New Reading...

The latest edition of the online, open-access Journal of Humanistic Mathematics is up here (where individual articles can be freely downloaded as pdfs):

http://scholarship.claremont.edu/jhm/

Meanwhile, the first post is now up at my new blog MathTango, a review of the latest work from David Berlinski:

http://mathtango.blogspot.com/2013/01/euclid-and-his-explicators.html

Another Dose of Hyperactive Devlin

Hope you're not too tired of hearing from Keith Devlin, because this is a brand-new fantastic interview (28 min.) with Dr. Devlin, author, entrepreneur, researcher, professor, mathematician, radio commentator… and, inquisitive-child-who-refuses-to-grow-up!:

The More the Merrier!?

News!!....

I'm branching out... For awhile now I've been thinking of some changes/tweaks to Math-Frolic, but am opting instead to simply initiate a SECOND blog strictly for the lengthier posts that occasionally appear here. The new blog, entitled MathTango will generally include book reviews, interviews, and simply longer posts than the more common daily fare posted here. An initial welcoming post is up at MathTango repeating this information, and tomorrow will have the first real post for the site, which is intended to have only a few postings per month.

Making Assumptions...

Patrick Honner, a NY award-winning math teacher who I previously interviewed here, gave this talk to Math For America about a month ago dealing with certain aspects and assumptions of standardized tests that he keeps an eye on (the audio isn't quite as crisp as one might like and may be better through earphones than over speakers):




In a slightly similar vein, Sol Lederman's latest podcast is with Glenn Van Brummelen who talks (and has a book) about "spherical trigonometry," which is a somewhat lost art that nonetheless remains valid and practical, even while planar trigonometry remains the brand we all learn routinely in school:

http://wildaboutmath.com/2013/01/27/glen-van-brummelen-inspired-by-math-18/

Sunday Afternoon Reading

just passing along a few things from the last week:

1) A nice little introduction to Cantor, for any who need it, from Curious Wavefunction over at Scientific American:

http://tinyurl.com/a4u5n8r

2) Another bit of interesting Ramanujan biography here:

http://tinyurl.com/b44jgyk

3) For educators especially, Dan Meyer brings up a discussion of 'pattern matching' as it may apply to Khan Academy (this relates back to the subject of Benny's Rules which I've written about previously):

http://tinyurl.com/agoyxyn

(be sure to read the comments as well)

4) and lastly, for sheer entertainment (more chemistry than math, but really general scientific literacy), this Wikipedia page came across my Twitter feed, originally I think from Alexander Bogomolny, on the "dihydrogen monoxide hoax":

http://en.wikipedia.org/wiki/Dihydrogen_monoxide_hoax 

(be sure to read the "Public Efforts..." section... and weep)

accompanying photo here:

https://twitter.com/CutTheKnotMath/status/295265488156622848/photo/1

 

A Blogger's Book...

Several bloggers in recent years have turned their blogs into book forms, sometimes quite successfully. So it is exciting to see that Mark Chu-Carroll, author of one of the longest-running math blogs ("Good Math Bad Math"), a blog with... shall we say, a bit of 'attitude' to it... has announced the availability of a book based on the blog's content. It is entitled simply, "Good Math," and he outlines the contents as follows:

1) Numbers: some basic number theory, what numbers mean, how they're constructed
2) Funny numbers: a collection of strange but interesting numbers: 0, e, i, ...
3) Writing Numbers: Roman numerals, Egyptian fractions, continued fractions, ...
4) Logic: first order predicate logic, proofs, temporal logic, and prolog
5) Set theory
6) Computation and computing machines

I haven't seen the book myself, but Mark writes, it "should be a lot of fun for mathematically curious folks to read," and from my familiarity with his blog posts I would expect it to be quite good. His announcement is here:

http://scientopia.org/blogs/goodmath/2013/01/23/good-math-the-book/

...and the page for purchase is here:

http://pragprog.com/book/mcmath/good-math 

...As long as I'm mentioning books, I'll note the two new books I am currently reading: "The King of Infinite Space: Euclid and His Elements" from David Berlinski and "Naked Statistics" by Charles Wheelan. I'll eventually say more about them, and my guess is that I'll end up only able to recommend the first book to a sliver of the mathematical community, while recommending the latter to a wider, more general audience.

Talk Mathy To Me! ;-)

2 interviews to pass along today…

Over at mathblogging.org, their latest transcribed interview is with the always interesting mathematical physicist John Baez of Azimuth blog: 

http://mathblogging.wordpress.com/2013/01/18/john-baez/

And Sol Lederman now has up his second podcast interview with some fellow named Keith Devlin, who he first interviewed almost a year ago -- guess he's giving this Keith guy another chance to try and get it right this time… ;-))

http://wildaboutmath.com/2013/01/22/keith-devlin-%E2%80%93-inspired-by-math-17/

but… seriously… in it, Keith talks almost exclusively, and extensively, about MOOCs, "massive open online courses" (too late now, but I wish someone had dreamed up a better name for these ventures!) …his experience with them and their future. It's a long (100 mins.!) 2-part interview. Very interesting; very worthwhile stuff. I especially enjoyed the last 30 mins.-or-so where Keith discusses the future of education (and Sol points out that until recently online degrees and education were very much looked down upon, while Keith is predicting a very bright and expansive future ahead for digital education with the MOOC model). Also, at the end Dr. Devlin hints about a new, separate learning project he has underway that will be publicly debuting in about 3 weeks!

