As I often update old posts instead of writing new ones , below is the (possibly incomplete) list of most recent updates:

• The Top Ten Open Problems in Physics (last update:  January 16, 2010)
• How to Choose a Research Topic (last update:  January 14, 2010)
• How to Write Grant Proposals (last update:  December 26, 2009)
• Career advice from the Fields medalists and some other mathematicians (last update: November 11, 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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If an ape can make a discovery, so can you.

Richard P. Feynman

as quoted in this book

What do you think about this quote?

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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).

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They say it’s some form of recognition but I respectfully doubt.  In my case some [your favorite expletive goes here] have just copied my post on choosing a research topic and put it here: (no clickable link folks, I am not going to improve their search engine ratings!!!). No slightest shade of fun in this for me, unlike, say, in the case of Scott Aaronson.

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)?

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

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An important addition to my earlier post on writing grant applications: there is a series of articles on science funding in Science Careers. The author is someone going — quite appropriately –  by the name of  Grant Doctor.

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A list by Dmitry Podolsky

Update: another such list (this time of 24 problems) by Sean Carroll, the three most important open problems in physics by the Nobel Prize winner Vitaly Ginzburg, and a more extensive list (see also the updated book version of this list)  by the same author.

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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.

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According to Sir Michael Atiyah, the most important quality for a working mathematician is the ability to maintain concentration for a long time.  Via Konstantin Zuev (original post in Russian).

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Israel Gelfand (September 2, 1913 — October 5, 2009). R.I.P.

To learn more about him, see e.g. the excellent post by Terence Tao.