Princeton Companion latest

A quick post to give an update on the Princeton Companion to Mathematics. It’s been off my hands for a few weeks now. If all goes well it will be printed by the middle of September and should appear in bookshops about a month later. The illustration to the right is what the cover will be like. Click here if you want to see it in more or less full size. If you go to this page on the PUP website then you will find a podcast interview that I gave, which contains information that does not appear on this blog.

UPDATE 14TH OCTOBER: here are links to a few blog posts that have discussed the Princeton Companion recently. Terence Tao had a few thoughts on receiving his copy. Brian Hayes did too. Fred Shapiro, editor of The Yale Book of Quotations, has an interest in reference books and commented about the PCM in the New York Times Freakonomics blog. Dmitry Vostokov recommends the PCM for people wanting a broad overview of mathematics. Isallaboutmath points out that the Nautilus shell on the cover does not in fact have anything to do with the golden ratio. And the book has five reviews on Amazon, some more sensible than others.

FURTHER UPDATE (to which I’ll add as the occasion arises): Peter Woit has written a short review on his blog. Ian Stewart has written a review for The Times. Edmund Harriss has reviewed it on his blog. Alexander Bogomolny reviews it here. Does Antonio Cangiano like it? Perhaps you’d better judge for yourself. Having honed your interpretative skills, you’ll be in a better position to appreciate Scott Guthery’s helpful antidote. A different Scott, Scott Aaronson, reviews it on his blog. And Robin Wilson reviews it for the LMS newsletter. A nice review here, in French.

29TH OCTOBER: It’s been a long time coming, but I’ve just noticed that the PCM now appears to be available on Amazon UK, and not just from third-party sellers. According to them, it’s popular amongst geographers. If I knew how, I’d suggest they recategorized it.

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23 Responses to “Princeton Companion latest”

  1. Isabel Lugo Says:

    I couldn’t find a link to the podcast on the PUP website. But poking around the HTML source found me a direct link to the podcast which other readers might appreciate.

  2. gowers Says:

    I’m not sure I see the difficulty you were having, unless it’s the fact that the podcast is right there on the page I linked to (top right hand corner) rather than linked from it. But we might as well keep the direct link too.

  3. Isabel Lugo Says:

    It looks like in order to just work, the podcast requires the ActiveX plugin, which doesn’t come built-in with Firefox. I didn’t have it installed, and all I saw was the portrait and caption, with no indication that I needed to install the plugin to make the podcast play.

  4. gowers Says:

    I see. It worked with no problem on my Mac, but perhaps ActiveX does come with Safari. Anyhow, all the more reason for keeping the link you provided.

  5. isallaboutmath Says:

    I got the companion at amazon for 66 dollars. I like the book. I place a small review on my blog at

  6. Livro “The Princeton Companion to Mathematics” « problemas | teoremas Says:

    [...] título deste livro em fase de impressão. Nos links a seguir há uma intervista em Podcast com o editor, o matemático igualmente proeminente Prof. Timothy [...]

  7. Américo Tavares Says:

    Dear Prof. Gowers,

    Could you please inform which are the prerequisites/minimum knowledge one should have to be able to profit from reading the book, at least, partially?

    I would appreciate any answer.

  8. gowers Says:


    That’s a good question and one that doesn’t have a straightforward answer. When we started out on the book, we hoped to have a more or less uniform level of difficulty throughout. But it fairly soon became clear that that was not practical, since some parts of mathematics are much harder to explain than others, so we modified our goal to one of trying to explain everything as accessibly as possible (and ideally more accessibly than one could easily find elsewhere), even if that level of accessibility varied from article to article.

    The result? I would say that if you have done high-school mathematics and were good at it, then you will understand at least some of the book, enough to make it worth reading if you have a genuine interest in the subject, a wish to learn more, and a willingness to think quite hard as you read. If you are taking university courses in the subject, then the proportion you will understand will be much higher: some parts will be heavy going, but other parts will give you very useful insights into the concepts that are being thrown at you all the time. And if you are a graduate student or professional mathematician, then the book will be a very helpful resource if you are interested in getting at least some understanding of parts of mathematics that are not your own speciality.

    If you are in doubt about whether you want the book, I recommend having a look at it first. The best thing to do would be to find it in a bookshop, as then you will get a feel for the whole book. But a good second best is to look at the many sample articles that are available online. Some of these are linked from the Princeton University Press website. Others can be found at where you can login as Guest with password PCM, then click on Resources followed by Sample Articles. (The articles are slightly out of date, but they give an idea of the general level.)

