## Laure Saint-Raymond on the backpage of Libération

July 28, 2014

There are not many women in the french Académie des Sciences. So it was a great news when last december Laure Saint-Raymond got elected (in the mechanics section, due to her work on physics equations, rather than in the math section).

Today, there’s a portrait of her on the backpage of Libération (a nationwide french newspaper, see picture below). Great exposure for women in science.  And I have noticed that her work has been discussed (in french) in a recent article by her PhD advisor Golse in Gazette des Mathématiciens, while a few months ago there was another portrait of her in Le Journal du CNRS.

(There’s a quite bad typo in the Libération paper: they got the only equation in the text wrong, printing $y=x2/10$ instead of $y=x^2/10$. Sigh…)

## Proof assistants and the next decade

July 22, 2014

It is quite interesting to look, if only casually, at the two trends that are emerging regarding proof assistants:

1) the “natural language” trend: one finds there the work of Ganesalingam & Gowers (which, so far, uses full first-order logic and deals with metric spaces), but also the interesting work of Stovanovic, Narboux, Bezem & Janicic (which, so far, uses a fragment a first-order logic and deals with Geometry à la Tarski). The latter paper discusses the mild differences between these two approaches, and in both papers one can see examples of proofs that these programs produce.   See also Geoproof (maintained by Narboux), for example this nice animation shows a Coq verified interactive proof of Thales’ theorem.

2) the “univalent foundations” trend: Homotopy Type Theory (HoTT),  with these slides by Voevodsky providing a recent account.

All this begs the question: will these two trends merge productively over the next decade? I do hope so (creating a setting with as sound foundations as one would wish for, while ensuring the certified proofs produced are nicely human readable). And in that case, I’m wondering what can be reasonably anticipated.

Probably the gradual emergence of just a big website where mathematicians would write down their proof strategies, which would get accepted or refused in an instant. Obviously, in parallel this would mean the gradual end of some aspects of the technical side of peer-reviewing, but humans would still be left to decide which theorem is/isn’t interesting, which and paper is/isn’t well written.

On a longer time scale, one may envision a time when, with computers just generating indiscriminately all possible theorems by raw enumeration, humans will get completely out the game, and will be left with reading what computers have found. In something like 30 or 50 years time, that’s a distinct possibility.

July 6, 2014

## The strange world of contributed ICM talks and posters

June 29, 2014

ICMs are professional events, attended by thousands of mathematicians. There are Planary talks and Invited talks with first rate contributions by specialists. All of them are recorded in the proceedings volumes.

And then there are Contributed talks, and Posters, which are not recorded in the proceedings, apparently. And this seems to be leaving the door open to virtually any claim. Indeed, one can find there a mix between regular graduate student or postdoc contributions, and, shall we say, more dubious material.

In fact, in 1998 in Berlin, nothing suspect pops up among the talks announced in time, but the google cache tells us that the accepted late submissions included “Fermat’s Last Theorem, a Simple Proof based on Irrational Numbers“, and “NP = P“.

Unfortunately, I couldn’t manage to find the ones from 2002 in Beijing.

But, nil desperandum, there were also noticeable revelations in 2006 in Madrid, including “On Fermat’s historic marginal note: some significant left-out grains of truth leading to new proof of FLT“.

In 2010 in Hyderabhad, lots of creativity was again to be found, including “Four Errors in Cantor’s Proofs on the Uncountability of Real Number Set and The Foundation of Mathematics“, but also three new proofs of FLT ( “Fermat’s Last Theorem“, “Proof of Fermat’s Last Theorem (FLT)” and “Proof of Fermat’s Last Theorem“).

The 2014 one in Seoul promises yet more of the same, including “How to prove the Riemann hypothesis” (based on v16 of this paper, apparently).

I don’t quite understand why all this is allowed to happen…

## First Mathematics Breakthrough Prizes announced

June 23, 2014

As reported by the BBC, the first Mathematics Breakthrough Prizes, each endowed with \$3m, have just been awarded to (in alphabetical order): Simon Donaldson, Jacob Lurie, Maxim Kontsevich, Terence Tao and Richard Taylor.

A good mix of ages and topics (although it is perhaps surprising that no probabilist has been distinghuised in the first batch).

Curious to see whether they’ll keep the 5 laureates per year rate for long, but to launch the prize this looks like it was necessary indeed.

Edit: according to the New-York Times, from now on the plan is to have one mathematics laureate per year.

## 3D printing mathematical objects

June 21, 2014

With all the 3D printing craze, some folks have been trying to get mathematical objects. For instance here are some by fdecomite on flickr:

The details are a bit rough

but still it is quite decorative and I can imagine metal printing to be even nicer.

As for monochrome objects, some impressive ones have been attainable for a couple years, like this quadrifolium

## Plans for 2018 and 2022 ICMs

June 17, 2014

Although it is quite far in the future, it appears the Comité National Français des Mathématiciens is intent on making a bid for France as organizer of the 2022 ICM.