Math Rocks!!!

vintage 1967:




pssssst… one word to young people planning their future in 2013… "mathematics"

According to a longish piece from Bloomberg Businessweek, "Math Will Rock Your World." It reports on many of the already well-covered issues (positive and negative) surrounding how mathematics is invading/changing the digital world we now live in:

http://www.businessweek.com/stories/2006-01-22/math-will-rock-your-world

...some lines therefrom:

"The world is moving into a new age of numbers. Partnerships between mathematicians and computer scientists are bulling into whole new domains of business and imposing the efficiencies of math… Says James R. Schatz, chief of the mathematics research group at the National Security Agency: 'There has never been a better time to be a mathematician.'
"...companies are hitching mathematics to business in ways that would have seemed fanciful even a few years ago…
"Top mathematicians are becoming a new global elite. It's a force of barely 5,000, by some guesstimates, but every bit as powerful as the armies of Harvard University MBAs who shook up corner suites a generation ago...
"One significant challenge to the math revolution is to build new businesses from data without sacrificing privacy… The goal now is to create systems that share group information while shielding the individual… Mathematicians are at the heart of the privacy battle -- on both sides...

"As more of the world's information is pooled into mathematics, the realm of numbers becomes an ever larger meeting ground. It's a percolating laboratory full of surprising connections, and a birthplace for new industries. Yes, it's a magnificent time to know math."

 But so much for the world of business… At least once a year I find some excuse to link to Jonathan Coulton's rousing "The Mandelbrot Set" song, 'cuz… HEY... it… just… ROCKS… too!! Usually I link to this YouTube version:

http://www.youtube.com/watch?v=gEw8xpb1aRA

…but here is Coulton actually singing the song live (not a great recording, but follow along the marvelous lyrics below. You can also download the tune from Jonathan's website: http://www.jonathancoulton.com/ )



 Lyrics:

Pathological monsters! cried the terrified mathematician
Every one of them is a splinter in my eye
I hate the Peano Space and the Koch Curve
I fear the Cantor Ternary Set
And the Sierpinski Gasket makes me want to cry
And a million miles away a butterfly flapped its wings
On a cold November day a man named Benoit Mandelbrot was born

His disdain for pure mathematics and his unique geometrical insights
Left him well equipped to face those demons down
He saw that infinite complexity could be described by simple rules
He used his giant brain to turn the game around
And he looked below the storm and saw a vision in his head
A bulbous pointy form
He picked his pencil up and he wrote his secret down

Take a point called Z in the complex plane
Let Z1 be Z squared plus C
And Z2 is Z1 squared plus C
And Z3 is Z2 squared plus C and so on
If the series of Z's should always stay
Close to Z and never trend away
That point is in the Mandelbrot Set

Mandelbrot Set you're a Rorschach Test on fire
You're a day-glo pterodactyl
You're a heart-shaped box of springs and wire
You're one badass fucking fractal
And you're just in time to save the day
Sweeping all our fears away
You can change the world in a tiny way

Mandelbrot's in heaven, at least he will be when he's dead
Right now he's still alive and teaching math at Yale
He gave us order out of chaos, he gave us hope where there was none
And his geometry succeeds where others fail
If you ever lose your way, a butterfly will flap its wings
From a million miles away, a little miracle will come to take you home

Just take a point called Z in the complex plane
Let Z1 be Z squared plus C
And Z2 is Z1 squared plus C
And Z3 is Z2 squared plus C and so on
If the series of Z's should always stay
Close to Z and never trend away
That point is in the Mandelbrot Set
Mandelbrot Set you're a Rorschach Test on fire
You're a day-glo pterodactyl
You're a heart-shaped box of springs and wire
You're one badass fucking fractal
And you're just in time to save the day
Sweeping all our fears away
You can change the world in a tiny way
And you're just in time to save the day
Sweeping all our fears away
You can change the world in a tiny way
Go on change the world in a tiny way
Come on change the world in a tiny way
-------------------------

(...you'll never get that from Justin Bieber ;-))

ADDENDUM: p.s. for any who don't know, Benoit Mandelbrot passed away a couple of years back. His memoir, "The Fractalist" was published last year.

Of Patterns and Publishing...

Two bits today:

1) At some point recently, the following tweet crossed my screen and I copied it down only to later re-look at it and be intrigued…:

"OK. So mathematics is the science of patterns. I can dig that. But what, exactly, is a pattern?"

As someone interested in semantics, words, meaning, and tautology, this struck me as a fair and deeper question than it appeared at first glance… how does one define pattern without falling into some tautological trap? Anyway, that led me to a few pages worth passing along:

First of course, was the always handy Wikipedia, which essentially defined a pattern as 'elements repeating in a predictable manner'… that's probably about as good as it gets, even if it evokes the further questions of what actually constitutes an "element" and when is something precisely corroborated as "predictable"?

Anyway, it turns out that the Mathematics Assoc. of America has also previously tackled this topic a bit in a multi-part series here:

http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=437&bodyId=465

…the theme of the piece is that the notion of math as the 'science of patterns' is actually a modern approach to mathematics (Keith Devlin has certainly been a popular exponent of it) and that early mathematics was quite a different kind of study.

a quick excerpt:

"It is in view of this, I want to consider the often-heard definition of mathematics as the “science of patterns.”   Specifically, I want to show, by comparing Euclid and Steiner, that while this is presented to students as a timeless—that is, non-historical—definition, in fact, it represents a modern view of mathematics.  I shall show that Greek mathematics, for example, is not a search for patterns but for concrete properties of concrete mathematical objects; and I shall show, conversely, that it is when mathematics becomes symbolic that patterns, as such, are suggested to mathematicians and become objects of their thought."

