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“).
I don’t quite understand why all this is allowed to happen…
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.
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
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.
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…
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)
U of Arizona (mostly Arithmetic Geometry)
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…)
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).
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.
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 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 . 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  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 , 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).
There’s been some recent articles about MOOC experiments by french mathematicians, here’s a quick recap, please read the interviews for much more information:
- in the april issue of Gazette des Mathématiciens, an interview of Arnaud Bodin and François Recher, who set up a 6 weeks course (on France Université Numérique) on elementary arithmetics & cryptography (intended level: first-year university students). There were 1400 subscribers, of which 300 actively participated, and 145 mastery certificates were given. Mean age was 30, and most participants had already a degree.
- in the may issue of Statistique et Enseignement, there are three interviews:
– Sylvie Méléard, Jean-René Chazottes and Carl Graham, helped by three graduate students and a programmer, have run a 13 weeks course (on Coursera) on probability (intended level: third year university students). They mention 9600 subscribers, of which 5900 visited at least once, 750 followed everything, 624 posted on blogs/forums, and 250 got an attendance certificate (the course wasn’t offering a certificate of mastery). Quite a lot of american participants even though the course was in french, with a mean age about 30 too, and 60% with at least a masters degree.
– Avner Bar-Hen and Jean-Louis Piednoir have run a 5 week course (on France Université Numérique) on fundamentals of statistics (intended level: about second or third year university students). Both are interviewed separately. 8000 subscribers, no mention of other figures but lots of hands-on remarks.
– finally there’s an interview of Paul Farnet, a recent HEC graduate who cofounded themoocagency.com with recent Polytechnique graduate Aurélien Crocq, that’s a startup offering help to design and run a MOOC.
The first ever calculus textbook, according to wikipedia, appears to have been published in 1696 (that’s 318 years ago) by Guillaume de l’Hôpital (following lectures given to him by Leibnitz) under the name Analyse des Infiniment Petits pour l’Intelligence des Lignes Courbes.
Handily, it’s available on Gallica. It is explicitely stated at the outset that letters from the start of the alphabet are taken for constants, while the end of the alphabet is reserved for variables. Then on page 4 there’s the very modern-looking statement
La différence de est .
One would say la différentielle nowadays, but otherwise the notation was in nice final form.
Already on page 9 some computations appear that might be demanding for first year students nowadays:
And while the first few graphs are just what one would expect:
it does become quite intricate beyond that: