcast online earlier today, and those handwritten notes indeed attracted interest, with a little fight between the floor and online bids ending at €1,300.

## A (probably) useless reformulation of the twin prime conjecture

February 8, 2015

In light of the previous post the following is obviously a long stretch, but I can’t resist mentioning it.

The way Jones-Sato-Wada-Wiens construct their polynomial is to start from the characterization of primes by Wilson’s theorem (namely that $k+1$ is prime iff $k+1$ divides $k!+1$), to convert that into a system of exponential equations, and this is itself converted into a larger system of polynomial equations, which are finally assembled into one big polynomial.

Now twin primes can be characterized also by a Wilson-like statement, namely $k+1, k+3$ are twin primes iff $(k+1)(k+3)$ divides $4(k!+1)+k+1$.

So one could construct a polynomial in several integer variables $P_{2}$ along the same lines, and end up with the (difficult to exploit) reformulation of the twin prime conjecture : there are infinitely many twin primes iff $P_{2}$ takes on arbitrarily high positive values on $\mathbb{N}^m$ (where $m$ is the number of variables). Said differently, a disproof of the conjecture would follow from an absolute bound.

By Polymath8b, a similar polynomial $P_{246}$ for the case of pairs $(n, n+246)$ is known to indeed take arbitrarily high positive values, while of course the same is true for the original Jones-Sato-Wada-Wiens polynomial since there are infinitely many primes.  So those two “sandwich” $P_2$ somehow, and there just might be hope to say educated things about that (which I obviously can’t, but the learned reader is encouraged to do so, should that seem to be a good idea).

Update: for sake of completeness, I should have mentioned that the Wilson-like characterization of twin primes goes back to a paper of Clement in the Montly from 1949, and the analog for pairs of primes $n, n+2k$ has been worked out by Lee and Park to be that $n(n+2k)$ divides $2k(2k)!((n-1)!+1)+((2k)!-1)n$.

## What do solutions of the Jones-Sato-Wada-Wiens polynomial look like?

February 1, 2015

As soon as one comes across the story of the set of primes being the positive values taken by the Jones-Sato-Wada-Wiens polynomial of degree 25 in 26 variables (see also the senior thesis of Cabusora, or, for french-speaking readers, this RMS paper by Collet and Vidiani), one wants to start playing with it, and see some solutions.

But the aforementioned sources don’t mention any, and neither do more recent books like Denef’s on Hilbert’s tenth problem, the one by de Koninck and Luca on analytic number theory, the one by Crandall and Pomerance on a computational perspective on primes, the one by Everest and Ward on introductory number theory.

Fortunately, there is an Msc thesis by Gupta which does take the trouble to find the values of all 26 variables for the prime 2, and it is informative. Using his notations, these values are:

$k=0$, $g=0$, $f=17$, $n=2$, $p=3$, $q=16$, $z=9$, $w=1$, $h=2$, $j=5$, $e=32$ (parameter of a Pell equation), $a=7901690358098896161685556879749949186326380713409290912$, $o=8340353015645794683299462704812268882126086134656108363777$ (these two being the smallest solution of that Pell equation), $y=2a$, $x=2a^2-1$, $m=a$, $\ell=1$, $i=0$, $v=2a-3$, $b=0$$s=1$$t=0$, $r\simeq 10^{10^{52}}$, the final $u, c, d$ being larger still.

The basic idea is that the built-in Pell equations inside the polynomial quickly lead to very large values indeed. No hope to play with 26 small integers, say less than $10^6$.