Matthew Watkins... Off the Beaten Path!

Math-Frolic Interview #10

"Ultimately, what I found myself learning about undermined all of my previous ideas about what mathematics IS (or, more particularly, what the system of natural numbers is). I felt compelled to share this awareness as widely as possible."
-- Matthew Watkins


It was an absolute thrill to be in touch with, and 'interview,' someone as prominent as Keith Devlin. Today I have a thrill exactly for the opposite reason... the thorough delight of getting to learn more about someone I don't know at all, but found intriguing from the one book of his I've read.

Mathematician Matthew Watkins is the author of "The Mystery of the Prime Numbers," a beautifully-produced, self-published book out of Britain that has little presence in the math landscape, and yet as I said in my Devlin interview, is "one of the most fascinating/extraordinary math books for a mass audience I've ever read" (AND, it is just the first volume of a trilogy!)
Dr. Watkins is, as you'll see, a rather independent, eclectic sort, 'doing his own thing,' but doing it fascinatingly!
He currently holds "an honorary research position at Exeter University's School of Engineering, Computing, and Mathematics," and his homepage is here: http://empslocal.ex.ac.uk/people/staff/mrwatkin/index.htm
Below, are his lengthy and interesting responses to my questions (once again, I've bolded a few bits here and there of particular interest). ...Enjoy! 
(And, if you're interested in prime numbers and number theory, I strongly recommend getting hold of his book!)

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1) Most of the folks I'm interviewing here at Math-Frolic are math bloggers… you are not, but are a math author who I chose because your volume, "The Mystery of Prime Numbers" is so fascinating. But first, let me ask if, besides your home pages, you have any social Web presences (Twitter, Facebook, Google+, etc.) that we should know about?

No. I'm generally quite distrustful of these new social media. I have a particular aversion to Facebook. I can see some possible advantages of using Twitter, but also how it could become a terrible distraction.  As a self-publishing author trying to promote my work, I do realize that these media are generally considered indispensable, but I'd rather sell less books than get caught up in these worlds which I want no part of.  Encouraging people to "like" me or "follow" me would just seem pathetic and distasteful.

[I can relate to this, as I also am very Facebook-averse and use social media rather minimally. I love Twitter, but yes, it's a huge distraction!]

2) How did your interest in mathematics originally come about, and when did you know you wanted to pursue it professionally?

It was something I naturally excelled at from my earliest schooldays, presumably just something to do with the way my brain works.  And not being very good at athletic or artistic pursuits, being a slightly weird-looking, awkward kid, I naturally identified with the thing I was good at.  At that stage, I liked it because I was good at it, as simple as that. I think that's probably quite a common backstory for adult male mathematicians.
My family moved from England to the USA when I was 9, and because of the relative backwardness of the school system I arrived into, I began to REALLY excel at mathematics.  They ran out of work to give me and my 6th grade teacher bought me a big algebra book from which I taught myself how to factor polynomials, etc.  I was the weird brainy English kid at the back of the classroom!  From there I went on to teach myself calculus. By my mid-teens I was determined to return to the UK, and the most realistic strategy was to secure a place at a university here. Because a US high school certificate is worth almost nothing in that context, I somehow managed to squeeze in 34 mathematics credits at the local campus (the whole of a 'major' at that time) while finishing high school, thinking that this might just get me a place.  It paid off, as the University of Kent put me straight into their second year (of a three year course). I was extremely focused and confident as a student, and two years later, I was given a fully-funded opportunity to do a Ph.D.

But by my mid-teens, I had become far more passionate about the arts, philosophical ideas, cultural and political movements, etc. than I was about mathematics.  If I'd have been able to, I probably would have done a degree in the humanities.  So the fact I ended up with a maths PhD was more the result of following a path of least resistance than following my abiding interests.

It was only halfway into my PhD that I suddenly awoke to the beauty, wonder and sheer 'otherness' of mathematics, something I'd been entirely blind to up to that point.  But I was also becoming rapidly disillusioned with the over-specialisation and competitive nature of academia, so I was destined to leave that path behind.

