Mother, Country, and Apple Pie, er, uhh, Mathematics

(via his Cornell page)

What is there not to love about Steven Strogatz… in the popular math arena, he is becoming, like Martin Gardner and Raymond Smullyan, another American gem. In this short (7 min.) speech before the American Academy of Arts and Sciences he wears not only his love of math on his sleeve… but his love of mother and country as well:

http://www.wgbh.org/articles/Thinkers-and-Doers-the-American-Academy-of-Arts-and-Sciences-7375
(it's the 4th audio segment down on the page)

[p.s...A quick note of thanks to those who've sent in suggestions for interviews here, and tomorrow morning I'll have another from my original list of folks that I really think readers will enjoy, and yet don't imagine you'd guess ahead of time who it is (no, it's not Steven).]

A Bit of Serendipity

Since the prior post was heavy with some Tim Gowers material I can't help but point out another cosmic synchrony ;-) that materialized on the Web… A short while back Patrick Honner (who I just interviewed recently) posted this note on his blog:

http://mrhonner.com/2012/10/24/this-is-not-a-trig-function/

...basically, he notes that a purported sine wave curve on a NY State math exam simply didn't look right to him at a glance ("too rounded"), and then goes on to show that his visual hunch was indeed correct upon closer inspection. The ensuing comments to his brief post are fascinating as well, but the capper is that about 10 days later, in a bit of serendipity, Tim Gowers writing on Google+ noted his immediate sense that a British air traffic control tower he'd passed by recently did not conform to a "mathematically natural shape," and wondered aloud "how acute this sense that mathematicians have is," at which point he stumbled upon Honner's post:

https://plus.google.com/u/0/103703080789076472131/posts/VhHE8TuJhcm

…it reminds me a wee bit of the old retort (applied when you succeed at something, and someone else says it was 'just luck'), that it seems 'the more I practice the luckier I get!' ...or, in-other-words, it's a skill developed from experience.
Having said that though I s'pose it's a bit difficult to know which is the cart and which is the horse here: i.e., do mathematicians have a special knack for recognizing certain patterns and forms because it's something their minds have experienced repeatedly (practiced)… or, is it that people who have a special or inborn aptitude for form and pattern recognition are more likely to end up in mathematics???


[p.s... if anyone hears the result of Tim Gowers' recent heart surgery and how he is doing, please report to us in the comments; I'm sure many would like to hear that all went well.]

ADDENDUM 11/10/12: Tim now has a detailed post up that he is back home recovering (with some discomfort) from the hopefully successful surgery:
http://gowers.wordpress.com/2012/11/09/what-actually-happened/

Mochizuki, Gowers, Alan November

First, a wonderful article from The Boston Globe emphasizing how difficult it will be to check Shinichi Mochizuki's lengthy claimed proof of the ABC conjecture, because of the complexity and newness of the math involved:

http://tinyurl.com/a8srze4

The piece ends thusly:

"And this, [Minhyong] Kim thinks, might pose the greatest challenge of all. 'When you’ve been wrapped up in your own research program for a long time sometimes you lose a sense of what it is that other people don’t understand,' he says. 'Other people feel quite mystified as to what he’s [Mochizuki] doing and part of him, I suspect, doesn’t quite understand why.'"

On a simpler note, do you wish to engage your own math students… well, so does Tim Gowers...
British Field Medalist Gowers (who deserves to be read/discussed whenever possible) has a piece in The Spectator regarding math education:

http://www.spectator.co.uk/features/8744071/should-alice-marry-bob/

from it: "...rather than explaining mathematical ideas (about statistics, say) and then discussing how they can be applied to the real world, a teacher should instead start with a question that is interesting for non-mathematical reasons and keep a completely open mind about what mathematics has to contribute to the discussion."

Gowers' take is that teachers need to be utilizing real 'real-life' examples in the classroom, not the 'if 2 painters can paint 2 houses in 5 days how many houses can 4 painters paint in 15 days' sort of story problem that often gets passed off as an application.

This is more-or-less a followup to a fantastic earlier piece he did on same subject:

http://gowers.wordpress.com/2012/06/08/how-should-mathematics-be-taught-to-non-mathematicians/

[On a side note, just yesterday, Gowers put up another interesting post about probabilities and surgery he is undertaking for an atrial fibrillation condition… hopefully, we'll soon hear that all went well!]:
http://gowers.wordpress.com/2012/11/05/mathematics-meets-real-life/

Finally, hat tip to John Golden for leading me to this TED video (~16 mins.) by Alan November that piggy-backs nicely onto Tim Gowers' views, in describing student engagement in learning:

Sol Lederman is Wild About Math

 Math-frolic Interview #7

"Making math fun and accessible" -- Sol Lederman (from his blog)


Another delight for me today... I suspect anyone reading my blog is well-familiar with Sol Lederman's "WildAboutMath" blog -- it's been around a long time, and makes virtually every list of 'best math blogs on the Web' that ever comes out! Sol was actually the first person I asked for an interview, but being a busy guy, later requests to others actually got back to my email box faster. But better late than never!