 2) Almost exactly a year ago, renowned mathematician Tim Gowers launched a broadside at (and boycott of) journal publisher Elsevier, and probably, to his own surprise, struck a nerve with a great many other academics (not just mathematicians) who joined the fray with their own pent-up feelings about glossy publishers. I won't replay all the discussion that took place over the matter, except to say that arguments against the stranglehold of expensive professional journals versus more open-access forms of publishing in the digital age continue, and Gowers (with others) remains at the forefront with his announcement of new open-access journals on the way.
This Aperiodical article summarizes what Gowers is up to (with direct links back to Gowers' latest posts on it):

http://aperiodical.com/2013/01/the-good-the-bad-and-gowers/

...and Nature has good coverage of the effort as well, here:

http://www.nature.com/news/mathematicians-aim-to-take-publishers-out-of-publishing-1.12243

Even for those of us not involved in research and its publish-or-perish world, watching this inevitable evolution play out in the open is fascinating.

Devlin, Dunbar, Dominoes...

1) Registration for the second run of Keith Devlin's Stanford MOOC course, "Introduction to Mathematical Thinking" is underway (course beginning Mar. 4 for 10 weeks). More details here (where it states, "The goal of the course is to help you develop a valuable mental ability – a powerful way of thinking that our ancestors have developed over three thousand years").:

https://www.coursera.org/course/maththink

I've previously (highly) recommended the 92-page book Keith authored for this course (same title as course), but it would be incomparably better if read in conjunction with the course itself, than on its own.  I've not taken the course myself, but sincerely hope that some readers here do imbibe in Dr. Devlin's offering (and maybe even report back to us!?). There is very little computational math involved, but the ideas/work required for completion still may not be easy (depending on your background).

2) I wrote about the so-called "Dunbar number" here last year (the notion that neurological constraints limit one's close friendships or interpersonal relationships to very roughly 150 people). Now a much longer general article on Dr. Dunbar and his illustrious number:

http://www.businessweek.com/articles/2013-01-10/the-dunbar-number-from-the-guru-of-social-networks#p1

3) A recent nice little tutorial on the number e and ln here:

http://tinyurl.com/bnpfle6

 4) And lastly... how to knock over the Empire State Building with dominoes… and a little physics (a short, fun, but also educational, video):

Monday Potpourri

Time to catch up on a few things from the past couple days.

Readers seem to always enjoy 'quickies' as I call 'em, so here's a delectable one from a recent Twitter feed for all the foodies out there:

https://twitter.com/nerdfaced/status/289867477305937920/photo/1

'Wild About Math's' latest podcast is with Mircea Pitici, the editor of the annual "The Best Writing On Mathematics" series. The ~hour-long podcast is here:

http://wildaboutmath.com/2013/01/13/mircea-pitici-inspired-by-math-15/

I reviewed Pitici's latest 2012 edition on the blog HERE, and also included it in my book shopping list recommendations for Christmas a couple months ago.
[ADDENDUM: Yikes! Sol is churning out the podcasts lately and already has a lengthy, newer one up with Steven Strogatz -- haven't had a chance to listen yet, but undoubtedly HAS TO BE good stuff!]

Finally, what's worrying mathematicians these days…? We get a hint from John Brockman.
Brockman's cutting-edge/contemplative 'Edge' site has posted responses to its 2013 question "What should we be worried about?":

http://edge.org/contributors/q2013

Lots (150+) of good contributions of course, but I'll just link to three of the mathematicians who replied, and pique your interest with the first couple of lines from their entries:

Keith Devlin: http://edge.org/response-detail/23783

"Are we about to see advances in mathematics come to an end? Until last year, I would have said no. Now I am not so sure."

Clifford Pickover: http://edge.org/response-detail/23670

"I used to worry that our mathematical and physical descriptions of the universe grow forever, but our brains and language skills remain entrenched. Some of our computer chips and software are becoming mind-numbingly complex."

Steven Strogatz: http://edge.org/response-detail/23820

"In every realm where we exist as a collective — in society, in the global economy, on the Internet — we are blithely increasing the coupling between us, with no idea what that might entail."

"The Shooting Room" … a Doozy!

I loves me a good paradox, and am surprised to have never encountered this one before, 'cuz it's a doozy! (another simple probability conundrum… and apparently fairly well-known within certain philosophy circles).
Called the "shooting room paradox" Futility Closet recently ran it in Greg Ross's always succinct manner.

I'll re-state it in my own fashion here:

The situation involves a theoretically infinitely large room and infinitely large population of players… and, 2 dice. The first 'player' enters the room and the 2 dice are thrown. IF the result is double sixes, the player is shot and game over. Otherwise the player leaves the room unscathed and 9 new players enter. Once again the dice are rolled, and IF the result is double sixes, ALL 9 are shot. If not, they leave, happy and healthy, and 90 new players enter the room….

This pattern continues, with the number of players increasing tenfold with every new round of play. The game simply goes UNTIL double sixes ARE rolled and an entire room group is shot, at which point the game is over.

IF you are in the pool of players how worried should you be for your safety? ...perhaps not very, since your chance of being shot is NEVER more than 1 in 36, or < 3% (the chance of double sixes).

BUT, your wife discovers you are in a group about to enter the room, and she is petrified, because she understands that inevitably ~90% of ALL players who participate will be shot before the game is over! Who is perceiving the odds correctly?

 In a quick Google search of the problem (some of the 'meatier' papers on it were unfortunately behind paywalls), what I garnered from a few links is that the basic explanation for such divergent perspectives is that the 90% figure is of course an aggregate figure, and even though it's eventually true and accurate, once the game is over, it doesn't change the real in-the-moment probability of harm for any single individual, which is only 1 in 36 ...in-other-words, one cannot evoke reverse causation in adjudging the probability at a given point-in-time.

...I hope this is adequate explanation, but if someone feels they can state it more clearly or differently in the comments, please feel free to do so (I'm leaving out certain nuances and fine semantic points of the puzzle, which can be argued over, to try and convey the gist of it here).

Have a Little Math With Your Weekend

For some weekend entertainment….