3) A quote from one of your Webpages reads: "...we can confidently say that nothing like this book has been created before. It's not just another 'popular science' book about prime numbers (neither is it a book of woolly New Age number mysticism!) – rather, the issue of prime numbers acts as a gateway into some truly strange philosophical territory whose relevance extends well beyond abstract mathematics and which is genuinely worthy of the word 'mystery.' "
Can you briefly describe what you are attempting to accomplish with your interesting "trilogy" of books that relate to number theory, especially as different from what other books on the subject have done before? And where did the idea for your books originate -- has it slowly evolved over time, or did you pretty much know from the start what your approach and content would be?

Originally it was going to be one book, but when Matt Tweed (illustrator) and I sat down to formulate a plan, it became apparent that it would end up being an intimidatingly fat tome.  Hence the idea of a more manageable trilogy.  The original book has been brewing since the late 90's, really.  I had dropped out of academia to pursue other interests after a year's post-doc research in Belgium, but before too long I became drawn back in to mathematics, albeit in a very different way.
A strange chain of events led me to consider the philosophical implications of the irregular distribution of prime numbers, which led to my becoming aware of some very strange, unexpected work (mostly post-70s) applying ideas from number theory to physics, and vice versa.  I hadn't specialized in number theory and my knowledge of physics was fairly patchy, so there was a lot to learn (and still is). But this led to my "Number Theory and Physics Web-archive" [http://empslocal.ex.ac.uk/people/staff/mrwatkin/zeta/physics.htm], my attempt to encourage some dialogue between the number theory and physics communities about what this might all mean. Many active mathematicians still express surprise that number theory has any physical applications (beyond cryptography), but the fact that physicists might shed light on the inner workings of the number system is profoundly weird, even to me after years of thinking about this stuff.  It suggests a very different kind of relationship between the numerical and physical worlds than has previously been put forward, and quite possibly will end up informing the ongoing philosophical debate concerning the "mind-body problem" (more accurately the relationship between psyche and matter).

Ultimately, what I found myself learning about undermined all of my previous ideas about what mathematics IS (or, more particularly, what the system of natural numbers is). I felt compelled to share this awareness as widely as possible.  Philosophers and 'generalists' should be discussing these matters, I feel, but they're currently the domain of a relatively tiny group of specialists in the mathematical sciences. In my attempts to explain my interests to my friends (none of whom has any mathematical background), I developed a repertoire of metaphors, analogies, visualizations and other techniques to convey key ideas.  Developing the Web-archive was taking up a lot of my time, and was entirely unfunded, so people started to suggest that I put together a book version.  There were a number of false starts, due to the sheer size of the undertaking and the problem of trying to write for such a broad range of mathematical abilities, and the project was almost completely abandoned at least twice.  But once Matt Tweed got hold of a rough draft, his enthusiasm and sense of wonderment were so encouraging that we decided to just go for it, regardless of commercial considerations.

4) Your books are self-published, which means they are not readily available in American bookstores. Nor do I see much discussion of them among mathematicians/teachers here which seems a shame. Are your books better known and distributed in your own country of Britain? And were you unable to get a traditional publisher for the volumes, or did you deliberately choose self-publishing for some other reason?

No, my books aren't in bookshops in Britain either. It's practically impossible to get self-published works into stores on either side of the Atlantic.  It's hard enough to even get reviews. Publications that feature book reviews tend to use the publishing industry as a "filter" - if it's not been conventionally published, the thinking goes, then it probably isn't worth reviewing.  But in my case, I decided from the outset to bypass traditional publishing and do everything myself.  I'd read enough about the publishing industry to have become horrified, and I just wasn't prepared to compromise in the way that I almost certainly would have had to in order to make the book(s) more marketable on their terms.  What I learned basically told me that my books would be "unpublishable," but for whatever reason I decided to just go ahead and publish them anyway.

Despite this, we've had a few good reviews, mostly on blogs, but also Prof. Brian Josephson's (he's the Nobel physics laureate from Trinity College, Cambridge) in the Times Higher Education. For that esteemed organ to review a self-published work was almost unprecedented.  It led to a spike in sales for a couple of weeks, but they dropped off again quite soon after.  People are just bombarded by so much media these days, that to promote something you just have to get out there in the marketplace and shout louder than everyone else (or employ someone else to).  This doesn't come naturally to me.  But I'm patient, and have much faith in the value of what we're doing.  Most importantly, the core content of these books will remain valid indefinitely, as it's not subject to social or cultural trends.