Sol loves talking with people who are "inspired by math." I'm not sure though that he realizes just how inspiring HE has been to many of us in the blogosphere… I would never have attempted a simple and sometimes light-hearted math blog aimed at a general readership, had Sol's "Wild About Math" blog not blazed a path showing there was an audience for a not-too-technical approach. Moreover, his recent podcast series was the inspiration for the interview series here.
So without further delay ....he-e-e-e-e-ere's Sol:

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

1) To start, could you tell readers a little about your background or anything else pertinent to your becoming a math blogger…

I've loved math forever. And, I enjoy writing. Some years ago I became burned out on my techie work and wanted to make a change. So, I jumped ship and started blogging. That was five years ago. I didn't stay away from tech for very long, though. I'm back doing programming, tech support, and other related things. But, I still blog occasionally although far far less than I once did.

2) Beyond writing a blog, where does math fit into the rest of your life or work? (if not already covered above)

Math for me is about logical thinking AND about creative expression. Depending on the task, I sometimes get to do creative thinking at work. Certainly the mathematical qualities of problem solving, pattern matching, associating one idea with another, and attention to detail carry over from my math to my work.

3) What are your favorite aspects of mathematics (that you yourself most enjoy studying)?

I'm very intrigued with the question of how to make math more understandable to the masses. Just today I was having a conversation with my boss about how fractions work and why the techniques we have for manipulating fractions actually work. Why is it that we can multiply fractions? What does it mean to divide a fraction by another fraction? How much of this is pure abstraction vs. grounded in something that students can understand and touch? Anything that demystifies math is exciting to me.

4) "Wild About Math" has been one of the most popular and consistently-highly-rated math blogs on the Web (it recently had it's 5-year anniversary!). Can you tell us how it first came about in your mind, and how confident were you that there would be an audience for it?

I once thought that I'd like to lead workshops with kids where we would explore the "wilds of math." I did do math circles in Santa Fe for nearly a year but I never did create the workshop for kids. But, the idea for a name stuck, and became Wild About Math!

5) Are there any funny or entertaining behind-the-scenes stories you can tell from having run a blog for 5 years?

Early in the blog's history I wrote a post, Impress your friends with mental math tricks. I wrote that post quickly and without a huge amount of thought or editing. That post got 45,000 views one day, mostly from folks at StumbleUpon. It made the front page of Digg and put the blog on the map. And, that humble post continues to bring traffic five years later. No other post has ever come close to achieving that status!

Me: ...WOW!, 45,000 that's amazing… I was thrilled in the very early days of my blog when YOU once linked to a puzzle I presented and I immediately got several hundred additional visitors, and as you indicate, I still today get visitors to that post every single week from your original link. So I hear what you're saying even though I've never experienced it on that scale.

 6) Are there certain blogposts you've done that stand out for you as personal favorites or ones that were the most fun to work on? And from the other side, which posts seem to have been most popular or attention-getting with your readers?

This fun post is the second most popular article from the blog. It gives 8 simple math-based games that kids can play with paper and pencil. My favorite posts are the recent podcast interviews I've done with people making a difference in math education.

7) Name some of your favorite math books that you like reading for enjoyment, and/or books that you recommend to people who are interested in math but may lack a strong academic background in it.

I recommend any of James Tanton's books, books by Theoni Pappas, Keith Devlin, and the late Martin Gardner, of course.

8) You're very interested in math learning and education. What's your view of Khan Academy and the ongoing controversy that seems to surround it in some quarters? Are there online instructional math sites that are your favorites? And have you taken any online courses yourself (perhaps Keith Devlin's latest offering)?

I've not taken online math courses and I'm not impressed with most instructional math sites. Regarding Sal Khan's work, I feel he's doing the same old paradigm, lecturing to students, but on video instead of in a classroom. I am VERY excited, though, about the work of Scott and Jen. They are doing phenomenal stuff with online game-based education. They are the only online site I'm excited about.

Me: Interesting, hope readers check it out...

9) For awhile now your blog has focused on podcasts with individuals who, as you say, 'are inspired by math, and inspire others'. Is that the format (podcasts) you see the blog taking for the foreseeable future, or any plans to return to more written posts at some point, or do you have any other vision for the future of your blog? And can you say anything about which 'math inspirers' we may look forward to in future podcasts?

For the foreseeable future, yeah, I plan to keep doing podcasts. I like doing them much more than writing book reviews. Princeton University Press and the MAA send me a fair number of books that I really like so you can expect to see me interviewing their authors. But, I'm open to interviewing a wide variety of authors. I feel like my momentum for math blogging has been slowing down. I've got other interests I'm pursuing so I don't expect to do much more than the monthly or so interview that I'm doing these days.

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

I sincerely appreciate your interest in interviewing me and I've said more than once that I really enjoy your blog. I don't read math blogs very often these days but when I'm in the mood to scan a few I always make it a point to check out yours.

Me: Thanks for the kind words; much appreciated, and great to know you're a fan! 

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

Sol further asked about my availability for a podcast on his blog, but for now, I think he has too many really interesting, knowledgeable people to choose from before I take up his time! Maybe one day though....

Thanks for participating here Sol, and congratulations on 5 great years of successfully making math fun and accessible!! (And I've added a permanent link to WildAboutMath podcasts in my right-hand column "podcast" listings.)

Math and Writers...

