Is Shinichi Mochizuki’s work slowly being absorbed ?

October 30, 2014

While I do not speak japasese, I’ve noticed a conversation somewhere, from which it appears that :

(a) Go Yamashita has a paper in preparation titled ‘A proof of abc conjecture after Mochizuki’, and he also is in the middle of a string of lectures on that topic : 18 hours of talks at RIMS last september titled ‘Inter-universal Teichmuller theory and its Diophantine consequences’, and two further weeks of lectures (68.5 hours in total) next march at a RIMS workshop titled ‘On the verification and further development of inter-universal Teichmuller theory’ ;

(b) Chung Pang Mok is in the process of giving an introductory talk to some of Mochizuki’s ideas at several places : a few weeks ago at MSRI and at UC Santa Cruz, and in the coming weeks at U British Columbia, and at Duke.

And just today, Mochizuki himself has posted to his ‘what’s new page’ the workshop announcement

Voevodsky’s fascinating interview

October 18, 2014

The october issue of Gazette des Mathématiciens  has a transcript in french of a really fascinating interview of Vladimir Voevodsky, as part of a dossier on Théorie des types et mathématiques certifiées.

The hour long video of that interview, in english and conducted by Gaël Octavia from Fondation Sciences Mathématiques de Paris (see also a blog set up for the ICM for context) is the following on Vimeo (and a must-see) :

 

Epijournals are around the corner

September 9, 2014

Browsing the episciences.org website recently, I’ve noticed that while math journals are not up yet, a first epijournal has seen the light of the day back in june : the Journal of Data Mining and Digital Humanities.

That’s a good opportunity to see how the project is intended to work : here’s the page for one of the first papers. One observes the following:

- a layout which includes title, journal reference, abstract, submission & publishing dates, bibTeX citation, social widgets, and access stats

- when downloading one gets a file (with a funny extension not readily recognized as pdf, the website developpers might want to add some .pdf suffix there) and that file is exactly the accepted version of the arxiv preprint, nothing added on top to say it has been published somewhere and no .sty file provided

- the website offers to log in (I haven’t tried yet)

 

It looks nice, but clearly some choices have been made, in particular : there’s no built-in comment system, no link to the authors’ own websites, no names of the editors who handled the article next to it (one has to guess from the editorial team page). It is unclear at this stage whether all those choices are valid for all future journals or whether this is customizable.

Anyway, I’m rather curious to see what the first few math journals will be : some specialized and some generalist probably, but will they all be new or will we see some known journals move to that platform? Verdict soon, hopefully…

 

 

ICM items

August 17, 2014

A few ICM-related things spotted:

- the talks seem to be all recorded, and should appear here in due course, which is great news

- here’s a close-up of a shiny medal in Avila’s hand

- there’s been a fairly absurd war of edits on the wikipidia page for the Fields medal, related to (dual-)nationality and place of birth

- a not so pseudononymous blogger has posted not very kind comments about some medalists

- the 2018 ICM will indeed take place in Rio (it had been confirmed some time ago apparently)

2014 ICM prizes announced

August 12, 2014

Don’t know if it’s bug or feature, but ahead of the ceremony the IMU has just put up on its website the names and press releases:

Fields medal: Artur Avila, Manjul Bhargava, Martin Hairer and Maryam Mirzakhani.

Rolf Nevanlinna Prize: Subhash Khot.

Carl Friedrich Gauss Prize: Stanley Osher.

Chern Medal: Philipp Griffiths.

Leelavati Prize: Adrián Paenza.

ICM Emmy Noether Lecture: Georgia Benkart.

Probably the best thing to do for now is to celebrate the historical event of a woman being awarded the Fields Medal :-)

Edit: Quanta Magazine has just advertised on twitter (where I first learned about the prizes) a set of 5 nice videos and articles about the winners. Probably much more to come from the worldwide press in the next few hours…

Live broadcast of the ICM opening ceremony

August 11, 2014

On the facebook page of ICM2014 it says that the live broadcast on aug 13 (aug 12 in the americas) will be on http://www.ebs.co.kr/onair?channelCodeString=tv and will last for 70 minutes.

It will start at 9:20am Korean time, so that’s:

04:50am Teheran time (aug 13)

2:20am Paris and Vienna time (aug 13)

1:20am London time (aug 13)

9:20pm Rio time (aug 12)

8:20pm NYC time (aug 12)

5:20pm LA time (aug 12)

So, not too bad for those in Asia or the Americas, more difficult for those in Europe and the Middle East…

Some pre-ceremony stats (inspired by the wikipedia page) that may or may not change:

Number of previous women winners: 0

Age of youngest winner: 27 (Serre)

At least one Russian winner (true since 1994, so 5 in a row so far)

All winners are in the 36-40 age bracket (was true in 2010)

At least one winner works in Probability broadly speaking (true in 2006 and 2010)

No winner born in the US (true since 2002)

At least one of the winners has held a permanent position in France at some point during his/her pre-medal career (true since 2002)

About 24 hours to go…

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…)

lsr_libe_small

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.

Summer hiatus

July 6, 2014

Patrimonio, by Daniel Cremona on flickr

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…

 


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