My attitude has been to let the books prove themselves on our own terms, and then if a traditional publisher wants to license them (without making any substantial changes) and handle the distribution/promotion, that would be great - unless it was Rupert Murdoch's HarperCollins or some other dubious corporate entity. That's the other problem with the publishing industry - like the music industry, small independents are rapidly being subsumed into corporate behemoths which are increasingly impersonal, homogeneous and entirely profit-driven, and I'd rather not get involved in that!

This is the first time in the history of books that it's possible for someone like me, with almost no capital and no business premises, to distribute a professionally printed and bound book worldwide. That in itself I find exciting.  My sales have been in the 100s rather than the 1000s, but with every copy that gets sent out to Japan, Brazil, Canada or Finland, I feel a small sense of victory.

5) I've only read (and enjoyed) your first volume thus far... can you give a hint of where the final (third) volume will eventually lead readers? (what sorts of ideas/conclusions)

As I hinted in an earlier answer, my aim is to convince readers that the number system is something very different than what they had previously thought, that we just don't know what we're dealing with.  The physics side of things comes in quite heavily in Volume 3 (it took the first two volumes to get to a point where that can meaningfully happen), as well as some of my own philosophical/cultural/psychological insights into "what it all might mean" - although I'm being very careful to avoid any kind of ideology or dogma.  The subtle relationships between number, matter and psyche are what interest me more than the technical details of maths and physics, hence "Prime Numbers, Quantum Physics, and a Journey to the Centre of Your Mind" [Vol. 3].  But I don't want to give too much away, you'll just have to wait and see!

6) Can you tell us some of your own favorite math books that you like reading for enjoyment, and also any additional math books that you'd especially recommend to lay people?

The honest truth is that I don't read mathematical books for enjoyment.  I read a lot, but almost entirely in other subjects.  Years ago, I read an Ian Stewart book where he outlined a number of major unsolved mathematical problems (I can't recall the title) - that was quite useful for me at the time, to get a general overview of areas of the subject which I was unfamiliar with.  And I read four popular books on the Riemann Hypothesis as part of the research for the SoC trilogy (Sabbagh, du Sautoy, Derbyshire, Rockmore) - that was mainly to be sure that I wasn't duplicating anything of those authors too closely.  Those are all worthy books in their various ways, but I find a lot of the 'popular mathematics' literature has an unspoken ideology built into it which I instinctively rebel against -- it's that narrative of "Great Men" with their "Great Ideas" ascending some kind of mountain of technical progress, a sort of self-congratulatory conquest. I don't buy into the Western myth of "Progress". Also, there's a subtle matter of denying the "shadow" side of mathematical thinking, which troubles me.  Mathematics has allowed humanity to reshape the world faster than our wisdom can keep up, and this isn't being addressed. It's presented as something which solves our problems, but almost never as something which can also create them.  Yes, it has led to some cool little gadgets... but who exactly chose to reshape society so that practically everyone you see in a public environment these days is semi-permanently distracted by some kind of screen?  Who decided that we should all be plugged into a global economy at the mercy of wholly selfish derivatives traders employing complex algorithms, wreaking havoc on whole populations?  Electronic surveillance?  Drone warfare?

One book which that analysis doesn't apply to is Douglas Hofstadter's incredible "Godel, Escher, Bach," although it's not exactly an easy read (it was the only existing book I could initially compare the SoC trilogy to when I was still considering dealing with conventional publishers). I read that as a teenager and it definitely influenced me.

If I had to recommend a book for lay people, it would be quite an unusual one: Michael S. Schneider's "A Beginner's Guide To Constructing The Universe" (1995) which takes what I'd consider to be a more healthy, holistic approach to number-related issues.  Also, just the other day I saw a copy of Keith Critchlow's "The Hidden Geometry of Flowers" (2011), which although not purely mathematical, I would strongly recommend to people seeking to get some insight into the underlying mathematical layers of physical reality.  Some of Clifford Pickover's books which I've leafed through look quite engaging (although some are a bit too "recreational mathematics" for my liking). And having seen some of Martin Gardner's articles, I suspect his books are probably worth checking out - there's one called "Meta-mathematical Themas" which was once recommended to me.
[Actually the title is "Metamagical Themas" and it's another Hofstadter book, not Gardner. It IS a FABULOUS volume, but not a lot of math. Hofstadter, by the way, has a new book to look forward to, due out this year, "Surfaces and Essences."]