An interesting (if a bit esoteric) essay in the current New Yorker on "Why Writers Should Learn Math":

http://www.newyorker.com/online/blogs/books/2012/11/writers-should-learn-math.html#ixzz2B9nnHVvv

some quotes from the piece:

"What ballet is to football players, mathematics is to writers, a discipline so beguiling and foreign, so close to a taboo, that it actually attracts a few intrepid souls by virtue of its impregnability. The few writers who have ventured headlong into high-level mathematics—Lewis Carroll, Thomas Pynchon, David Foster Wallace—have been among our most inventive in both the sentences they construct and the stories they create."

"As the mathematician Terence Tao has written, math study has three stages: the 'pre-rigorous,' in which basic rules are learned, the theoretical 'rigorous' stage, and, last and most intriguing, 'the post-rigorous,' in which intuition suddenly starts to play a part."

"If Hemingway’s writing is algebraic in its precision, then [David Foster] Wallace’s is quantum calculus..."

and a couple of other quotes included in the article:

 “A mathematician, like a painter or a poet, is a maker of patterns... The mathematician’s patterns, like the painter’s or the poet’s must be beautiful; the ideas like the colours or the words, must fit together in a harmonious way. Beauty is the first test.” --G.H. Hardy

"Those who’ve been privileged (or forced) to study it understand that the practice of higher mathematics is, in fact, ‘an art’ and that it depends no less than other arts on inspiration, courage, toil, etc.” --David Foster Wallace

As Conan O'Brien Might Say…

…'Where are the la-a-a-adies???'

I'll be posting Math-frolic Interview #7 on Sunday, and while I'm thrilled with the guest, it is the 6th time out of 7 with a male interviewee (and the majority of inquiries that I'm waiting to be returned are also guys)… soooo, a little more representation of the Emmy Noether gender would be nice. 

One problem is simply that most math bloggers are likely male, and secondly I've discovered that many female bloggers don't as readily post their email addresses, making initial contact difficult.  There are likely a number of female math bloggers/teachers though that I'm just not very familiar with; so again, please feel free to make recommendations if you think someone would make a good interview.
…Oh, and don't everyone mention Vi Hart at once -- of course I'd love to interview Vi but suspect she may be toooo busy at the moment to squeeze it in (though I did attempt to send her an email, which she may or may not have received?). But after Vi, who else?

Meanwhile, for some reading entertainment (especially if you're going out to eat this weekend), an interesting little story that made waves a couple months back, about the 'rounding' of restaurant bills up or down to do away with the need for pennies (the story focused on Chipotles, but it happens elsewhere, and there can be pros and cons):

http://tinyurl.com/d3fge3d

'Best Of' Math 2012...

A quick blurb about "The Best Writing On Mathematics 2012" which I received a review copy of. It is once again edited by Mircea Pitici, and I believe this is the best edition thus far. Upon reading the first edition in 2010, it seemed a wonderful idea, the execution of which would improve in coming years. The 2011 volume was better than 2010, and this year's version has hit its stride even further, especially in containing more pieces that should appeal to a wider audience.
There are several well-known names (Terry Tao, Tim Gowers, Mario Livio, Brian Hayes, John Baez…) in this edition. The Foreword by David Mumford is a wonderful delineation of pure versus applied mathematics (also throwing physics into the mix). And I enjoyed most all the early entries in the volume. It slogged along a bit more in the middle and toward the end (for me), and, like most anthologies, overall, contains a mix for many different tastes. I doubt that anyone will enjoy every single entry, but that is in the nature of such (somewhat disjointed) compilations. At the end of the text, editor Pitici gives a list of other articles considered for inclusion that didn't make the cut. Of course several of them look quite interesting as well, although I don't know how readily available they are for lay readers.

There may be fewer technical pieces in this edition than previous ones, and I'll warn readers there is a lot of material on philosophical and historical underpinnings of mathematics -- topic areas I find rich and enjoyable, but some do not, and will be less enamored than I of certain portions of the book. There is still some fairly technical reading involved as well, so I'll also warn that this remains largely a volume for those already inclined toward mathematics and having some preparation; it is not for the general reader hoping to be newly engaged by the "best writing" to be found on mathematics. Unlike, say the 'best science writing in 2012' which might still appeal to a non-scientist, large chunks of 'the best writing in mathematics' will still only be accessible to math buffs.

The two oddest or quirkiest offerings (to me), came near the end: an essay by Fernando Gouvea on whether or not Cantor was truly surprised (and over what) when he famously wrote (in translation), "I see it, but I don't believe it" (essentially upon proving that a line segment contained as many points as a multi-dimensional geometric form), and the very last piece by Mark Colyvan on mathematics and dating/mating algorithms.

My favorite piece also was toward the end... I only discovered Brit Richard Elwes a couple years ago and he has quickly vaulted forth as one of my favorite math explicators. His essay bringing the subjects of Cantor set theory, infinity, and the Continuum, up-to-date with current ideas of an "ultimate L" logic-world promoted by Hugh Woodin is excellent and mind-bending. I'll be going back to re-read his and several other of the entries more slowly/carefully when time permits, and looking forward to next year's edition as well! For now, this series seems to be Pitici's 'baby,' and I don't wish to take anything away from his efforts, but it would be interesting to see what different editors each year would come up with (as is the practice with the more famous annual "best American writing" series that's been around for awhile).
Despite what the public might think, math is an incredibly diverse field of study, and therefore difficult to anthologize. If you're not already acquainted with Pitici's series I recommend this 2012 volume as a place to start.

