Thinking Machines?

The (2015) annual Edge question (which essentially asks if you believe machines will ever be able to think) and responses have been posted; a lot of good reading here, though I've only scanned a handful of responses thus far:
http://edge.org/contributors/q2015

Very few mathematicians included, but I do especially like Keith Devlin's answer (apologies if readers are sick of hearing me say that, but I genuinely do!):
http://edge.org/response-detail/26099

Keith sees "no evidence to suggest that such [machine-thinking] may even be possible," noting that just "because something waddles like a duck and quacks, does not make it a duck." Machines can make decisions, but that doesn't mean they think. But he does worry about "the increasing degree to which we are giving up aspects of our lives to machines that decide, often much more effectively and reliably than people can, but very definitely do not think."

Another writer I enjoy, William Poundstone, takes a different tack from Devlin, accepting the possibility more seriously:
http://edge.org/response-detail/26043

A couple of other responses (out of ~180) I've liked so far:
Roger Schank:  http://edge.org/response-detail/26037   [corrected link]

Frank Wilczek:  http://edge.org/response-detail/26039  [corrected link]

A number of writers make the same point that "thinking machines" already exist on Earth: they're called "humans" (although I think this merely highlights the semantic variability in how people interpret the word "machine").

I also love Freeman Dyson's simple, succinct response... leave it to Freeman to reply to a deep Edge question in 3 sentences... 'nuf said:  http://edge.org/response-detail/26254

Can't help but notice that Ray Kurzweil isn't included among the respondents... not sure which, if any, of the responders are associated with him or his work???

Seems roughly like an even split between those who believe thinking machines are impossible or at least unlikely, and those who think them possible, if not inevitable (but I haven't done a careful tally, so could be wrong). More encouraging, is what seemed a predominant view, that even if thinking machines develop they will not be prone to malevolence, and will either remain under human control, or have ethics built in.

I presume these essays (per usual) will soon be available in paperback book form, but haven't seen the volume yet.

It's interesting, by the way, that just recently, Google announced they will discontinue making the current version of their much-ballyhooed Google Glass, a product that many of us, without even trying it, could see little market enthusiasm for. Similarly, I won't be surprised if Google cars totally flop in the near-future (even though, longer-range, there's no doubt a place for something like them). Much of the wild speculation about machine-thinking likewise seems wholly premature... just as Arthur C. Clarke's HAL of 2001 was waaay ahead of its time. As a student 40 years ago, I remember so many musings and predictions of coming advances that have yet to transpire. We're often quite inept at predicting the usefulness and timetable of new technology. Heck, I'm still waiting for my commuting battery-powered jetpack that the Jetsons had in 1962. C'mon Google (actually, one of my favorite companies), get with the program ;-)

Bountiful Potpourri + a Special Note

Another very mathy week gone by... some things that caught my attention, AND a special note below:

1)  This was different... from Futility Closet a post about math, poetry, the Fibonacci sequence, and Zeckendorf’s theorem:
http://www.futilitycloset.com/2015/01/11/math-and-poetry/

2)  Jason Rosenhouse offers up an "especially clever and elegant proof" of the Pythagorean Theorem":
http://tinyurl.com/pyjy4f5

3)  Last weekend, NPR's RadioLab re-ran their wonderful episode on "Numbers":
http://www.radiolab.org/story/91697-numbers/

...definitely worth a listen if you've never heard it, or worthy of a second listen if you have! (covers some cognitive psychology, Benford's Law, Erdös numbers, and Steven Strogatz's "Calculus of Friendship").

4)  Another piece this week on the frustrations surrounding Mochizuki's asserted proof of the ABC conjecture:
http://www.zmescience.com/science/math/mathematician-numbers-12012014/

5)  As she often does, Joselle Kehoe connects up the neuroscience of mathematics, cognition, and abstraction in a post earlier in the week:
http://mathrising.com/?p=1230

6)  Presh Talwalkar goes over the "game theory" of airfare pricing (as highlighted by a recent airline lawsuit against a consumer website):
http://tinyurl.com/o3o5t89

7)  Alex Bellos reports on the newly-discovered "Harriss spiral," stemming from earlier golden-ratio work:
http://tinyurl.com/lnlxnsz
The latest "MathMunch" also looks at the Harriss spiral:
http://mathmunch.org/2015/01/15/harriss-spiral-math-snacks-and-set/

8)  The latest "Carnival of Mathematics" has been posted:
http://www.andrewt.net/blog/posts/carnival-of-mathematics-118

9)  Cathy O'Neil offered a link to her Prezi talk on data journalism at the recent JMM meeting in San Antonio:
http://tinyurl.com/pkrjptl