As for the 2018 ICM, the deadline for bids was in november 2012 and the location will be announced next august, I think. There is a bid from Brazil, and I couldn’t find others online.

Speaking of ICMs, the medalists probably know who they are by now (they usually get a call in may). There’s been an interview last month in Le Journal du CNRS of Martin Andler (otherwise known as energetic Animath president) where he says that

Pour les lauréats, le secret est tout de même lourd à porter, notamment vis-à-vis des autres candidats possibles à la médaille. Dans les semaines qui précèdent la cérémonie, la tension est palpable entre les mathématiciens !

Which I’d roughly translate as

For the laureates, the secret is still quite heavy to bear, in particular with respect to the other possible candidates for a medal. In the weeks that precede the ceremony, tension between mathematicians is palpable!

The format of it all certainly seems a bit devoid of understanding of human emotions…

## Research level math videos

June 9, 2014

It is a bit unfortunate that no single place for research-level maths videos yet exists (when one can even find a list of Paris places bearing the name of a mathematician). Here are some URLs that I could find:

[Edit: there's a very nice list of videos on Pinterest which focuses on courses and colloquium-style talks, some being taken from the pages below, but that list doesn't include most of the dozens of more specialized talks mentionned on those pages.]

MSRI (tons of workshops…)

IAS (includes Minerva Lectures…)

Newton Institute (tons of workshops…)

Institut Henri Poincaré (includes workshops and recent Bourbaki seminars…)

IHÉS  (includes recent courses…)

PIMS (under the name mathtube.org)

ICTS (lots of courses…)

University of Oregon (includes Moursund Lectures).

Hebrew university of Jerusalem (includes Landau Lectures)

HIM (lots of seminars)

ICM (from 1998 Berlin ICM onwards)

Cornell University

Stony Brook

U Texas at Austin

IMPA

Clay Mathematics Institute

U of Arizona (mostly Arithmetic Geometry)

Mathnet Korea

MRC (Stanford)

IMA (tons of workshops…)

Math-net.ru (lots of seminars…)

U of Washington (includes Milliman Lectures…)

Michigan State U (includes Phillips Lectures…)

Topology seminars filmed by Carmen Rovi (UK, Oberwolfach…)

BIRS (lots of workshops…)

Institut Fourier (several summer schools…)

Columbia (Eilenberg lectures…)

Feel free to mention other relevant ones in the comment section (the post will be periodically updated accordingly, with most recent additions at the end of the list).

Obiously, a nice global interface with search by keywords or names would be much more appropriate (I just might set it up later, if not too much work, and not too expensive).

## Journal de l’École polytechnique has been relaunched

May 29, 2014

Very recently it has been announced that the Journal de l’École polytechnique (JEP), has been relaunched last year, with a first a paper appearing a couple months ago (they say it had existed during the period 1795-1939 and that it’s where Poincaré published Analysis Situs for instance.)

Apparently the aim is for it to become a high prestige journal:

It aims at reaching the best level, when compared to international mathematical journals, in all domains of applied and fundamental mathematics.

It is hosted by Cedram.org, and is published under the Creative Commons license BY-ND. It is effectively diamond open access since it does not charge a fee to anybody (authors and readers alike).

One minor, strange, point is that (see their copyright section):

Access to the database containing the bibliographical references of all the articles is totally free via the “search” and “browse” functions. The database itself is the property of the Journal de l’École polytechnique, and contains elements covered by copyright. Any copy or reconstruction of a significant part of the database using data from the Journal de l’École polytechnique site is a counterfeit punished by law.

Anyway, I’ve added that journal to my list of serious open access mathematics journals that don’t charge any fees.

## The “Arithmetic Site” of Connes and Consani

May 25, 2014

A week ago, Connes and Consani posted to the arXiv a 6 pages note titled The Arithmetic Site (and submitted to Elsevier owned CRAS).

The abstract ends with:

This note provides the algebraic geometric space underlying the non-commutative approach to RH.

which sounds important enough… And at the end of the introduction that same sentence is repeated, followed by:

It gives a geometric framework reasonably suitable to transpose the conceptual understanding of the Weil proof in finite characteristic as in [7]. This translation would require in particular an adequate version of the Riemann-Roch theorem in characteristic 1.

which sounds like there is still some distance before a proof of RH occurs (the reference [7] is this 1958 paper by Grothendieck, and wikipedia has some background for the notion of a site, and the Riemann-Roch theorem).

I’ve now noticed that this paper had been preceded by some lectures by Connes and Consani at Ohio State University.

Connes started working on a noncommutative geometry approach to RH in 1996 with a note in CRAS (freely available in Gallica) followed by this long 1998 paper. In recent years, with Consani and Marcolli, they have more and more evolved away from the physics interpretation side towards algebro-geometric notions such as the field with one element $F_1$, and tropical geometry.

If some readers with a good command of those topics wish to make informative comments on the latest note, they are very welcome to do so (comments are moderated but should appear within 24 hours).