Strogatz, Zero, and Probability

Well, it's not with me :-( but nonetheless a nice interview with Steven Strogatz from Wired.com here (turns out he has a special fondness for the number 1/7, and admits to a prior ignorance of the arithmetic operation of "casting out nines"):

http://www.wired.com/wiredscience/2012/10/the-beauty-and-delight-of-mathematics-qa-with-steven-strogatz/

Meanwhile, the various dangers of 0 (psssst... DON'T divide by it) are explained in this recent 13-min. Numberphile video:



And lastly, a nice little counterintuitive probability conundrum from Futility Closet involving bridge hands and aces:

http://www.futilitycloset.com/2012/10/17/the-paradox-of-the-second-ace-2/

(somewhat reminiscent of the more-famous boy-or-girl paradox or even the "boy born on Tuesday problem")

Thoughts With You...

Under the circumstances taking a moment to go off-topic... and just send a note out to the people of New York, or otherwise in the path of storm Sandy:

Patrick Honner of MrHonner

Math-frolic Interview #6

"What I enjoy the most about mathematics is the moment when a solution, a relationship, or a structure becomes evident.  It's a powerful feeling when you conquer a challenge, or see and understand the real essence of something for the first time." --Patrick Honner

Patrick Honner is an award-winning New York state secondary math teacher who is quite active on the Web.

He blogs at MrHonner.com and has given a TedxTalk as well, in addition to also being a contributor to the NY Times Learning Network (and is @MrHonner on Twitter).

He kindly answered my inquiries as follows:

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

1) How did your interest in mathematics originally come about, and when did you realize you wanted to pursue math professionally?

I've always enjoyed math.  I recall participating in math contests in elementary school, and I consistently had good math teachers through junior high and high school.  When I started college I wasn't sure what I was going to do, but I knew I would keep taking math classes.  I never really did figure out what I was going to do, so I just kept taking math classes and moved on to graduate school.

2) What are your favorite aspects of mathematics that you most like studying/reading about?

What I enjoy the most about mathematics is the moment when a solution, a relationship, or a structure becomes evident.  It's a powerful feeling when you conquer a challenge, or see and understand the real essence of something for the first time.   I still regularly experience that feeling now, as I learn new mathematics, or learn to see old mathematics in new ways.  It's part of what makes teaching math so wonderful.

3) How do you go about selecting the topics you blog about? And what do you think is the strongest 'draw' for your blog, out of so many 'math education' blogs?

 I write about my mathematical experiences, which range from the mundane--like over-thinking prices in the supermarket--to the academic--like finding novel proofs and derivations of facts and theorems.  Mathematics plays a substantial role in how I understand and engage with the world, so it's always present in my mind.

I think the depth and variety of my experiences, both in mathematics and in teaching, give me a unique perspective in this field.  And I think the way I look to celebrate and appreciate math--through compelling questions, interesting stories, and beautiful images--makes math accessible and enjoyable in a novel way for some readers.

4) A controversial editorial ran in the NY Times awhile back questioning whether algebra should be a required course for ALL high school graduates. Many responses appeared on the Web to that piece, and eventually YOU had a full response in the Times itself. Can you tell any backstory to that (or post-story for that matter)? Did you approach the Times about doing a reply, or did someone there approach you specifically for a response? And are you pleased with the overall discussion the episode generated?

My initial reaction to the editorial in question was to notice, as others did, that Andrew Hacker didn't really seem to understand what algebra is.  After all, he suggested that we replace algebra with, well, algebra.
I have been contributing math content (like lessons, activities, and quiz questions) to the New York Times Learning Network for several years, and I thought the controversy surrounding "Is Algebra Necessary?" created a perfect opportunity to demonstrate to students and teachers how the tools and techniques of algebra can be used to explore what anyone can find in the Times.

 The response to the piece was great.  Despite being up for less than a month, "N Ways to Apply Algebra with the New York Times" was one of the Learning Network's top-viewed posts of the past year.  And lots of teachers and students responded with comments.

5) You also took on the "establishment" with a series of blog posts about flaws in a NY state math examination… has anything substantive resulted from those critiques?
And you're actively involved in various efforts to improve secondary math education in the U.S. where there seems (to me, as an education outsider) to be a lot of disagreement/controversy over how best to proceed. How well do you think matters are proceeding, and are you optimistic that math education, nationwide, will be much improved for future generations, or will there always be unresolved controversy over methods?
 
Nothing substantive has resulted from my critiques of math problems on New York state exams, nor do I expect anything to happen.  I'm simply trying to raise the point that the quality and validity of these standardized exams are rarely, if ever, called into question.  If the tests aren't good, how can they possibly determine if teachers should keep their jobs or schools should remain open?
Public education will always be, in part, a political issue, and thus will always be subject to the controversies (both real and manufactured) that politics brings to everything it touches.  I think the best avenue for improving math education is a sustained focus on elevating the profession of teaching: more support for teachers at the ground level; more opportunities for growth in content-knowledge and pedagogy; and real opportunities for teachers to collaborate, share, and actively shape the profession itself.