10)  Another episode of "avoiding thinking in math class" from Ben Orlin:
http://mathwithbaddrawings.com/2015/01/14/mmm-strawberry-rhuburb-root-2/

11)  Manifolds, triangulation, and weird topology conjectures, from Quanta Magazine (interesting, if you can follow along the topology!):
https://www.quantamagazine.org/20150113-a-proof-that-some-spaces-cant-be-cut/

12)  As many already know, the obituary of Alexander Grothendieck (by Mumford and Tate) that drew some controversy weeks ago, has now been published in Nature (and is freely accessible for another 10 days or so):
http://tinyurl.com/nx9l2xf

13)  More on designing the "flipped classroom" from Crystal Kirch:
http://flippingwithkirch.blogspot.com/2015/01/flipping-with-kirch-designing-flipped.html

14)  An old 'birds in a lorry' physics puzzle solved, supposedly:
http://tinyurl.com/pj3m2wv

and another fascinating physics-related piece (by Tom Siegfried) here, on "quantum math":
http://tinyurl.com/otfgkzc

15)  Per usual, check out MikesMathPage to see what Mike Lawler and the boys have been up to this week (I haven't had time to follow him much this week :-( :
http://mikesmathpage.wordpress.com/

16)  And earlier in the week I re-looked at an older Ian Stewart book that I now recommend to all math fans:
http://mathtango.blogspot.com/2015/01/letters-from-mathematician.html

Closing Note:  

Lastly, a bit unusual... but a shoutout or tip-of-the-hat to Ed Frenkel who this last week (in the wake of the Charlie Hebdo killings) conducted an amazing Twitter dialogue with at least 2 Islamic adherents who I believe were trying to account for what gives rise to such violence (I hope that's a fair-enough statement of what their goal was?).  I've never much believed that intelligent, meaningful discussion (let alone debate), can even take place on Twitter (without quickly degenerating), but I really respect Dr. Frenkel's patient, passionate, resolute attempt to do so. Despite some heated moments, both sides I think ultimately maintained decorum while expressing very different views, through dozens of tweets back-and-forth. Mathematicians are NOT all about equations and formulas only! 
You don't need to go back and read through the long Twitter threads, but I do recommend if you're not already following Dr. Frenkel (@EdFrenkel) you should be. He is interesting enough when talking mathematics... and even more interesting and remarkable when he's talking about other matters! We're lucky to have him here (dang, Ed, Keith Devlin, and Fawn Nguyen, all from other countries, and all now in California -- that state needs to share the wealth a little better!! ;-))
Some of the essence of what Dr. Frenkel tweeted is covered in this talk he gave a few months back regarding 'no easy answers' and 'life is not a paragraph' (no technical math here):
https://www.youtube.com/watch?v=YnqQ-BWMHrE

The last 15 minutes-or-so (it's a 38-min. talk) are among the 15 most evocative minutes you may ever encounter from a professional mathematician -- try to find time for this video if you've not already viewed it.

[And on Sunday morning, in light of Charlie Hebdo, in light of Ed Frenkel, in light of the MLK Holiday (U.S.) on Monday, and in light of so much going on in our world today, the Math-Frolic 'Sunday reflection' will stray a little from the usual fare.]

Letters From a Mathematician

Several years ago I skimmed through Ian Stewart's little book, "Letters To A Young Mathematician," and it didn't register much with me, not really being a fan of "Letters to..." sorts of books. But I just re-read it, with the benefit of a few more years immersion in mathematical debates, and especially Keith Devlin's notion of "mathematical thinking," and suddenly enjoyed it immensely! Indeed, I now wonder if any of Keith's thinking was influenced by Stewart's ideas, or was the influence in the opposite direction(?), from Devlin to Stewart, so similar are many of the viewpoints expressed (Stewart's discussion of "proofs" especially mirrors a recent view voiced by Keith).

I won't review this instructive (and surprisingly rich) little volume, since it's from 2006, but will note that I think every prospective math major should ponder it before they get too far along their path. In a quick 200 pages it covers a lot of backdrop to a mathematics career.  And even though it was written almost a decade ago, it includes discussion that is pertinent to the ongoing debates in math education right now. It also contains more thoughtful passages I'll be considering for "Sunday Reflections" than almost any other book on my shelf! I especially like the whole second half of the volume.

Lest it not be clear to people, I should mention that these "letters" are fictitious missives written to a fictitious niece; which gives Stewart a lot of freedom to say what he wants in the way he wants to say it.  In fact, Stewart sees the book as a sort of update to G.H. Hardy's "A Mathematician's Apology."

For fuller reviews here are a couple of old ones from AMS and from American Scientist:
http://www.ams.org/notices/200705/rev-carberry-web.pdf
http://www.americanscientist.org/bookshelf/pub/port-and-walnuts

As one of the reviewers sums up, "'Letters to a Young Mathematician' succeeds well in opening a door into the world of mathematics and enticing the reader inside."