Sol Lederman's latest installment of his "Inspired by Math" podcast series is with Ian Stewart, one of the most prolific and widely-known of all modern math popularizers. I've been pleasantly surprised by the degree to which 'math people,' including such prominent and busy ones as Stewart, Keith Devlin, Steven Strogatz and others, are willing to share themselves with the learning community, through such online outlets. It is really wonderful, and I think a reflection of the desire on the part of mathematicians to transform their subject from one that is too-often feared to one for eager engagement. So set aside an hour and listen to Dr. Stewart talk about what inspires him:

http://wildaboutmath.com/2013/01/11/ian-stewart-inspired-by-math-14/

There is also a new math blog in the blog corral of Scientific American: "The Roots of Unity" from Evelyn Lamb; subheading "Mathematics: Learning It, Doing It, Celebrating It" -- looks like it'll be good (and I've added it to the right-hand column links):

http://blogs.scientificamerican.com/roots-of-unity/

Read All About 'Em!

Today, just a list of links to Wikipedia for many of the best math popularizers/writers around. I've included Martin Gardner (deceased), but otherwise all others are still alive (at time of posting) and are listed in alphabetical order. Some Wikipedia entries are much more extensive than others:

Arthur Benjamin: http://en.wikipedia.org/wiki/Arthur_T._Benjamin
Gregory Chaitin: http://en.wikipedia.org/wiki/Gregory_Chaitin
John Conway: http://en.wikipedia.org/wiki/John_Horton_Conway
Philip J. Davis: http://en.wikipedia.org/wiki/Philip_J._Davis
Keith Devlin: http://en.wikipedia.org/wiki/Keith_devlin
Persi Diaconis: http://en.wikipedia.org/wiki/Persi_Diaconis
Martin Gardner: http://en.wikipedia.org/wiki/Martin_gardner
Tim Gowers: http://en.wikipedia.org/wiki/Tim_Gowers 
George Hart: http://en.wikipedia.org/wiki/George_W._Hart
Vi Hart: http://en.wikipedia.org/wiki/Vi_Hart
Reuben Hersh: http://en.wikipedia.org/wiki/Reuben_Hersh
Mario Livio: http://en.wikipedia.org/wiki/Mario_Livio
Eli Maor: http://en.wikipedia.org/wiki/Eli_Maor
Barry Mazur: http://en.wikipedia.org/wiki/Barry_Mazur
Joseph Mazur: http://en.wikipedia.org/wiki/Joseph_Mazur 
Danica McKellar: http://en.wikipedia.org/wiki/Danica_McKellar
John Allen Paulos: http://en.wikipedia.org/wiki/John_Allen_Paulos
Ivars Peterson: http://en.wikipedia.org/wiki/Ivars_Peterson
Clifford Pickover: http://en.wikipedia.org/wiki/Clifford_A._Pickover
Alfred Posamentier: http://en.wikipedia.org/wiki/Alfred_Posamentier
Rudy Rucker: http://en.wikipedia.org/wiki/Rudy_Rucker
Marcus du Sautoy: http://en.wikipedia.org/wiki/Marcus_du_Sautoy
Raymond Smullyan: http://en.wikipedia.org/wiki/Raymond_Smullyan
Ian Stewart: http://en.wikipedia.org/wiki/Ian_Stewart_%28mathematician%29
Steven Strogatz: http://en.wikipedia.org/wiki/Steven_Strogatz

Egan Chernoff aka MatthewMaddux

Math-Frolic Interview #11


You might not know the name "Egan Chernoff"... but you may know "Matthew Maddux" which is a sort of alias for Dr. Chernoff on the Web. And if, perchance, you've always wondered where that name stems from, well, just think about the word "mathematics" spoken a little differently.
Anyway, Dr. Chernoff is a Canadian university professor (webpage HERE) who writes what he calls "MatthewMadduxEducation" on the Web. But I'll let him tell you more of what he does...: (again, I have bolded bits of the content)

************************************

1) To start, could you tell readers a little about your background or anything else pertinent to your math presence on the Web...

Well, “math presence on the web,” to me, is a bit of a stretch. With that said, thank you for the kind words and, also, for your thoughtful questions. 

Looking back, this all started when I decided (way back in Grade 12) that I wanted to become a high school teacher. While in university I initially had plans to be a Chemistry major (thus, eventually, a Chemistry teacher), but that was until I took an Organic Chemistry course; and then a Geography major (thus, eventually, a Geography teacher), but that was until I found out the path I was on would lead to a BA and not a BSc, which, for some reason, mattered to me at the time. Ultimately, I decided to major in mathematics after taking a third year probability course in my second year of university. After that, for the next two years, I took some great mathematics and statistics courses from some great teachers of mathematics (e.g., Denis Acreman, Shane Rollans). With my degree I was able to then join the Secondary Mathematics Integrated Project (SMIP) at the University of British Columbia (UBC), where I would obtain my BEd. At this point, for the province of British Columbia, I had everything I needed to be a high school math teacher...except a job. In the end, I got a job rather quickly. For the next five years I taught high school mathematics (at Lord Byng Secondary and Killarney Secondary). What happened next is, perhaps, most pertinent to my “math presence on the web.”

My friend, Dave Cacchioni, and I were sitting in a pub, drinking beer, talking ellipses and the idea of going back to school was broached. Although, at the time, we both lived quite close to UBC, we decided to pursue our graduate studies at Simon Fraser University (SFU). SFU had a Secondary Mathematics Education Master’s, which appealed to us for three reasons. First, there was an MSc (not just an MEd) option. Second, we were excited that three of the six courses we had to take were math courses offered by the Department of Mathematics. Third, the program was designed such that we would take one course each semester and, as a result, could continue our teaching careers. A few courses into my Master’s and I was approached to concurrently pursue my doctorate at the David Wheeler Institute for Research in Mathematics Education, SFU. I said yes, which, looking back, signified my transition from the high school classroom to the university classroom. Soon I was teaching half time at my high school and half time at SFU. One year later, I had left the high school classroom and was working at SFU as a research assistant and sessional instructor teaching math and math education courses. Smash cut to few years later and I was living in Saskatoon working as an assistant professor of mathematics education at the University of Saskatchewan.