I have been very fortunate to be a part of Math for America, an organization that does all of this in the most supportive, least restrictive way imaginable. It has made a huge difference in my career, and in the careers of many others.

6) What are some of your favorite math books to read for enjoyment, and how about math books you'd especially recommend to lay people with some math interest?

I enjoy doing math more than reading it.  I greatly enjoy solving problems, creating new problems to solve, or creating new ways to think about mathematical ideas.  In terms of books about math for lay people, I'm not sure anyone does it better than Steven Strogatz.  His "The Calculus of Friendship" and "The Joy of X" are both wonderful.  John Allen Paulos has also written several excellent, accessible books that I've enjoyed, like "A Mathematician Plays the Stock Market".

7) What online math resources do you find especially useful in the classroom? And do you use your blog or any social media in your classroom as well?

Alexander Bogolmony's Cut the Knot is one of the best math websites around for both teaching and learning.  He has a unique perspective on math and teaching, and he has produced many wonderful interactive mathematical explorations that I and my students enjoy.  I am a huge fan of Geogebra, and I find myself using Desmos more and more.

I try to use my website as a bridge between the classroom and the greater world of mathematics for my students, a place for us to continue our conversation and share new experiences.  I have students create blogs as part of projects, and have experimented with other social media technologies as teaching and learning tools as well.

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

Participation in the digital mathematics and math education communities has profoundly impacted me, both personally and professionally.  Thanks to everyone out there who reads, writes, tweets, and posts; this is truly a remarkable community to be a part of!

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

-- Thanks Patrick for participating here, and even more-so for your active engagement in the wider field of math education. As they say, 'keep fighting the good fight!'

[...and if readers have anyone you would particularly like to see interviewed here let me know.]

Keith Devlin Wrapping Up

"For sure I’ll offer another version of this course next year, with changes based on the huge amounts of data you get with a global online class of 64,000 students. Despite the enormous effort in designing, preparing, and running such a massive enterprise, there are three very good reasons to pursue this…
"...there is a huge, overall, feel-good factor for those of us involved, knowing that we can help to provide life-changing opportunities for people around the world who would otherwise have no access to quality higher education." --Keith Devlin

Keith Devlin has begun writing his wrap-up to his 5-week MOOC (Massive Open Online Course), "Introduction To Mathematical Thinking," offered through Stanford University. Fascinating, insightful reading… and a must for anyone interested in the future of education and online learning.

http://mooctalk.org/2012/10/26/answering-the-64000-students-questions/

He touches upon research opportunities, the "feel-good factor," trolls, and grade obsession, among initial topics he's addressing, with more to follow.
The lecture hall is now the world.

Mandelbrot On the Bookshelf

 "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"  --Jonathan Coulton

If the life of Benoit Mandelbrot interests you then a new book coming out shortly will be of note, a posthumous autobiography, entitled "The Fractalist." [Mandelbrot died just 2 years ago this month.]
I haven't read it, but from what I can tell, if you're interested primarily in the details of Mandelbrot's mathematical contributions this volume may not be a good choice, but if you're interested in his life this is a definite read:

http://www.tabletmag.com/jewish-arts-and-culture/books/114766/a-math-genius-sad-calculus?all=1

More on Mandelbrot here:

http://www.nndb.com/people/752/000022686/ [biographical]

http://www.ted.com/talks/benoit_mandelbrot_fractals_the_art_of_roughness.html [TED Talk]

http://www.guardian.co.uk/science/2010/oct/17/benoit-mandelbrot-obituary [obituary]

And hey, STILL a wonderful math video (the Mandelbrot Set zoomed to Jonathan Coulton's rousing lyrics):

The Maddening Set

 I can never read (or write) about the 'Cantor Set' without thinking to myself, "Well, of course Cantor was driven to madness…!" (an infinite number of points having 1-1 or 0 measure might do that):

http://tinyurl.com/44szvot

Paul Erdos... Still Publishing After All These Years

 

“A mathematician is a device for turning coffee into theorems.” --Paul Erdos

(via kmhkmh at WikimediaCommons)

John Cook notes at his blog that Paul Erdos, the most prolific mathematician of all time (who died in 1996), is STILL publishing an occasional paper now and then, because of all the collaborators who started papers with him way back when, that were put aside, and are only now being completed. John's short post here:

http://www.johndcook.com/blog/2012/10/23/dead-man-writing/

The above leads in turn to a fresh hour-long podcast (from "Relatively Prime") on Erdos here:

https://itunes.apple.com/us/podcast/relatively-prime/id560923828

...Several of the personal stories told therein are quite wonderful.

And some more Erdos reminiscences here:

http://www.maa.org/features/erdos.html

Finally, Paul Hoffman's classic biography of Erdos, "The Man Who Loved Only Numbers" remains a great read.