Ian Stewart is yet another Brit who has a knack for communicating mathematics to a public that is often resistant to it. I've enjoyed several of his past works. And funny how time changes perspectives... as this particular volume springs from being completely off my radar to now being one of my favorites from him -- at the risk of sounding like a broken record, I'll credit Keith Devlin for that, since reading him made me so much more receptive to Stewart's thoughts here.

The last chapter isn't necessarily representative of the book, but it is the most poignant chapter... I'd almost like to quote it in entirety, but will settle for some words from the final two pages:

"Our minds may indeed be just swirls of electrons in nerve cells; but those cells are part of the universe, they evolved within it, and they have been molded by Nature's deep love affair with symmetry. The swirls of electrons in our heads are not random, not arbitrary, and not -- even in a godless universe, if that is what it is -- an accident. They are patterns that have survived millions of years of Darwinian selection for congruence with reality....

"Perhaps we have created a geometer God in our own image, but we have done it by exploiting the basic simplicities that nature supplied when our brains were evolving. Only a mathematical universe can develop brains that do mathematics. Only a geometer God can create a mind that has the capacity to delude itself that a geometer God exists.
"In that sense, God is a mathematician; and She's a lot better at it than we are. Every so often, She lets us peek over her shoulder."

[On a side-note, Sol Lederman interviewed Stewart almost exactly two years ago for his "Inspired By Math" podcast series (just one of a jillion Stewart appearances on the Web!):
http://wildaboutmath.com/2013/01/11/ian-stewart-inspired-by-math-14/ ]

Br-r-rimming-over Potpourri

Biggest potpourri I've yet done for your weekend catching-up, if you missed many of these:

1)  Nice extended (and fun) discussion of correlation and causation here:
http://statswithcats.wordpress.com/2015/01/01/how-to-tell-if-correlation-implies-causation/
(HT to Patrick Honner for this one, and a blog that was new to me)

2)  I suspect every long-time teacher out there has a story to tell similar to Fawn Nguyen's in "Let's Not." I just don't know if they can tell it as well as she does:
http://fawnnguyen.com/lets-not/
...and in another post she challenges her students to go beyond the book:
http://fawnnguyen.com/rigid-transformations/

3)  An interesting entry from Jeremy Kun looking at math authenticity in the entertainment industry... and thusly, finding for himself, a niche business opportunity!:
http://j2kun.svbtle.com/authenticity-of-background-math

4)  Interesting and fun first-of-year posting from "Gödel's Lost Letter" on the Breakthrough Prizes, a new book, and yearly predictions:
http://rjlipton.wordpress.com/2015/01/04/mathematics-its-about-the-future/

5)  No younguns (or video) in this one, as Mike Lawler explains how financial bonds can yield a surprisingly high return in a falling interest environment:
http://mikesmathpage.wordpress.com/2015/01/05/an-interesting-math-example-coming-from-finance/
(And as usual there is still more interesting stuff up at Mike's page from the week.)

6)  A basic introduction to prime numbers (with plenty of basic links) from "Solve My Maths" here:
http://solvemymaths.com/2015/01/04/complements-4-prime-numbers/

7)  Another (transcribed) Ed Frenkel interview, on AI, math education, and the future:
https://math.berkeley.edu/~frenkel/interview-VEJA.pdf

8)  John Baez has an interesting, if pessimistic, piece about Google giving up on their search for cheap renewable energy (the comments are as interesting as the post):
http://johncarlosbaez.wordpress.com/2015/01/05/why-google-gave-up/

9)  I've previously pointed out this long, rich Lior Pachter post on mathematics and biology, and was a bit surprised it didn't draw even more comments than the ~30+ it had at last check -- but perhaps it's so long and complex that it scared readers off!? Anyway, I did recently discover (h/t to Gerald Thurman) a lot of additional comments, or at least chatter, over at this aggregator site, for anyone wanting to peruse more discussion:
https://news.ycombinator.com/item?id=8819811

10)  In his latest piece for Huffington Post, Keith Devlin asks, "How badly do we want 21st-century, relevant, first-class education for the nation's children?," and offers an update on what's happening with educational technology in K-12:
http://www.huffingtonpost.com/dr-keith-devlin/edtech-investment-is-at-record-levels_b_6405226.html
In the end he says that "revolutionizing K-12 education within a decade requires a transformative, national, public-private initiative, perhaps reminiscent of, but much less expensive than, the NASA Apollo Project to put a man on the Moon"!

