A (de?)motivating Feynman’s quote

January 8, 2010

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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If you want to go beyond the Princeton Companion to Mathematics then the Oxford User’s Guide to Mathematics could be an answer

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 🙂

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Hunting Down the Old References

June 5, 2009

While writing the research papers one quite often needs to get back to the full texts of old (pre-Internet or at least pre-arXiv) references. Of course, having access to a good library and/or the interlibrary loan usually solves the problem but can be somewhat time- and cost-consuming.

It is not that well known, however, that there is a fair chance to find the old paper or preprint you need online for free. Of course, the first thing to try is Google or perhaps another search engine of your choosing. However, if this does not work, you still have a fighting chance, at least as far physics and mathematics are concerned. The places to try are:

  • the KISS preprint server (you can also try the umbrella interface at SPIRES)  allows you to search in (and get to the full text of) a huge database of scanned preprints  going back to the 1970s at least. The database covers mostly high-energy physics and related areas, including a fair share of mathematical physics and mathematics. For instance, you can find there a number of preprints by Richard Feynman, including the unpublished ones.
  • the Digital Mathematics Library
  • NUMDAM and CEDRAM (French mathematical journals)
  • The Project Euclid
  • MathNet.Ru (Russian mathematical journals)

All items but KISS are purely mathematical databases (to be precise, MathNet.Ru includes several physics, mechanics and mathematical physics journals as well).

If you know of other similar databases (be it in physics, mathematics, life sciences,…), please feel free to drop a comment with the relevant link(s).


How Much Passion Do You Need to Succeed in Science?

May 24, 2009

This very interesting and very controversial issue is discussed here, here and here. The discussion was triggered by this post at the YFS blog on the all not-too-nice kinds of people one encounters in science and on losing one’s illusions down the road into the academe (see also here for a related post at the RS blog); for a kind of alternative point of view see here.

Academia or Industry?

May 23, 2009

See this article from the Science Careers (hat tip: ZapperZ)

Update: on the broader issue of leaving academia see also here, here, here, and here. There also is a fair number of blogs and web sites addressing this issue, for instance:

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How to Choose a Research Topic

May 9, 2009

Choosing a research problem to work on is a tough decision to make, and the relevant advice is rather scarce.

So far I have found only a handful of reasonably looking tips:

  • work on important problems (R. Hamming, You and Your Research)
  • go for the messes, i.e., for the areas far from being crystal clear
    (S. Weinberg, Scientist: Four golden lessons)
  • look for an unoccupied niche that has potential (this and some other good tips can be found in the paper Picking a research problem — the critical decision which is primarily addressed to the researchers in biology and medicine but can be of interest to the other scientists too)
  • keep several (if possible, not too closely related) problems of varying difficulty to work on, so that you can switch to another problem when you get stuck (for more on this see e.g. here)
  • try to move beyond the subject of your Ph.D. thesis (if you have already defended one, indeed) or your postdoc (or your postdoctoral mentor, for that matter); more broadly, beyond your current area of research (see e.g. this post of Terence Tao). This has an extra benefit of reducing the risk of being scooped as discussed here.
  • regularly attend the conferences and join (or run) a seminar and/or a journal club: the talks can be an important source of inspiration
  • do something you will enjoy doing and what you feel you can do
  • your work should rather open the way to new breakthroughs than close the whole subject down

The last three tips are somewhat of a common wisdom and can be found in a number of places; see e.g. the article Choosing a research topic by Richard Reis, which contains some further interesting thoughts on the subject.

See also:

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On Giving a Talk

April 21, 2009

Some good advice on the subject is here, here and here (the last two are primarily intended for the mathematicians), here (this one is primarily on giving short talks) and here (this one also contains some helpful links to writing tips). As for the job talks, see e.g. this article by Richard Reis. On a related note, see also his article on getting the most of your conference trips.

Update 1:  Presentation Guide for Scientists by Ad Lagendijk

Update 2: How to Give a Good Talk (see also the video) by Uri Alon and

How to Conquer Public Speaking Fear by M. Orman

Update 3: How to Give a Great Presentation at the To Done blog

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