My math presence on the web started June, 2009 when I joined Twitter as @MatthewMaddux. My goal, at the beginning, was to use Twitter so that the members of the Master’s cohort I started would stay in touch outside of the classroom. Soon after, however, I realized that Twitter and other forms of social media could be used for much, much more. Over the past few years I adopted other forms of social media, but, more recently (as I detail below), I have started to focus on just a few services over the last little while. I think what I am trying to do now is akin to the “slow-news movement.” However, “slow-social-media for mathematics (education)” doesn’t have a nice ring to it. One last thing pertinent to my math presence on the web. In June, 2009, when I started this all, I asked myself one question: Will “digital service” be required of university professors in the future. I said yes. So, you can consider my math presence on the web the union of personal interest and, what I call, digital service.

2) Most of the folks I'm interviewing are math bloggers, so you're a little different in that regard. While you're very active in social media, you don't have a math blog of your own (I'm aware of you mostly through your Twitter feed), but what you do is actively "curate" math information that others are posting around the Web, at your site called "MatthewMaddux Education." Can you explain that a little further and what got you started with it? What is the ultimate goal for the MatthewMaddux site?

On the one hand, I disagree, I do have a math blog. Here’s the link: www.matthewmadduxeducation.  On the other hand, I agree, I am not a math blogger. Is it possible for someone who is not a math blogger to have a math blog? Yes. How is this possible? Microblogging. Taking all this into account, technically, I’m not a math blogger, but I am a math microblogger; and, technically, I don’t have a math blog, but I do have two math microblogs: my Twitter feed (@MatthewMaddux) and my Tumblr site (www.matthewmadduxeducation.com). (Worthy of note, if a microblog is a blog, or a form of blogging, then, technically, I am a math blogger and have a math blog. Clear as mud!)

Essentially, “MatthewMaddux Education” began when I moved my microblogging from Twitter to Tumblr, that is, from @MatthewMaddux to “MatthewMaddux Education.” The ultimate goal for “MatthewMaddux Education” is the same as it was for @MatthewMaddux: develop a permanent, central, digital repository for the mathematics (education) information I find via the web. Honestly, I probably would have stayed with Twitter for my microblogging, but it became, for me, too conversational, too “in the now,” too “stream of consciousness” and, definitely, too difficult to access earlier tweets (although I understand this has now changed). In fact, if you were to look through all (approximately) 7700 of my tweets, you would find a microblog dedicated solely to mathematics (education) information  — not the “dry turkey sandwich I had for lunch” or “the jerk that cut me off in traffic.” I even made some attempts to try and capture what I wanted out of Twitter (which lead to an iBook, @MatthewMaddux 2011: Chronicled Tweet by Tweet), but, in the end, I decided I could better achieve my ultimate goal with Tumblr.

3) There is now SO MUCH math content being put on the Web it seems like a very daunting task for one person to attempt curation… do you feel at times overwhelmed by it, or do you feel you have it under pretty good control at this point? And what sorts of criteria do you use for selecting what you do and don't curate?

 There have definitely been times where I have felt overwhelmed. While detailing my use of social media for mathematics education during the inaugural lecture of the Wheeler Institute in Second Life (here’s a link: http://blogs.sfu.ca/research/davidwheeler/projects/), I discussed my first “Twitter crisis.” At the time, I wasn’t (for some stupid reason) skipping any of the tweets from the 100+ people I was following (which is why I consider Tweetbot both a blessing and a curse). The “Twitter crisis” occurred when I turned on my iPad after the three (long) flights I took in order to get to Poland for a conference. Let’s just say there were too many tweets to handle and a few short minutes later the number of people I was following went from 100+ to 0. 

Actually, that feeling of being overwhelmed comes back every once and a while, but, at this particular point in time, everything is under control. There are two reasons for my current state of confidence (which will be shattered when the next technological “advancement” comes along). First, my use of Tumblr and Twitter is hierarchical. In other words, all my Tumblr posts are automatically posted to Twitter (and, actually, to Facebook). Working in the other direction, however, Twitter posts do not show up on Tumblr. Second, although I followed as many as 200+ people on Twitter in 2012, I currently don’t follow anyone. The way things are currently set up, my use of Google alerts (sent via email and RSS), RSS feeds, Evernote, and Instapaper captures nearly 100% of what I was looking for on Twitter. 
The criteria I use for selecting what information to curate is quite simple: does the information resonate with me? (As for what information is of interest to or resonates with me, that is a very complicated question; however, as the “MatthewMaddux Education” archive gets larger and larger it will concurrently paint a better and better picture of my interests.) If so, then I will curate the information and, if not, then I won’t curate the information. Alternatively stated, if the information resonates with me then it is a “signal” and, if not, then it is “noise.” If I deem the information a signal there is, however, one last step. I need to determine whether the signal is a “clear” signal or a “noisy” signal. Clear signals end up on Tumblr (which automatically end up on Twitter) and noisy signals end up on Twitter. As a result, Tumblr has a “better” signal to noise ratio than Twitter.

4) Approximately how much time per week do you spend on your "curation" activities?

That’s a good question and is one that I am often asked. The short answer, not as much time as one would expect. To be clear, I don’t count my reading or watching or listening of the information as time spent on curation activities — I would be doing that anyways.