11)  If you thought donuts were just for breakfast, you were wrong -- donuts are for math class (and fun blog posts):
http://lifethroughamathematicianseyes.wordpress.com/2015/01/06/donuts-make-it-better/
(...perhaps, best to read this with a nice hot cube of coffee!)

12)  Ben Orlin has started a series of posts addressing 'thinking in math class' -- the introductory one is here:
http://mathwithbaddrawings.com/2015/01/07/how-to-avoid-thinking-in-math-class/

13)  "MathTechbook" from Discovery Education (for online math learning) is coming. Read about it here:
  http://tinyurl.com/menyjqt and http://tinyurl.com/mwxm9hw

14)  Dana Ernst on IBL (inquiry based learning)... must-reading if you're a teacher and not already familiar with IBL:
http://maamathedmatters.blogspot.com/2015/01/the-twin-pillars-of-ibl.html

15)  Another little geometry beauty from Futility Closet; and it falls under the equally-beautiful heading of "sangaku":
http://www.futilitycloset.com/2015/01/08/cutting-up/

16)  Interesting New Scientist update on frustrations surrounding Shinichi Mochizuki's "proof" of the ABC conjecture:
http://tinyurl.com/ofhv9br

17) Princeton University Press has put up a pdf of their current math-related offerings, including several forthcoming works:
http://press.princeton.edu/catalogs/math15.pdf

18)  Lastly, just this morning I've posted over at Math-Frolic James Tanton's first video offering in support of Common Core. Must-viewing for all involved in that debate.

Happy weekend everyone!

(as always, let me know of any broken or misdirected links ASAP)

Proverbial Look Back

Wasn't planning any sort of (2014) year-end review post, but have read so many from other blogs got inspired to do one (same thing happened last year). Way too many posts at Math-Frolic though to sort through, so initially picked out 7 from here (MathTango had fewer than 30 postings for the year, if "Potpourri" posts aren't included), and then I've added a few "Sunday Reflections" from Math-Frolic at the end.
Without further adieu...

1)  In June I reviewed (like a zillion other people) Jordan Ellenberg's "How Not To Be Wrong" and already realized it would likely be my favorite volume for all of 2014:
http://mathtango.blogspot.com/2014/06/how-not-to-go-wrong.html

2)  Will just mention one other book review from 2014 because the volume didn't get the attention it deserved. That was Jason Rosenhouse's tribute book to Raymond Smullyan (both Jason and Raymond are deserving of more attention, as well). I covered it in April:
http://mathtango.blogspot.com/2014/04/master-of-logical-legerdemain.html

3)  I interviewed several wonderful people in 2014 for the blog, but one especially stood out, by her "passion personified"....learning why Fawn Nguyen is a rock star in the math education blogosphere was a joy:
http://mathtango.blogspot.com/2014/05/fawn-nguyen-passion-personified.html

4)  In March I got a few things off my chest with this cathartic harangue about the ills of 'big data':
http://mathtango.blogspot.com/2014/03/annuities-annuities-annuities.html

5)  Keith Devlin frequently appears in posts here, as he did when I wrote somewhat philosophically about "proofiness" in November:
http://mathtango.blogspot.com/2014/11/proofiness.html

6)  And Keith was also there for what (for some reason?) was by far my most trafficked post of the year in April, dealing with education:
http://mathtango.blogspot.com/2014/04/keith-devlin-explains-my-past-maybe.html

7)  The post I most enjoyed writing, oddly, was a sort of stream of consciousness elegy to author David Foster Wallace in July:
http://mathtango.blogspot.com/2014/07/infinity-and-angst-david-foster-wallace.html

This last one was actually the lone "Sunday Reflection" that appeared at MathTango (because of its length), instead of Math-Frolic (where all others reside). Five of my other favorite "Sun. reflection" passages from the prior year are below:

1)  http://math-frolic.blogspot.com/2014/12/an-epiphany.html   (Steven Strogatz on the epiphany of mathematics)

2)  http://math-frolic.blogspot.com/2014/08/prime-synchrony.html   (Dan Rockmore on an intersection of Freeman Dyson and Hugh Montgomery)

3)  http://math-frolic.blogspot.com/2014/08/somethings-going-on-here.html   (William Byers on the intuition behind mathematics)

4)  http://math-frolic.blogspot.com/2014/06/proofs-as-artifacts.html    (an odd, self-reflexive passage from David Berlinski I just happen to enjoy)

5) http://math-frolic.blogspot.com/2014/06/math-as-monasticism-math-as-dynamite.html   (Jordan Ellenberg on how mathematics is practiced )

Hope you'll peruse/enjoy some of these, if you missed them.