7) I almost get a sense that you are kind of  'doing your own thing' out on the math sidelines… I've often commented that Britain produces a lot of great math writers and communicators… have you worked with or collaborated much with any names we might recognize, or are you indeed sort of out there in your own arena?

I'm afraid I'm out on my own! I did send promo copies of Volume 1 to Ian Stewart and Marcus du Sautoy, just to see what reaction I'd get. Ian Stewart was very encouraging, really liked it and said it "deserves to sell a lot of copies."  But he also warned me of the difficulties of getting any traction with self-publishing, and gave me some helpful promotional advice.  Marcus du Sautoy never responded (I sent him Volume 2 as well).  No doubt he's very busy, but I was mildly disappointed, as he's currently "Simonyi Professor for the Public Understanding of Science" at Oxford (having taken over Richard Dawkins' post), so I thought he might recognize the value of what we're doing. Perhaps he sees it as competition for his "Music of the Primes" (although they're wildly different books in tone and content). We met briefly at a random matrix theory conference in 2001. A few of us were standing around, slightly awkwardly, as mathematicians at conferences tend to do, and he started enthusing about my web-archive, without realizing I was responsible for it! That felt very encouraging at the time (this was before I'd decided to do the book thing).  Shortly after that, at his request, I helped him out with a few little bibliographic references for his book, but he didn't acknowledge that either. He must be very busy.

8) To round yourself out a bit, when you're not doing mathy things, what are some of your main interests/hobbies/activities?

Since 1994 I've been playing a seven-stringed Turkish instrument called a saz.  I've never learned the traditional Turkish style, but it's a very versatile instrument, and I've done an awful lot of writing and playing and jamming in a lot of different styles with people I've met over the  years.  I've been involved in quite a bit of free improvisation (I helped to found the Exeter improv collective 'Children of the Drone', still going after a decade, see http://www.childrenofthedrone.net).  Playing "free" music is one of the only situations where my rational/analytical mind shuts down and allows the more intuitive/creative side some airtime.  So that's very important to me.  I also blog about my musical adventures and about various music I discover, both the current, vibrant scene in Canterbury where I'm currently based, as well as a great diversity sounds from all times and places.  And I've been curating a series of monthly podcasts about the so-called 'Canterbury scene' of the late 60's and 70's (a sprawling amalgam of psychedelia, progressive rock, minimalism, experimentalism and jazz fusion) [http://canterburysoundwaves.blogspot.co.uk]

I do a lot of walking, exploring the nooks and crannies of the English countryside, visiting megalithic sites and old churches, etc.  I read a lot (as widely as possible), and love helping out with other people's gardening (although sadly I'm not a natural gardener -- I need to be told what to do!). 

Generally, I'd say, I'm interested in "everything, and how it all joins together." I'm a generalist.  Reality is fascinating!  Analytic number theory just happens to be the area I've focused on in recent years.

9) Any parting words, not covered above, you'd care to pass along to a math-oriented audience?

How about this: "what we don't know is hugely more significant than what we do know"?
That sounds appropriately meaningful!  I just think we should humble ourselves and recognize that in previous eras where the levels of mathematical/scientific knowledge now appear laughably inadequate, people at the time still imagined themselves to be at the cutting edge, having almost explained everything (rather like the dominant stance these days).  We'll always just be dipping our toes into the vast Ocean of the Unknown, and we'd probably do ourselves a big favour to recognize that, rather than continually congratulate ourselves on how "advanced" we supposedly are.

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Wow, this has been a fascinating set of responses from someone a bit off the normal beaten path of math. And I'll reiterate that I believe Dr. Watkins' first book is a wonderful read -- I ordered it through Amazon and received it in short order... hope word of it spreads.
Thanks for participating here, Matthew!

ADDENDUM: Sol Lederman at "Wild About Math" blog just announced he'll be doing a podcast with Dr. Watkins in the future. Something to look forward to. Sol (very) favorably reviewed Matthew's first book well over a year ago:
http://wildaboutmath.com/2010/09/24/review-the-mystery-of-the-prime-numbers/