James Grime, SingingBanana

Math-frolic Interview #5

"My videos are generally what I think is cool that week. Sometimes it's just a statement I see in passing somewhere, and I go look up the maths and the stories of who invented it and why. Working out how to present that information is like a glorious jigsaw puzzle. I don't treat it as a job, or work." --James Grimes

If you follow mathy videos on the Web you are almost certainly aware of British "mathematician, juggler, and comedy nerd" James Grime through one of his puckish incarnations on SingingBanana or  Numberphile (also, on Twitter HERE and Facebook HERE).  He consistently and exuberantly offers some of the most entertaining math output for general audiences. So much so, that I doubted he would have time to respond to an interview request from me... but, graciously he did so! (in fact from the replies I'm getting to such requests it seems clearer to me now that math-folks like to share their love for their much-maligned subject with any-and-all who will listen!)
So it's a special joy for me today to present answers from James Grime to my questions:

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

1) To start, can you tell readers a little about how your background brought you to the world of mathematics? And when did you know that you wanted to do mathematics professionally?

It all began with children's television. I don't come from an academic background, but there was programming for children in the UK about maths and science. This included people like Johnny Ball who made maths fun and interesting. And that's when I made my choice - to work in television!... Or maybe I'll be one of these 'Doctors of mathematics' I've heard about.

I also wanted to run a sweet shop.

2) What are your favorite mathematical areas of specialty to study or read about?

I study Group Theory. Group Theory is the study of symmetry, such as the rotations of a cube - but in maths symmetry means there is something you care about that you want to stay the same - that might be shape, volume, angle, or magnitude. Then you can start to mess with it, but that property you care remains invariant.I also have a soft spot for probability and statistics - the maths of games, gambling and predicting the future. This is one of the most obviously useful areas of maths, that everyone uses on a daily basis. I have been accused of being a frustrated statistician in the past - and they might be right.

Yet, you will often find me talking about Cryptography, which is one of the more interesting and exotic uses of mathematics - it's all about secrets and spies! And yet, underneath, it uses all my favourite mathematics, symmetry, combinatorics, number theory, probability and more.

3) I don't know of anyone who does more joyous, fun math videos than you do. Your enthusiasm is infectious (...in a good way ;-)! Is that a persona you've cultivated for the Web, or are you simply that expressive by nature with any topic you're interested in?

I'm probably like that for everything I'm interested in. People are very quick to passionately talk about things they hate, I wish they would talk with as much passion about the things they love! How can I expect people to be excited and enthusiastic about maths if I am not leading by example! I guess I'm taking a leaf from from the children's TV presenters that inspired me.

4) Approximately how much time per week do you spend working on your various math efforts on the Web, and how do you select the topics you present?

The topics are a result of a short attention span and craving for novelty! My videos are generally what I think is cool that week. Sometimes it's just a statement I see in passing somewhere, and I go look up the maths and the stories of who invented it and why. Working out how to present that information is like a glorious jigsaw puzzle. I don't treat it as a job, or work.


5) What are some of your favorite math books that you like to read for enjoyment, and how about math books that you'd especially recommend to lay people with some math interest?

One of the books that inspired me was Fermat's Last Theorem by Simon Singh (watch the documentary too). This book showed me the beauty of mathematics, the fascinating rich history of mathematics, and what it could be like to be a mathematician - a world with which I had no other connection.

For enthusiasts who like a bit of recreational mathematics, the puzzle books of Martin Gardner, Sam Loyd, and my pal Johnny Ball are ones I constantly like to dip into.

6) I've commented previously on my blog that it seemed as if Britain produces more excellent math communicators (per capita) than the U.S. Would you possibly agree or disagree with that? And, if you agree, care to speculate on why Britain has so many wonderful math writers? (I once asked on my blog, whether it was because of the way math is taught in Britain or the way writing is taught???)

I can only speak for myself and what has inspired me. Again, it was shows like the Royal institution Christmas Lectures which is a series of science lectures for young people televised around Christmas.

My opinion is that maths and science programming for adults and children creates a culture of more maths and science communicators. These programmes may not be to everyone's interest, but it provides an exposure to science that some children would not otherwise get.

And so that is my aim with my videos on YouTube. You don't need to chase an audience, indeed we can make videos as high-brow or as low-brow as we want them to be, and the audience will find you. But by putting that stuff out there, you can get into homes that would never have seen these ideas otherwise.

7) Mathematics education in the U.S. is quite controversial, with a lot of different/opposing viewpoints. Is that more-or-less true in Britain as well, or is the approach to math education in Britain any more unified? Also, you are involved in an educational endeavor called the "Millennium Mathematics Project" in Britain… care to elaborate on that and say how it's going?

I'm sure that is the case in the UK too, but I try to stay away from those sort of arguments!

The Millennium Mathematics Project involves a number of projects all trying to bring mathematics to life. In particular the MMP includes the NRICH website (http://nrich.maths.org) which is a free website of mathematical problems and investigations to enrich kid's mathematical diet; Plus Magazine (http://plus.maths.org) with news and articles for the older students; and roadshows for students of all ages, and a speaker will come in and run activities in your school.

I run one of these roadshows, called the Enigma Project (http://enigma.maths.org) all about the history and mathematics of codes and code breaking - including a demonstration of an original WWII Enigma Machine! Very cool.

My job is to inspire and motivate (children, teachers and the general public alike), I travel all over the UK and the world, and speak to thousands of people. Great fun.

Here's a fun game, try to guess when the Millennium Mathematics Project was established...

8) Can you explain where the "SingingBanana" name for your blog originates from (or is that top-secret)?