As for the non-reading, non-watching and non-listening components of my curation activities, RSS feeds and Google Alerts, for me, are key. They’re like an inbox for the internet. Once set up, you just sit back and wait for the information to come to you. Of course, every once in a while, one has to venture out to find more feeds or create new alerts, which is where following people on Twitter (and looking at the people they follow) is a big help. The other key for me is that programs like Evernote, Readability, Pocket, Instapaper, Reeder and Tweetbot now all work “seamlessly” across my iMac, MacBook Air, iPad and iPhone. As the hardware becomes more and more ubiquitous, I’m never really too far away from a device that will allow me to “check in” on see what’s going on. 

While finding signals doesn’t take much time at all, posting can be time consuming. Posting to Twitter is a snap, but posting to Tumblr is a little more time consuming — I like to post a snippet that could persuade a reader to click through to the full article. Trying to put a number on it, when I sit down for one of my sessions I can produce roughly 20 posts in an hour and, given that I average about 80 posts a month, my current activity on “MatthewMaddux Education” takes a couple of hours a week (minus the reading, watching and listening). 

5) Do you recall when you first fell in love with math and when you decided to pursue it professionally?

I do not pursue mathematics professionally. So, perhaps a more accurate way of phrasing your question would be as follows: Do you recall when you first fell in love with [probability] and when you decided to pursue [probabilistic knowledge and thinking] professionally. 
Yes, sort of, my affinity for probability definitely began during my undergraduate studies, but truly blossomed during the five years I tried to account for high school students incorrect responses to basic probability questions. The moment I decided to professionally pursue probabilistic thinking and knowledge, however, is crystal clear. During my graduate studies at SFU, when I was reading A Mathematician Reads the Newspaper by John Allen Paulos, I came across the heuristics and biases research of psychologists Amos Tversky and Daniel Kahneman. I immediately got out of the bed I was reading in, went over to the computer and downloaded their seminal (1974) article, “Judgment under uncertainty: heuristics and biases,” from the journal Science. Reading Paulos’ book, thus Tversky and Kahneman article, ultimatley led me to investigate subjective probabilities derived from the perceived randomness of sequences of outcomes for my graduate studies. I continue similar research to this very day. Looking back I now realize, I should, one of these days, go back and finish Paulos’ book!

6) You seem to have an especially strong interest in aspects of probability…can you say what draws you to that particular area of mathematics? Is it (at least in part) because probabilities pretty much surround all of us in our daily lives and yet it is an area the average person usually greatly MISunderstands?
 

Yes, I do have a very strong interest in probability. In fact, it consumes me and most of my time. As for what draws me to probability, there are numerous factors (e.g., the late emergence historically, the multiple interpretations, the famous questions, our perceptions of randomness, gambling, quantum mechanics and the list goes on), but, definitely, the counter-intuitive nature of probability is one of the biggest factors that draws me and my research to this particular area of mathematics. 
As Martin Gardner wrote in aha! Gotcha, "more than most branches of mathematics, probability swarms with results that are strongly counterintuitive, with problems for which the correct solution seems utterly contrary to common sense" (p. 85). The part that really draws me in is that it is not just the “average” person that has difficulty with probability. The use of misconceptions, misperceptions, heuristics, biases and logical fallacies is found across a wide swath of individuals (including, but not limited to, doctors, lawyers, teachers, professors, psychologists, nurses and, yes, even mathematicians and statisticians). Come on, even Paul Erdos, according to Paul Vazsonyi, when shown the solution to the Monty Hall Problem (initially) said “No, that is impossible, it should make no difference.” How could you not love probability?!
What I’m really interested in, however, yes, even more than the probability itself, is trying to get a handle on “what’s going on” when people solve probability problems. Currently, I’m investigating the probabilistic content knowledge of prospective mathematics teachers. My research, in general, contributes to the limited research on teachers’ probabilistic knowledge. More specifically, my work has led to the development of a variety of theories, models and frameworks, which account for relative likelihood comparisons (e.g., which coin flip sequence is least likely) made by prospective teachers. Currently, I am incorporating more recent developments from the field of cognitive psychology (e.g., attribute substitution), which (I argue) have largely been ignored by those investigating teachers’ probabilistic thinking and knowledge. In addition, I am establishing that informal logical fallacies (e.g., the fallacy of composition, the appeal to ignorance and others) are an effective means to account for normatively incorrect, inconsistent, sometimes inexplicable responses to a variety of probabilistic tasks. To me, the union of probability, psychology and education is a wonderful place to conduct research.
 

7) What are some favorite (non-technical) math books that you like reading for your own enjoyment, and how about math books that you'd especially recommend to lay people with some math interest?

Whether it’s audio, video or print, I’m a big fan of people who popularize mathematics. As such, here is a list of people I recommend to those who have some interest in math: Alex Bellos, Alexander Bogomolny, Amir Aczel, Card Colm Mulcahy, David Spiegelhalter, Ian Stewart, Ivars Peterson, John Allen Paulos, Keith Devlin, Marcus du Sautoy, Martin Gardner, Samuel Arbesman, Steven Strogatz, Carl Bialik, and The Numberphile Team (found here: http://www.numberphile.com). 
I also think it’s important that people read Paul Lockhart’s "A Mathematician’s Lament" (found here: http://www.maa.org/devlin/LockhartsLament.pdf). In addition, G. H. Hardy’s "A Mathematician’s Apology" (found here: http://www.math.ualberta.ca/~mss/misc/A%20Mathematician's%20Apology.pdf). 
Oh yeah, for those who are perhaps more mathematically inclined, I would recommend Pitici’s recent series: The Best Writing on Mathematics 2010, The Best Writing on Mathematics 2011 and The Best Writing on Mathematics 2012. Good stuff!