New Year Potpourri

Happy 2015, all... and with no further adieu, some of the surprisingly full week of math posts that were out there:

1)  Yet another remembrance of Alexander Grothendieck:
http://education.lms.ac.uk/2014/12/alexander-grothendieck-some-recollections/

Also, a reminder, if you haven't already read Lior Pachter's incredible longread post (inspired in part by a Grothendieck obituary) about the disparate "two cultures" of math and biology, DO IT:
https://liorpachter.wordpress.com/2014/12/30/the-two-cultures-of-mathematics-and-biology/

2)  IF you're deep into chess, specifically machine-chess, you won't want to miss this Ken Regan post:
http://rjlipton.wordpress.com/2014/12/28/the-new-chess-world-champion/

3)  Blogger Kristin tries to analyze the meaning and role of "intuition" in math-learning in a post that was inspired by a Twitter "conversation":
http://mathmindsblog.wordpress.com/2014/12/28/intuition-in-learning-math/

4)  Presh Talwalkar solves an infinite exponential in less than 60 seconds (video)... be sure to read the comments as well:  http://ow.ly/GwcV9

5)  Deborah Mayo goes down memory lane with a post on power in error statistics:
http://tinyurl.com/jwffkan

6)  Mike Lawler reviewed his blogging year (although he's posted so much great stuff, I think he barely scratches the surface here):
http://mikesmathpage.wordpress.com/2014/12/29/blogging-year-in-review/
(...and of course check out Mike's other posts from the week, as well)

And Evelyn Lamb likewise did a year-in-review for her blog:
http://blogs.scientificamerican.com/roots-of-unity/2014/12/31/year-in-review/

7)  Another "Cavmaths" geometry problem:
https://cavmaths.wordpress.com/2014/12/29/a-nice-area-puzzle/

8)  This recent analysis of a year-old Marilyn vos Savant puzzle is a bit hard to follow, but perhaps interesting if you can follow it:
http://gottwurfelt.com/2014/12/29/one-of-these-things-is-not-like-the-others/

...and for some entertainment read the comments at one of the forums where this was originally discussed:
http://usa.rightwingamerica.com/index.php?topic=6458.0

9)  Longish-read: some backstory on Common Core (h/t to Frank Noschese for this one):
http://tinyurl.com/pghy5nf

10)  Keith Devlin's latest post on the need for "radical changes" in education here:
http://devlinsangle.blogspot.com/2015/01/your-fathers-mathematics-teaching-no.html
...and I've just posted a response to it at Math-Frolic as well:
http://math-frolic.blogspot.com/2015/01/teach-children-well.html

11)  I'll end with a fun post from M.C. Burke closing out last year:
http://mrburkemath.blogspot.com/2014/12/two-taylor-swifts-and-sliding-yardstick.html

A Sunday Potpourri

I was expecting a slow week in the math blogosphere... but, I was WRONG! ...PLENTY to read; here's some of it:

1)  The latest "Math Teachers At Play" Carnival here:
http://tinyurl.com/nso9c9t

2)  Five "math gems" passed along from a UK secondary math teacher:
http://www.resourceaholic.com/2014/12/gems19.html

3)   Early in the week The Aperiodical pointed out a new math app game called "Just Get10".  Check it out here (hard to tell how popular it might become; I never expected 2048 to be the 'hit' that it was):
http://www.veewo.com/games/get10/

4)  A conversation with award-winning mathematician Ken Ono:
http://tinyurl.com/pxy8xqa

5)  We hear a lot about chess, but here's a little bit of interesting checkers history from Futility Closet:
http://tinyurl.com/oya9g46

6)  The world of big data/statistics is attracting more and more STEM women:
http://tinyurl.com/n995edt

7)  Statistics making the world a better place? (via Andrew Gelman):
http://andrewgelman.com/2014/12/23/using-statistics-make-world-better-place/

8)  Fun geometry from Mike Lawler (via James Tanton and James Key and a 3-D printer):
http://tinyurl.com/lzg2kl4

9)  Another interesting piece from Evelyn Lamb, this time on the homotopy of "holes" (which end up being like Santa Claus!):
http://blogs.scientificamerican.com/roots-of-unity/2014/12/25/what-is-a-hole/

10)  A quick list from AMS of some celebrities who enjoy mathematics:
http://blogs.ams.org/mathgradblog/2014/12/26/celebrities-math/#sthash.TqNwebIC.dpbs

11)  In the unlikely event that some of my readers can even comprehend it, here is a recent update related to Mochizuki's proof of the ABC conjecture:
http://tinyurl.com/mw337nc

12)  Will end with another fine geometry puzzle from Stephen Cavadino:
https://cavmaths.wordpress.com/2014/12/27/rectangle-puzzle/

Friday Potpourri

This week's grab-bag (and I will either have NO weekly potpourri next week, or else it will appear on Sunday, rather than on Friday, the day after Christmas):