Oh, well, now that you've put it like that I'll have to keep it a mystery! I can tell you I do reveal the answer in one of my videos, but which one? I guess people will have to watch them all!

Fair enough, and a suggestion I would second!

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-- Sincere thanks Jim for taking time from a busy schedule to tell my readers more about yourself and your thoughts on math. Keep up the great work... and I hope some day you have that sweet shop!

Great Minds Think Alike... ;-)

A quick note: I've just discovered that mathblogging.org also recently (early Sept.) began a series of brief interviews with math bloggers, called "Mathematical Instruments" available here:

http://mathblogging.wordpress.com/category/mathematical-instruments/

The thought for my own series arose a few weeks later, inspired by Sol Lederman's "Wild About Math" podcast series, and without realizing that mathblogging had already started a similar endeavor.
Luckily, our questions are slightly different and with so many math presenters to choose from duplication may not be too great… anyway, a diverse set of opportunities to learn more about the multitude of online math enthusiasts.
Check out the mathblogging series, which already has 7 interviewees under its belt, if you weren't already aware of it! And later tonight I'll be posting my own #5 interview!

Some Longreads et.al.

While I'm working on interviews other things have a way of building up... so another list of links to pick-and-choose from today:

1) Long but GREAT presentation of 'simple groups' by Richard Elwes (from a few years back) that I've been meaning to pass along:

http://plus.maths.org/content/enormous-theorem-classification-finite-simple-groups

2) Nice small collection of classic "counterintuitive conundrums" here:

http://datagenetics.com/blog/may12012/index.html

3) Interesting, recent long read on "insanely long proofs" from John Baez:

http://johncarlosbaez.wordpress.com/2012/10/19/insanely-long-proofs/

4) And if you're not too phobic of philosophical (and perhaps computational) discussion you may enjoy this longish post on the "many worlds" interpretation of mathematics:

http://math.andrej.com/2012/10/03/am-i-a-constructive-mathematician/

5) On the more practical side, a list of resources for math teachers, of possible interest (but I haven't checked them out thoroughly myself):

http://new-to-teaching.blogspot.com/p/web-20-tools.html

6) And lastly, some quickie visual entertainment... I don't often link to optical illusions, because there are just TOO MANY good ones on the Web, but I hadn't seen this simple, effective one before, so passing it along:

https://twitter.com/Todd_Roy/status/231144475290923008/photo/1

....late Mon. or early Tues. I'll have interview #5 up-and-running, and it's from someone I was especially delighted to have take part!... but I'll hold you in suspense 'til then! ;-)
[The tab below the blog header above, btw, will take you to an ongoing list of all the interviews conducted.]

The Math Hombre, John Golden

Math-frolic Interview #4

John Golden is a Michigan math professor and proprietor of the MathHombre blog. He especially enjoys using games and interactive activities in the math classroom, and his enthusiasm for math shines through in most all his posts!
You can get a sense of the range of John's interests from his Pinterest page here: http://pinterest.com/mathhombre/pins/

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1) For starters, can you say a little about your background or anything else pertinent to your becoming a math blogger…

I got a PhD from Penn State in Mathematics, index theory, but along the way got more and more interested in the teaching and learning of math. I was on my way to get certified in secondary teaching, when a visiting position came up at Grand Valley State University and I got to both be in K-12 schools and be a teacher educator. Dream job!

2) When do you remember first loving mathematics, and when did you know you wanted to pursue it professionally?

I always hated how repetitive math class was. The homework and even the year to year re-covering. And then …algebra. Now, I think it was how that unified and generalized everything we did, but then I just loved it. Then I had the good fortune to have an amazing mentor in undergrad, John Hocking (http://mathhombre.blogspot.com/2011/08/hocking.html), and it was all she wrote.

3) What are the aspects of mathematics that you most like studying/reading about?

Connections among seemingly unrelated ideas (hence, index theory) and the beautiful intersection of math and art. And games.

4) There are MANY 'math education' blogs out there... is there anything in particular that you feel sets yours apart from the crowd, or if not, what do you think is the strongest 'draw' for your blog?

I have no idea. It started for me to share the fun stuff out there from people like Dan Meyer and Kate Nowak and Sue Van Hattum with my students and then it became good for my work by reflecting and synthesizing. If there's any appeal it might be that I try to honestly share my math and teacher thinking. I got a lot of linkage on math games and tech for math, GeoGebra in particular.

5)  Are there certain types of posts that are your favorites to work on? Do you have any specific posts that were favorites to write, or alternatively, seemed to be favorites with your readers?

Playing games that result in learning is always exciting to share, and I guess original activities in general. I have an odd affection for my weirdest posts like Jonah (http://mathhombre.blogspot.com/2010/07/jonah-math-teacher.html) or Screwtape (http://mathhombre.blogspot.com/2011/03/screwtape-for-teachers.html) - but those don't get much traction. Mr. Slope Guy (http://mathhombre.blogspot.com/2012/03/mr-slope-guy.html) was a fun project with my middle school son that has been popular.

6) You're a huge fan of "GeoGebra"… want to explain a little about what that is and how you utilize it?

