February 12, 2012
It all began with the blog post Elsevier — my part in its downfall by the Fields medalist Timothy Gowers which has caused quite a stir and culminated in the creation of the web site thecostofknowledge.com with an online petition to boycott the Elsevier publishing house (see also this recent post by the Fields medalist Terence Tao).
What is more, the ongoing discussions on the future of math journals, see e.g. [1 2 3 4 5], have now got quite a momentum. The physicists have also launched a similar incentive SCOAP3, and there is a proposal for pre-print peer review by Sabine Hossenfelder.
It is apparent that we need to improve many aspects of the existing publishing system, and the forthcoming change will hopefully also affect the peer review (see e.g. here), and I would like to stress here one aspect of this change which remains somewhat implicit at the background of the ongoing discussions. The suggested versions of Peer Review 2.0 appear to agree in one thing: we need the reduction of subjective bias of the worst sort (culminating in the referee reports essentially saying nothing but “I think this paper is not good enough for this journal”), and I do hope that we, the science community, can bring at least this particular change forth.
August 27, 2010
Elon Lindenstrauss: watch online | download FLV file
Ngo Bao Chau: watch online | download FLV file
Stanislav Smirnov: watch online | download FLV file
Cedric Villani: watch online | download FLV file
For a discussion of their work see e.g. this post of Terence Tao and the official laudations.
In hindsight it’s rather funny to look at the rumours on the names of the awardees that have circulated on the net for some time.
May 21, 2010
Walter Rudin died on May 20, 2010 at the age of 89 after a long illness.
From Dick Askey:
Many of us learned mathematics from some of his books or papers. His being at the Univ. of Wisconsin was one of the main reasons I came here. His book on real and complex analysis was written for a course needed here. It provided a book which made it possible to teach enough real and complex variables so students could move to more specialized courses in analysis after a year of graduate study rather than the two years needed previously when there were year courses in real variables and complex variables. Informally among graduate students, his books were called the blue Rudin, the green Rudin, the yellow Rudin, etc. The fact that he wrote them seemed to many to be more important than using the title of the book.
To learn more about W.R., see also here.
March 6, 2010
1. Work at several problems at a time. If you only work on one problem and get stuck, you might get depressed. It is nice to have an easier back-up problem. The back-up problem will work as an anti-depressant and will allow you to go back to your difficult problem in a better mood. John told me that for him the best approach is to juggle six problems at a time.
2. Pick your problems with specific goals in mind. The problems you work on shouldn’t be picked at random. They should balance each other. Here is the list of projects he suggests you have:
- Big problem. One problem should be both difficult and important. It should be your personal equivalent to the Riemann hypothesis. It is not wise to put all your time into such a problem. It most probably will make you depressed without making you successful. But it is nice to get back to your big problem from time to time. What if you do stumble on a productive idea? That may lead you to become famous without having sacrificed everything.
- Workable problem. You should have one problem where it’s clear what to do. It’s best if this problem requires a lot of tedious work. As soon as you get stuck on other problems, you can go back to this problem and move forward on the next steps. This will revive your sense of accomplishment. It is great to have a problem around that can be advanced when you do not feel creative or when you are tired.
- Book problem. Consider the book you are working on as one of your problems. If you’re always writing a book, you’ll write many of them. If you’re not in the mood to be writing prose, then work on math problems that will be in your book.
- Fun problem. Life is hardly worth living if you are not having fun. You should always have at least one problem that you do for fun.
3. Enjoy your life. Important problems should never interfere with having fun.
This advice from J.H. Conway is excerpted from the blog post of Tanya Khovanova
January 6, 2010
1. Raise your quality standards as high as you can live with, avoid wasting your time on routine problems, and always try to work as closely as possible at the boundary of your abilities. Do this, because it is the only way of discovering how that boundary should be moved forward.
2. We all like our work to be socially relevant and scientifically sound. If we can find a topic satisfying both desires, we are lucky; if the two targets are in conflict with each other, let the requirement of scientific soundness prevail.
3. Never tackle a problem of which you can be pretty sure that (now or in the near future) it will be tackled by others who are, in relation to that problem, at least as competent and well-equipped as you.
The original text of the rules together with the author’s comments can be found here (HTML) or here (PDF).
December 24, 2009
The Princeton Companion to Mathematics was extensively reviewed, and often praised, all over the mathematical and scientific blogosphere, see e.g. here, here, here and here. Most of this praise is probably well deserved. But where should an interested student (or even a professional mathematician who wants to extend her or his professional range, for that matter) go in order to deepen the knowledge acquired from PCM without getting bogged down into the details of the proofs and other such subtleties that abound in the specialized literature?
Of course, there is plenty of possible answers to this one, and you are welcome to share yours in the comments. However as far as “classical” (basically more or less up to the early XXth century level) mathematics goes, the Oxford User’s Guide to Mathematics appears to provide, at least for me, a reasonable, if not quite perfect, enhancement for PCM.
OUGM has many omissions of its own and certainly could use more editing and proofreading — in particular, in order to make it somewhat more self-contained, but nevertheless this book provides a fairly broad and reasonably deep (for the beginner) panorama of the “classical” mathematics as defined above. For instance, it does not cover category theory and related stuff. However, by and large, OUGM does a quite decent job in helping the beginner to advance her/his understanding of a great number of mathematical disciplines from abstract algebra to probability theory, and I certainly recommend to have a serious look into this book if you really want to deepen your knowledge of the “classical” subjects beyond the PCM level.
P.S. I just cannot miss this opportunity to wish merry Christmas and happy New year to the readers of this blog 🙂
November 7, 2009
I have found (hat tip: Yuri Kryakin) a great interview in Russian with Ivan Panin, where he reminesces, inter alia, about his teacher, a prominent mathematician Andrei Suslin and the way he works. The whole text is pretty long and very interesting but it is quite difficult to find reasonably self-contained excerpts to translate into English for those who don’t speak Russian, so let me give you just one bit as a teaser:
Suslin tackled the problems roughly as follows: first we see [the problem or the result to prove], then we believe [that we can solve it or that we can prove the result], and then we prove it. Because if you don’t believe, you will not have your vision materialized.