1)  Recent New Zealand interview with Marcus du Sautoy here:
http://www.radionz.co.nz/national/programmes/saturday/audio/20160965/marcus-du-sautoy-maths-and-art
...related Sautoy article here:
http://www.odt.co.nz/lifestyle/magazine/326897/painting-numbers

2)  The best puzzle and game theory posts from Presh Talwalkar ("Mind Your Decisions") for 2014 -- catch up if you missed any of these:
http://ow.ly/FYgYZ

3)  Fascinating report on the "Umbral Moonshine Conjecture" (...no, I'd never heard of it either!, but related to the Monster Group):
http://www.sciencedaily.com/releases/2014/12/141215114816.htm

4)  Technical post from Terry Tao on latest work regarding "long gaps between primes":
http://terrytao.wordpress.com/2014/12/16/long-gaps-between-primes/

5)  "Boolean" vs. "additive" thinking from Andrew Gelman:
http://andrewgelman.com/2014/12/18/key-part-statistical-thinking-use-additive-rather-boolean-models/

6) "Why Should You Learn Math?"... one student's answer:
http://3010tangents.wordpress.com/2014/12/18/why-should-you-learn-math/

7)  I'm always eager to shine light on Dr. Keith Devlin and his endeavors in math communication. This week someone else did it for me:
http://mathematicalmysterytour.blogspot.com/2014/12/professor-keith-devlin-on-youtube.html

8)  And for your smile-of-the-week:
http://tinyurl.com/jvg5ts6

Big Helping of Potpourri

The good and diverse mathy stuff just keeps on comin'... ICYM any of these:

1)  First, this wonderful, ranging interview with fascinating polymath Eric Weinstein ought not be missed:
http://tinyurl.com/q4mt2c7

2)  Interesting interview with Caltech's Xinwen Zhu (former student of Edward Frenkel), who works on the Langlands program:
http://www.caltech.edu/news/prime-numbers-quantum-fields-and-donuts-interview-xinwen-zhu-45000

3)  The Bayesian/frequentist debate goes on:
http://tinyurl.com/nkjs273

4)  A bunch of "puzzles and starters" from Stephen Cavadino here:
https://cavmaths.wordpress.com/puzzles-and-starters/

OR, if you need a stronger challenge here are some 2014 Putnam problems:
https://mathproblems123.wordpress.com/2014/12/08/putnam-2014-problems/

5)  A topic that will be increasingly crucial to newer generations... Teaching kids coding/programming as part of literacy:
http://www.davidketcheson.info/2014/12/09/teaching_kids_to_program.html

6)  More math and music/noise from Evelyn Lamb:
http://blogs.scientificamerican.com/roots-of-unity/2014/12/09/missing-fundamental-telephone-integers/

7)  Some mathematical commentary on increasingly-pervasive personal genetic testing:
http://plus.maths.org/content/23-and-maths

8)  Princeton University Press has sent along this short list of some upcoming spring/summer offerings in popular math:
http://blog.press.princeton.edu/wp-content/uploads/PR/Spring15Math.pdf

9)  I'm not sure it's even possible for Fawn Nguyen to write anything that doesn't leave you with a tear in your eye before the end:
http://fawnnguyen.com/four-square-and-other-questions/

10)  Keith Devlin's latest on math learning and math learning apps:
http://tinyurl.com/o5jeas2

11)  Andrew Gelman isn't the first, and won't be the last, to write about "the fallacy of placing confidence in confidence intervals":
http://andrewgelman.com/2014/12/11/fallacy-placing-confidence-confidence-intervals/

12)  The always-hard-to-predict Vi Hart was back this week (as probably everyone knows) with a lesson on our social/collective behavior via a mathematical game, "Parable of the Polygons":
http://ncase.me/polygons/

13)  The 117th Carnival of Mathematics is out now:
http://plus.maths.org/content/carnival-mathematics-117

14)  And per usual, check out MikesMathPage to see what Mike Lawler and the boys have been up to this week:  http://mikesmathpage.wordpress.com/

....there, that should hold you through the weekend.

A Nitpick With Publishers... but a Thumbs-Up to Matt Parker!

More from the book scene....