I'm familiar with all these, except for David Spiegelhalter, so I may have to investigate him further... looks interesting.
 

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

Thanks for asking. I’m a big fan of stand up comedy; I love listening to podcasts and CBC Radio (1 and 2); I walk my dog, Scout, for about an hour a day; I enjoy reading non-fiction; I enjoy good TV, but that is getting harder and harder to find these days; and, once a week, I play left wing for the Engineering team of the University of Saskatchewan’s Faculty and Staff Hockey League.
 
9) Any parting words, not covered above, you'd care to pass along to a math-oriented audience?
 
Yes, calculus is perilously perched at the "top" of school mathematics, it’s days are numbered and that’s ok... statistics is waiting in the wings.

Thanks for the opportunity to respond to your questions.

Egan Chernoff (@MatthewMaddux)

I'm not sure how much you're being completely serious and how much tongue-in-cheek, but the recent ascendency of Nate Silver, and some others, has certainly raised statistics to the limelight (in America at least)... its future emphasis in education will indeed be interesting to observe!

ADDENDUM: Egan has responded elsewhere that he was very serious about the above proposal, and one of the links he mentions to make the point is this fine 3-minute Arthur Benjamin TEDTalk:

http://www.ted.com/talks/arthur_benjamin_s_formula_for_changing_math_education.html 
 

************************************

Thanks for all the responses Egan.

Originally, I had postponed interviewing Dr. Chernoff because the video of him speaking on the Web (referenced above) covers him so well:

http://blogs.sfu.ca/research/davidwheeler/wp-content/uploads/2012/10/Chernoff_Maddux-Inaugural-Lecture-copy.mov

If you missed it the first time I linked to it, give it a play (about an hour-long, but it doesn't always load or play well).


...Lastly, I'll again appeal, that if any math communicator is willing to be interviewed here this is a good time to let me know, as I don't have any further interviews outstanding at the moment that I'm expecting to be returned (unless someone surprises me; YO! Vi Hart, surprise me... ;-)). The only incentive I can offer is a little added publicity for your blog or website, or books, if you're an author.

Numbers and the Mind

"Thinking In Numbers" is (autistic savant) Daniel Tammet's latest book. I enjoyed his first two books (HERE and HERE) a great deal, and enjoyed this one as well, although it isn't exactly what I was hoping for. It is a collection of 25 varied and entertaining (sometimes almost flight-of-fancy) essays, some far more math-or-number-related than others, that can be read out-of-order. It repeats, but may not add much new to what he has previously written about how he perceives and manipulates numbers in his own mind.

The most entertaining chapter for me came toward the end, Chapter 22, "Selves and Statistics," an essay on statistics and death... topics that might seem dry and morbid, but actually turned into a fun read -- reminded me a bit of some of Nassim Taleb's writing on how "black swans" and improbabilities actually rule the world moreso than high-probability events (I might even recommend that readers start with this chapter to set a tone and then proceed to other chapters).
I won't do a full review of Tammet's volume here, but will close with a passage I enjoyed from near the end, before simply passing along some other online links/reviews:

"Many people think of mathematics as something akin to pure logic, cold reckoning, soulless computation. But as the mathematician and educator Paul Lockhart has put it, 'There is nothing as dreamy and poetic, nothing as radical, subversive, and psychedelic, as mathematics.' The chilly analogies win out, Lockhart argues, because mathematics is misrepresented in our schools, with curricula that often favour dry, technical and repetitive tasks over any emphasis on the 'private, personal experience of being a struggling artist.'"

An interview with Daniel about the book here:

http://www.guardian.co.uk/books/2012/nov/11/thinking-numbers-maths-daniel-tammet

…and a couple of British reviews here:

http://tinyurl.com/8llkr35

http://www.independent.co.uk/arts-entertainment/books/reviews/thinking-in-numbers-by-daniel-tammet-8142910.html

Tammet's prior two books had wide distribution (and I think good sales) in the U.S., so I'm surprised this volume isn't more readily available in bookstores. Is it possible the titles of his first two books were simply perceived as more catchy and enticing: "Born On a Blue Day" and "Embracing the Wide Sky," while the current volume's title is viewed as too unappealing to a nation populated with math-phobes??? -- just a guess on my part.
Anyway, I give it a thumb's up, as a fun, entertaining, and interesting read, though if you're looking for deep math or science it may come up short.

Odds 'n Ends of Note... Enjoy!

An odd variety of sundry things catching my attention lately...:

1) Impressed?... plenty of folks might be. Math often bedazzles the easily impressionable! That's the basic conclusion of a study cited recently by both Mother Jones and the Wall Street Journal, demonstrating that just adding mathematics (even nonsense math!) to a journal article can increase its perceived quality among some reviewers:

http://www.motherjones.com/kevin-drum/2012/12/how-technical-sounding-nonsense-can-boost-your-career-prospects

http://online.wsj.com/article/SB10001424127887323374504578219873933502726.html

2) Mr. Honner recently highlighted a simple example (Google search), most of us can relate to, of how "conditional probability" operates in our everyday world:

http://mrhonner.com/2012/05/17/google-and-conditional-probability/

3) Is Henry Pogorzelski following in the steps of Shinichi Mochizuki…? A 90-year-old emeritus mathematics professor named Henry Pogorzelski believes he has proven the Goldbach Conjecture, but his effort may be too long and involved for anyone else to follow (similar to the problem mathematicians are having checking the complex work of Mochizuki on the ABC Conjecture); interesting Boston Globe piece:

http://www.boston.com/bostonglobe/ideas/brainiac/2012/12/math_even_mathe.html 

4) Futility Closet highlights a sort of self-referential geometric construction set from, as they say, "the ever-inventive" Lee Sallows:

http://www.futilitycloset.com/2013/01/03/construction-set/

Lee Sallows homepage is here: http://www.leesallows.com/

He is especially famous for his linguistic "self-enumerating pangrams" like the following:

"Only the fool would take trouble to verify that his sentence was composed of ten a's, three b's, four c's, four d's, forty-six e's, sixteen f's, four g's, thirteen h's, fifteen i's, two k's, nine l's, four m's, twenty-five n's, twenty-four o's, five p's, sixteen r's, forty-one s's, thirty-seven t's, ten u's, eight v's, eight w's, four x's, eleven y's, twenty-seven commas, twenty-three apostrophes, seven hyphens and, last but not least, a single !"

