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.

In addition to leaving a great legacy of mathematical theories, results and open problems, he authored a number of graduate and undergraduate textbooks (the best known perhaps being Mathematical Methods of Classical Mechanics) which were a major influence.

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.

• Career advice from the Fields medalists and some other mathematicians (last update: June 3, 2010)
• How to Choose a Research Topic (last update:  March 7, 2010)
• The Top Ten Open Problems in Physics (last update:  January 16, 2010)
• How to Write Grant Proposals (last update:  December 26, 2009)
• How to Write a Really Good Research Paper (last update: October 29, 2009)
• Hunting Down the Old References (last update: June 22, 2009)
• Academic Networking: on the Network and beyond (last update: June 22, 2009)
• Academia or Industry? (last update: June 6, 2009)
• How to Maximize Citations (last update: June 1, 2009)

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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

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Richard P. Feynman

as quoted in this book

What do you think about this quote?

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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).

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And that should have been a scientific blog (judging by the domain name)… Talk about plagiarism in science after that. Pathetic, isn’t it? Any suggestions as to what can one do about all this (remember, it’s a Chinese site, so I doubt that the standard things like writing them and asking to remove the content or contacting their ISP would be helpful)?

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

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