I briefly mentioned Matt Parker's new book (sight unseen), "Things to Make and Do in the Fourth Dimension," in my recommendations for the Holidays, based on reviews I'd seen, but am now reading it myself and can give an even more enthusiastic thumbs-up! It's a joyful read (unless you despise puns, in which case stay far, far away!! ;-)). It's really the only "recreational math" book on my list -- I did recommend Ian Stewart's latest puzzle compendium volume, but puzzle books are a bit different from recreational math which is a broader and rarer category these days.  In fact, this is one of the very few books that I think could be mentioned in the same breath with Martin Gardner's recreational writings. While reading it I even found myself contemplating the slight similarities between the names, "Martin Gardner" and "Matt Parker"!
Anyway, most of you are likely familiar with stand-up comic/mathematician Parker from various YouTube appearances or elsewhere, and he brings the same lucid, lighthearted, but still instructive style to this book that he exhibits on the internet. His own infectious delight with math comes through both in the wide-ranging text and even his(?) simple hand-drawn illustrations.  The book's subtitle offers some hint as to just how wide-ranging it is: "A Mathematician's Journey Through Narcissistic Numbers, Optimal Dating Algorithms, at Least Two kinds of Infinity, and More."  As the book flap says, it's "a grand tour... both playful and sophisticated." I won't attempt a full review here (not even sure when I'll complete reading it), but simply highly commend it to your attention.

BUT... I do have a minor beef with it... or, perhaps more specifically with the publisher. This book is over 400 pages long and an inch-and-a-half thick, with an American retail price of $28.00 (and I wouldn't recommend reading it on an eBook reader, but that's me). A lot of folks who are already a tad phobic, or just naive, about math will be intimidated by the look/feel of this volume, as well as discouraged by the price. That means a lot of people who could benefit from reading it, and who it is partly intended for, won't purchase it... which is a shame... also means lost sales/profits for the publisher. With slightly smaller print, less white space, maybe thinner paper, and perhaps even a softcover, this volume could've been brought in well under 400 pgs. and at a lower price... and, been less imposing to readers. (I don't know if the British edition is any different from the American edition.) Even the title (probably meant to be intriguing) I suspect is a bit imposing, abstract, and maybe overly long to many, and could've been better chosen.

Anyway, I mention all this because I've seen several examples in the last couple years where a book's sales might've improved simply with a little more attention paid to certain physical elements of the volume, and greater consideration of the target audience -- and the goal should be to get these books into as many hands as possible... or at least not to scare off any more readers than needed. Matt has his own wide following, so those folks are an automatic audience, but I'm interested to see a book like this swept up by readers who have never heard of Matt Parker, or who usually avoid math books. (If I'm wrong here and the book's final features/format were actually the result of massive test-marketing and research than I'll be happy to hear about it.)
Might add, as a side-note, that I've long thought Princeton University Press (not Matt's publisher) is a publisher that generally does a great job with the physical presentation of their popular math books... maybe they've been at it longer, or specialize in it to some degree, but kudos to them for whatever the reason.
Well, I need to get back to reading Matt's volume; some reviews say the second half is even better than the first! 

[And now that I've finished reading it, I've added another short blurb about it HERE.]

First Potpourri of December

Dig in....

1)  For the puzzle-minded, John Allen Paulos wrote up this clever one last weekend:
http://tinyurl.com/kungkts

2)   Evelyn Lamb experiences "existential angst" over music and integers... and that's a fascinating thing for the rest of us (but what would Sartre think? ;-):
http://blogs.scientificamerican.com/roots-of-unity/2014/11/30/the-saddest-thing-i-know-about-the-integers/

3)  In praise of Inquiry-based Learning (IBL) (h/t to Patrick Honner for pointing out this AMS piece):
http://tinyurl.com/p4stnh8

4)   Laura at "Math For Grownups" wants to interview people about how they use math in their jobs/careers:
http://www.mathforgrownups.com/let-me-interview-you-for-a-math-at-work-monday-post/

5)  Matt Parker is excited about the Stern-Brocot sequence. See why, via Numberphile:
https://www.youtube.com/watch?v=DpwUVExX27E&feature=youtu.be

6)  Someone (I lost track of who) tweeted a link this week to this relatively new site that looks interesting (for sparking mathematical thought/ideas):
http://maththunks.weebly.com/

7)  Alexander Bogomolny reviewed "The Best Writing On Mathematics 2014" here:
http://tinyurl.com/p28acrz

8)  The fascinating case of a misprint in a 1970 math paper that gets Brian Hayes investigating:
http://bit-player.org/2014/four-fifths-a-fifth

9)  Not even exactly sure why, but a basic piece on prime numbers made it into the "Business Insider" yesterday:
http://www.businessinsider.com/prime-number-unsolved-problems-2014-12

10)  Per usual, you can check out MikesMathPage to see what Mike Lawler & the boys have been up to this week:  http://mikesmathpage.wordpress.com/
Since we're approaching gift-giving time, you might want to start with Mike's positive review of a recent new math board game from our fellow bloggers over at Math For Love:
http://tinyurl.com/pc6hxcu

11)  And lastly, I'm still curious (over at Math-Frolic) if anyone knows who "Andy Naughton" is and how did he end up reading minds? ;-) :
http://math-frolic.blogspot.com/2014/12/deja-vu-revisiting-flash-mind-reader.html

Have a good weekend all!....