You can see more examples here:

http://www.fatrazie.com/EWpangram.html

5) Just learned of this online journal, "The Mathematics Enthusiast," that's been around for awhile and should be of interest to educators:

http://www.math.umt.edu/tmme/ 

6) A recent Twitter feed asked for suggestions of inspiring books to recommend to HS math students. What surprised me was how often Douglas Hofstadter's "Godel, Escher, Bach" (or GEB as it is often called) came up. Dr. Watkins also mentioned it very positively in the interview I did with him a few days back. GEB, is one of my favorite books as well (and it has certainly won many awards); still, I've never thought of it particularly as a math book… a book for those interested in psychology or philosophy perhaps, or even computer science, but not necessarily math buffs. In fact, Wikipedia states:

"Hofstadter has emphasized that GEB is not about mathematics, art, and music but rather about how cognition and thinking emerge from well-hidden neurological mechanisms."

...and here's an older Slashdot review of it:

http://books.slashdot.org/story/99/04/23/147248/godel-escher-bach----20th-anniversary-edition

Great book; I'm just not sure I'd be recommending it to HS math students, unless they're also very interested in cognitive science. (On-the-other-hand, possibly one could argue that what GEB does touch upon is not math itself, but the kind of "mathematical thinking" that Keith Devlin so emphasizes... I'm not sure???)

7) Finally, for a bit of entertainment, a clever, fun bit of magic (...and cognitive science of a sort) from Richard Wiseman. Not really math, but one thing I've learned since doing this blog is that for a lot of folks "magic" is actually a gateway into an interest in math.
If you're familiar with Wiseman's "tricks" you may see through this one fairly quickly... or... you may not (if YOU'RE not fooled by it, try it on a friend):

Some 2012 Favorites...

It's often traditional for bloggers to wrap up the year by listing their favorite posts from the prior 12 months. So a little belatedly I'll list (especially for newcomers here) a varied set of posts from last year that were among my personal favorites:

from Jan: "Is the Answer Obvious, or Obscure"
from Feb.: "Seife, Wallace, and Infinity, Oh My!..."
from Mar.: "Sleeping Beauty... NOT Your Childhood Fairy Tale"
from July: "Another Prime Example..."
from Aug.: "Mind-wrenching"
from Sept.: "Joy To the World (of Math)"
from Nov: "Doing The Thing You Love..." and "Benny's Rules"
from Dec.: "Why Infinity Will Drive You Bonkers"

2012 was also the year I wrote my shortest post ever ;-):

http://math-frolic.blogspot.com/2012/11/i-guess-it-does-modified-from-twitter.html

But, my favorite posts of the year were the interviews I only initiated in October, that allowed me to better get to know several wonderful math enthusiasts/communicators, who I might otherwise never have had the pleasure of interacting with:

http://math-frolic.blogspot.com/p/blog-page.html

...I expect 2013 to be at least as much fun!

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!)

***********************************

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.

***********************************

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/

Catching Up On a Few Thangs

HAPPY NEW YEAR!!

An eclectic potpourri of links to get 2013 underway….

1) Last week, American Radioworks had a wonderful (hr.-long) show on the varieties of online higher education (not restricted to math education, but in general), entitled "Keyboard College." A highly worthwhile listen, if you missed it:

http://americanradioworks.publicradio.org/features/tomorrows-college/keyboard-college/

2) The Indian prodigy mathematician Ramanujan continues to amaze long after his death. Fascinating piece on mystical deathbed conjectures the young Indian made (inspired by a Hindu goddess) that have been proven true 90 years later:

http://www.dailymail.co.uk/sciencetech/article-2254352/Deathbed-dream-puzzles-renowned-Indian-mathematician-Srinivasa-finally-solved--100-years-died.html

...also, apparently a film of Ramanujan's life, "The Genius of Ramanujan" is due for release next March.

3) For William Thurston fans (of which there are many), a quite long read here on Thurston and the Haken conjecture:

http://www.scientificamerican.com/article.cfm?id=getting-into-shapes

4) The below site, I only recently learned of, may appeal to young math problem solvers and contestants out there:

http://blog.brilliant.org/

It offers up (level-appropriate) 'challenging' problems to participants on a weekly basis. Be sure to read the "FAQ," "How It Works," and "Blog" sections.

5) I remember Tom Lehrer as a satirical singer-songwriter in the 1960s when I was growing up. A recent post from another blog though reminds/informs? me that Lehrer was actually a professional Harvard-trained mathematician before he found entertaining on a stage more lucrative.
Anyway, as a victim of the 60's 'New Math,' this is how I remember him:



6) I haven't posted a puzzle on the blog for awhile, but here's a beautiful geometry one recently posted at "Futility Closet":

http://www.futilitycloset.com/2012/12/23/belt-loop/

7) And, in case that was too easy for you (though I doubt it) you can always download this PDF to learn about "the hardest logic puzzle ever" (originally stemming from Raymond Smullyan, and involving asking questions of gods):

http://www.snsanalytics.com/ask7y0


...and next up will be the first brand-spanking Math-Frolic interview of 2013... introducing someone most of you likely don't know.