'nother Week, 'nother Potpourri

I collected these, so you wouldn't have to ;-):

1)  "Reflections on Paul Erdös" from AMS in this his centenary year:
http://www.ams.org/notices/201502/rnoti-p121.pdf

2)   A film made based on the Twin Prime conjecture work of Subway sandwich maker, and mathematician ;-) Yitang Zhang:
http://aperiodical.com/2015/01/counting-from-infinity-a-film-about-yitang-zhang/

http://www.zalafilms.com/films/countingindex.html

also, another wonderful popular press piece (from the New Yorker) on the 59-year-old, sudden-celebrity Dr. Zhang and his work here:
http://www.newyorker.com/magazine/2015/02/02/pursuit-beauty

3)  Still another commentary on the roiling that has followed Mochizuki's claimed ABC conjecture proof:
http://tinyurl.com/ouwbqxb

...and Mark Chu-Carroll attempts to explain the ABC conjecture to the rest of us... before concluding that "...mathematicians are crazy people!" ;-):
http://tinyurl.com/nd3scqd

4)  Here's some fun with "deflategate," if you followed the sports story of the New England Patriots' deflated balls ;-):
http://flowingdata.com/2015/01/28/questionable-fumble-statistics-for-deflate-gate/

5)  Need an introductory post on Cantor and infinity for some young person? Nice, longish one here (gets heavier as it goes along), including several videos:
http://www.science4all.org/le-nguyen-hoang/cantors-infinite/

6)  A really fun read, newly-posted at AMS blogs, from Evelyn Lamb, on some different aspects of 'sucking at math' (with links to A.K. Whitney's writings on "Mathochism" over at Medium that I need to further check out):
http://blogs.ams.org/blogonmathblogs/#sthash.Q9DMgkiM.wLJHa8Yr.dpbs

7)  A couple of tweeted lines this week from Steven Strogatz (who is doing one flipped classroom this term) that just seem worth repeating:

"The students are so alive and engaged in my flipped class (nonlinear dynamics & chaos)."
"My other class this term is not flipped. Feels flat, almost inhumane..."

8)  And an article on math educator Jo Boaler here:
http://news.stanford.edu/news/2015/january/math-learning-boaler-012915.html 

9)  The increasing tension between U.S. mathematicians and the NSA gets some new coverage from Science Magazine:
http://www.sciencemag.org/content/347/6221/495.full.pdf

10)  Meanwhile, for your funnybone, SolveMyMaths posted some Dave Gorman comedy about perfect, friendly, and sociable numbers:
http://solvemymaths.com/2015/01/27/perfect-numbers/

11)  As always, MikesMathPage: http://mikesmathpage.wordpress.com/


...NEW feature! (potpourri bonus): Last week's grab-bag ended with a side-note, recommending David Pogue's new "Pogue's Basics" book. I may now try to incorporate a "potpourri BONUS" each week, pointing to 1 or 2 non-math links I simply found especially interesting during the week.  Here are this week's selections:

a)  One of the most jaw-dropping science stories I've heard (out of SO MANY from NPR), about blindness, echolocation, expectations (the story of Daniel Kish)... an hour-long episode; if you haven't heard it try to make time for it and see if you find it as flabbergasting as I did:
http://www.npr.org/programs/invisibilia/378577902/how-to-become-batman

b) ...I could probably fill these "bonuses" with just NPR programs!! Anyway, the 2nd selection is the first (21-min.) segment from last week's "This American Life" -- perhaps the most phenomenal (almost bizarre) story I've ever heard of a misogynist internet troll experiencing a change-of-heart:
http://tinyurl.com/pkx4mq5

The Friday Wrap-up

This Week's Grab-bag:

1)  An overview of the recent JMM meetings in San Antonio from Jordan Ellenberg: 
http://tinyurl.com/oyh9lq4

2)  This is a bit involved, but if set theory, logic, and paradoxes are your things than this post from Matt Baker may keep you occupied for awhile:
http://tinyurl.com/pw24nxg

3)  Another convert/enthusiast to the "flipped classroom":
http://fliplearnshare.blogspot.com/2015/01/in-love-with-flipping-again.html

meanwhile, Robert Talbert shared some of his evolving thoughts about the flipped classroom here:
http://tinyurl.com/nezn3h4

4)  A long statistical read from Deborah Mayo on questionable research practices (using a specific case as an example) and statistical power analysis:
http://tinyurl.com/mav9szg

also this week, Deborah re-ran a 2013 "statistical dirty laundry" post (more on research methodology than technical statistics):
http://errorstatistics.com/2015/01/21/some-statistical-dirty-laundry-2/

5)  Presh Talwalkar shows multiple solutions to a geometric puzzle he had previously posed:
http://tinyurl.com/n8mxdy3

6)  Interesting little discussion of math grading (and a Robert Talbert approach):
https://symmetricblog.wordpress.com/2015/01/21/talbert-was-right-i-was-wrong/

7)  Fun with "Plateau's Laws," surfaces, and bubbles:
http://thatsmaths.com/2015/01/22/plateaus-problem-and-double-bubbles/

8) And having fun with sequences here:
http://tinyurl.com/mf4tvv2

9)   A little overview of the Polymath Project from Peter Cameron:
https://cameroncounts.wordpress.com/2015/01/22/polymath/

10)   Patrick Honner tells how we can (and should) learn from technology failures, in this recently-uploaded YouTube video:
https://www.youtube.com/watch?v=tRT3QIt7w20

11)  MikesMathPage, always worth checking out:  http://mikesmathpage.wordpress.com/


...lastly,  a book-note: usually I just recommend popular math books here, but once-in-awhile come across a book I like so much or believe so useful I want to be sure readers are aware of it. Recently out, "Pogue's Basics," is one such volume. David Pogue has long been a favorite tech writer and this new volume of helpful hints -- what he terms "essential tips and shortcuts that no one bothers to tell you" -- is just a great little compilation of handy computer tips. It covers both Macs and Windows (not other systems directly), and while computer pros may not learn too much from it, I imagine most average computer users, and certainly newbies, will gain plenty of pointers. I turned down page corners, as I quickly read through it, to mark all the tips I wanted to go back and try out, and ended up with around 40 dog-eared corners.

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