Wrapping Up Books...

Holiday suggestions....

I didn't believe 2014 could be as banner-a-year for popular math books as 2013 was, and, I don't believe it has been... but, still a dang good year!

Back in June, I predicted Jordan Ellenberg's "How Not To Be Wrong" would end up as my favorite book of the year, and that's proven true, though with a bit of semi-stretching (I'll get to later) it has a strong competitor.  I've never seen a bad review of Ellenberg's book. If you haven't read it, get it! If you have read it, read it again!

Meanwhile, Alex Bellos gave us another fine effort this year with his "The Grapes of Math" (American title)... another fun, enjoyable, instructive read from Alex.

The above are the two main new volumes I recommend Xmas wrapping for a general readership of mathy stuff.

For the puzzle-lover on your list I don't think you can do much better than Ian Stewart's recent "Professor Stewart's Casebook of Mathematical Mysteries." Stewart's previous puzzle compendiums are just as good though, if you don't need to have his latest volume.
Also, worth noting that one of my favorite Stewart books, "Visions of Infinity," is newly-out in paperback (not a 2014 volume, but still worth suggesting).

Three more 2014 volumes I don't mind recommending to narrower audiences are: 1) "Mathematics and the Real World" by Zvi Artstein -- a volume I have some qualms about, but ultimately liked the overview it gave of math history  2) "Four Lives: A Celebration of Raymond Smullyan" from Jason Rosenhouse -- a volume suited primarily for Raymond Smullyan fans.  I often don't see Rosenhouse's volumes distributed very well -- honestly, I believe he needs a new agent or publisher(!), because he's one of the best, most consistent math writers out there (and I say that as someone who doesn't always agree with him, but always finds his arguments thoughtful and well-stated -- for this particular volume though, I'll note, he is just editor). Finally, 3) a volume I'll recommend without having finished it yet, is the latest "The Best Writing On Mathematics 2014" ed. by Mircea Pitici -- each edition of this series has been better than the one before, and I think that trend continues in this rendition, which seems full of interesting stuff. I'm always impressed with Pitici's diversity of choices, even though there are always ones whose inclusion I don't quite understand. Anthologies are typically a mixed bag, but hopefully the selections you don't care for will be outweighed by the number and quality of those you do enjoy.
A couple of quick mentions to two volumes I haven't read, but have seen consistently good reports on: 1) Tim Chartier's "Math Bytes," and 2) Matt Parker's (British book) "Things To Make and Do In the Fourth Dimension." [I've now written a bit more about Parker's volume HERE and HERE.]

One volume to throw in simply because it may be a hit for the holidays is "The Mathematics Devotional" from Clifford Pickover. Personally, I'll wait 'til there's a soft-cover version, if I purchase it at all (may eventually buy it simply as a source for more "Sunday Reflections" over at Math-Frolic). As much as I love Dr. Pickover's earlier popular math output, I've not been a fan of the recent, more 'formulaic' and visually-gaudy series from him -- just my personal preference. Having said that, anything that gets math/science into the hands of more people I'm all for, and his books have succeeded at that (or at least they're dwelling on a lot of home shelves and coffee tables). So give it a look if it suits your taste, but I can't honestly recommend this pithy, glossy volume for those on limited budgets, who need more bang for the buck. Also, know that a "Physics Devotional" is in the works.

Reaching back to 2013. A couple of wonderful books from that year, are now out in paperback: "Love and Math" by ever-inspiring Ed Frenkel, and "The Simpsons and Their Mathematical Secrets" from Simon Singh (one of the most fun math reads ever). Both must-reads for the math-enthused, if there's anyone left who has missed them.

Finally, here is my 2014-stretch (alluded to above): Richard Elwes put out two 2013 books that are fantastic (but poorly distributed in the U.S.): "Math In 100 Key Breakthroughs" (a GREAT reference source) and "Chaotic Fishponds and Mirror Universes" an informative, wide-ranging (ill-titled) book that I didn't acquire until 2014, and enjoyed almost as much as the Ellenberg volume -- it's hard for me to even recommend one over the other, but in-the-end, Ellenberg is set apart from all competitors by his witty, fanciful style, so rare (indeed difficult) in a popular math book, so I give him the nod, but do VERY highly recommend Elwes' book.

Anyway, these are some of the book stand-outs for a general audience from my view, but there were LOTS of other popular math offerings in 2014. If you had a favorite you wish to make sure readers consider, feel free to mention it in the comments. And let's see what 2015 brings our way (among other things a new biography of Martin Gardner is on the horizon).