  9. Américo Tavares Says:

    Thanks very much, Prof. Gowers!

    Your explanation covers different situations.

    Since I am a Portuguese retired engineer with interest in Maths
    I intend to order the book from Amazon.

  10. Nigel White Says:

    Any news on when it will be published in the UK. I was expecting it at the beginning of this week, and have had it on pre-order from Amazon for some time. But now it is no longer listed as available direct from Amazon in the UK, and other UK bookshops don’t appear to have it either.


  11. gowers Says:

    I happened to speak to someone from PUP yesterday, who said that there was a consignment of copies on its way. Apparently, it should arrive at a warehouse within a week or so, after which it will be sent out to people/institutions in the UK. Because the book is so heavy, they sent it by ship rather than air, which is why there’s a significant time lag between the UK and the US. I don’t think it will be in bookshops here for about a month or so.

  12. gelada Says:

    I have just published a fairly long review on my blog.


  13. rhersh Says:

    hello. Gowers! At my suggestion, the Santa Fe Institute Library bought the Companion which at this moment is my own companion here in my room at home in Santa Fe. Since it may be some time before I have swallowed the whole thing, I thought I could send you my first reaction.
    I would say the cover blurbs are not overstated, they are perfectly accurate. I am just starting on Michael Harris summary of French Mainly, I want to acknowledge your incredible feat of gathering optimally accessible explanations of research-frontier level mathematics of more kinds than I knew existed. It is so difficult even to get a single author to produce such an exposition! Remarkable, amazing. I am disappointed that Ian Stewart could be so lukewarm as to end up with “value for money.” It’s priceless, invaluable.

    Reuben Hersh

  14. Pete Riley Says:

    Thank you so much for an amazing book. I have only finished Part I so far,
    but I have never read anything quite like it. The level of the writing is ideal for the intended audience, and the prose is clarity itself. To cite one small, but telling example: the sentence on page 72 “…this showed that almost every real number (though not necessarily almost every real number you will actually meet) is transcendental.” is wonderfully wise. The parenthetical addition clarifies something a Calculus student, for example, would never think about. Examples like this fill every page of Section I.

    Pete Riley

  15. A Simple Introduction to Quantum Groups « XOR’s Hammer Says:

    [...] recommend that post (and his blog in general).  I also read the article on quantum groups in the Princeton Companion to Mathematics, which is an amazing book in [...]

  16. alocao Says:

    muy buen libro muchas gracias

  17. Nets Says:

    I only recently purchased my copy of the PCM and it arrived yesterday. Somewhat to my surprise, I was really charmed by it.

    I have ordered two more copies and am donating them to our department by the method of leaving them lying around in the
    lounge. (I think they would make great reading material for bored
    graduate students.)

    I have been warned that this all might not be such a hot idea because the books might be stolen. [I am not sure if it will be a good sign or a
    bad one if someone wants to steal the PCM.] I will update this post
    if the books are stolen.

  18. Carl Lumma Says:

    Dear gowers,

    I bet you get a lot of this, but I really want to buy your book. But there is no way I can justify storing, hefting, curating such a mass of cellulose in the 21st-century. My house is stacked to the ceilings with the stuff already. I would happily pay the $71.28 (current Amazon price), either to your publisher or directly to you, for a DRM-free PDF, and I’ll even promise never to let anyone else access the file.

    Let me know,

    510 306-7305

  19. gowers Says:

    Dear Carl,

    At the moment there is no electronic version, but from the way PUP were talking I’m pretty sure there will be at some point in the I hope not too distant future.

    I too have a book-quantity problem, but I just can’t stop myself buying the things. (On the other hand, I can’t wait for the demise of the paper journal …)

  20. If you want to go beyond the Princeton Companion to Mathematics then the Oxford User’s Guide to Mathematics could be an answer « Successful Researcher Says:

    [...] reviewed, and often praised, all over the mathematical and scientific blogosphere, see e.g. here, here and here. Most of this praise is probably well deserved. But where should an interested student (or [...]

  21. [z] 大牛们的blog « tommyHU Says:

    [...] to a Young Mathematician from the Princeton Companion to Mathematics (Timothy [...]

  22. Knighted for Services to Mathematics | Combinatorics and more Says:

    [...] of GAFA with her to bed.) But certainly Gowers’s services to mathematics include also the Princeton companion and the very short introduction, general-public presentations, Gower’s blog and Tim’s [...]

  23. useful links about general research | microfacet Says:

    […] to a Young Mathematician from the Princeton Companion to Mathematics Timothy […]

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