GeoGebra is this amazing free dynamic algebra and geometry software begun by Markus Hohenwater. Completely free, elegantly and compactly written and stupefyingly powerful. I use it for making activities for students, as a super-graphing calculator-plus tool for students to use, for generating mathematical images for documents, for solving math problems for myself, and - occasionally - for fun. I want to do everything I can to help make it accessible and usable to students and teachers.

7) What other online math resources do you like to use? And to what extent do you use your own blog or 'social media' as a classroom tool?

I have really enjoyed Twitter as self-professional development and networking. Amazing resource - can be almost overwhelming. I am a heavy reader of other people's blogs, and wish more university faculty used it, too. 

I use social media quite a bit as a teacher educator. Our student teachers use Twitter and blogging, I host class pages on Facebook now instead of Blackboard, there's a major wiki project (http://hs-mathematics.wikispaces.com/) in one of my classes, I encourage students/teachers to create for YouTube (http://mathhombre.blogspot.com/2010/12/change-channel.html) or GeoGebraTube, etc. I know our graduates will need support and I want to enable them to find it if it's not at their school. The math twitter/blogosphere is fantastic.

8) Can you name a few of your favorite math-related books, and any you'd recommend to people in general?

Post! http://mathhombre.blogspot.com/2010/01/recommended-reading.html

For teachers: Jo Boaler's What's Math Got to Do With It? (http://mathhombre.blogspot.com/2010/05/book-club-whats-math-got-to-do-with-it.html) , The Teaching Gap (http://mathhombre.blogspot.com/2012/04/teaching-gap.html) and Mosaic of Thought ( aliteracy book that I'm constantly referencing on my blog, e.g. http://mathhombre.blogspot.com/2012/10/why-questioning.html).

For fun: Math Curse, The Man Who Counted and The Phantom Tollbooth. I'd better stop there.

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

If you're enjoying what you find a on the web, try sharing for yourself! Tweet it, write about it, pin it, etc. Be a part of improving the profession. (Wise words from my awesome colleague Dave Coffey,  http://deltascape.blogspot.com/, distilled from The Teaching Gap)

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Thanks John for taking time to answer my questions, and any readers (especially teachers) not already familiar with MathHombre blog should stop by for a visit! John is also on Twitter at: @mathhombre

Thinking Of Gardner

(image via WikimediaCommons)

Truth be told, as much as I love Martin Gardner's recreational math writings (and his "Colossal Book of Mathematics" is certainly a fave), my VERY favorite Gardner outputs are his essays… on all manner of topics... and his books that anthologize them.
With the annual Gathering For Gardner celebration coming up this weekend (in honor of his birthday Oct. 21), and all the emphasis on Martin's mathematical contributions, I think it worth taking a moment to reiterate what an extraordinary essayist, in general, he was… succinct, clear, persuasive, logical, perceptive, thought-provoking, wide-ranging… on all manner of science, philosophy, and culture. I've remarked in the past (WITHOUT tongue-in-cheek), that I think American students would be better off if we tossed Shakespeare from the high school curriculum, and made reading Gardner's essays mandatory (...just my opinion).

Probably my single favorite of all Gardner's offerings is his volume, "The Night Is Large," a compendium of essays written from 1938 to 1995. "The Whys of a Philosophical Scrivener," "The Jinn From Hyperspace," and "Science: Good, Bad, and Bogus" are some other wonderful collections (and very little math in any of these), and there were others.

Gardner could also be a prankster-without-equal, pulling off certain classic April 1st jokes that played havoc with some of the erudite readers of his Scientific American column. However, possibly my own favorite shenanigan of his was a highly critical review/debunking (under the alias of 'George Groth') he himself wrote for the NY Times Review of Books of his own volume, "Whys of a Philosophical Scrivener." [in a quick search, I couldn't find a full (free) copy of the review online; if someone else finds it please send me the URL or give it in the comments].

I hope no one, in celebrating Martin, pigeon-holes him as a man of numbers, or of fun and games... he was most certainly a 'man of letters,' and I think, one of the finest this country has produced.

...Happy birthday Martin... ohh, and, have one hexaflexagon of a weekend everybody! ;-)

Wherefore Art Thou Alan Sokal...

(image via WikimediaCommons)

Too chuckle-worthy not to pass along… (it would be even more amusing if it weren't also troubling):

One "Marcie Rathke" seems to have composed a mathematical paper (kids, can you spell "r-a-n-d-o-m-w-o-r-d-g-e-n-e-r-a-t-o-r") that got accepted by an open-access math journal, yet makes even less sense than physicist Alan Sokal's 1996 venture into postmodernism.
One kinda expects this sort of escapade in some academic areas, but less so in mathematics (the math journal involved, "Advances in Pure Mathematics," despite the nice-sounding name, is one of the many less-than-kosher pay-to-play journals that have sprouted up in the digital age). One might also expect something better from any professor employed by the "University of Southern North Dakota at Hoople"... or, perhaps not.
(p.s. anyone know Alan Sokal's current university-affiliation?) ;-) Read all about the story at these links:

http://thatsmathematics.com/blog/archives/102

http://www.lrb.co.uk/blog/2012/10/17/paul-taylor/stochastically-orthogonal/

Hat tip to "Aperiodical" for bringing this story to my attention.

Oh, and for all you up-and-coming math majors out there who are in need of a little assist, here is where the paper was generated:

http://thatsmathematics.com/mathgen/