So You Want Some Math History...

Recently finished a quickread of history professor Amir Alexander's "Infinitesimal," which has received plenty of rave reviews, a few of which I'll reference below, (as I won't fully review it here):

http://tinyurl.com/pe2dd7w
http://tinyurl.com/nopb85a
http://tinyurl.com/mxchx6h

For whatever reason, I've never been much fascinated with math history (at least not pre-19th century history). This book recounts the sometimes surprisingly controversial disputes over the early history of infinitesimals in mathematics. It ends right before the part that I would've found interesting… the Newton - Leibniz rivalry and history of infinitesimals and limits since then (David Berlinski previously wrote a popular book, "A Tour of the Calculus," covering that history which I find more intriguing). Thus, though Alexander's writing is good, and the narrative sometimes dramatic, it wasn't subject matter that particularly grabbed me. But if history is among your foci this volume comes very highly recommended and you should definitely give it a look. It certainly captures events and conflicts that most people will be unacquainted with.

A few days back I briefly mentioned "Mathematics and the Real World" by Zvi Artstein… a read, which once again, because of its older historical context started off slowly for me. However, the last half of the book, moving into more modern math history, improved considerably. The writing is still somewhat stilted, but I did enjoy more of the material being covered from chapter 5 (an introduction to randomness) on, and especially the last few chapters. If you're looking for a more lively narrative and interesting story-line than "Infinitesimal" will better suit your taste, but if you want a broader sweep of math history I do recommend the Artstein book, even though parts of it are a bit of a slog. I'm not sure it's all that helpful, but the most extensive review of the book I've seen is here:
http://www.euro-math-soc.eu/review/mathematics-and-real-world

Recently on social media, Steven Strogatz and currently Evelyn Lamb have talked about teaching math history courses… don't know if this is a new trend, or such courses have long been around. In any event, both these works could be useful to an instructor of such a course -- the Alexander book, while perhaps more engaging, only deals with a sliver of history, while Artstein chronologically covers a wider swath and range of history, and is, I think, more useful. An older, more concise, historical overview of mathematics I've previously enjoyed, again comes from Berlinski, "Infinite Ascent."

By the way, I was not previously familiar with the name "Zvi Artstein," but he certainly appears to be a well-established, well-credentialed professional Israeli mathematician -- I mention this only to indicate he is not some crackpot opinionated writer, because of what follows:

Artstein finishes his volume with a 30-page, almost polemical, chapter on math education that is quite an assault on Dr. Keith Devlin's well-distributed viewpoint regarding "mathematical thinking." (He never mentions Devlin by name, but seems to clearly be directing much of his commentary toward Devlin's writings.) I've seen others sometimes voice arguments similar to Artstein's, but not with the same tenacity and self-assuredness of Artstein. I think Artstein makes some valid points along the way… but then too, I don't believe in any 'one-size-fits-all' solution to teaching youngsters math. He seems to favor a form of teaching first proposed by Louis Bénézet in the earlier 1900's that never caught on widely.
Anyway, Artstein asserts, "The truth is, there is no such thing as mathematical thinking." He argues there are only two types of thinking ('comparative' and 'creative,') which apply to most all disciplines, not just math, and that they can't be taught, but can only be learned through experience and practice!
He goes so far as to say that, "Presenting 'mathematical thinking' as a necessity, or as beneficial to life beyond mathematics and its applications, is likely to cause harm." I won't try to fully explain Artstein's viewpoint (because I'm afraid I would misstate it in some manner), but he does offer many examples, and it makes for an interesting, if oddly contentious, final chapter (in fact, I suspect he could write a whole 'nuther controversial book based on the ideas expressed in this chapter -- the chapter sticks out oddly from the rest of the book, though I think in his mind it was more of a natural conclusion that the book was always building towards).
So, I do recommend the Artstein offering (despite sometimes pedantic writing style, and the harsh ending), based on the second half historical discussion he delivers, and issues he will force you to think about.

On short notice, I asked Keith Devlin (via email) if he'd care to respond with any comment about Artstein's views -- I haven't heard anything back, but will add it here later if I do.


[ ==> housekeeping note: the usual Friday potpourri links here will, this week, begin appearing either late Friday or early Saturday (instead of early Friday) -- this is simply a practical change to better accommodate capture of Friday math posts that were showing up hours after my linkfest was being posted.]

Friday Grab-bag

This week's mathy selections:

1)  Been wantin' to catch up on your Babylonian math history? …well, Evelyn Lamb is right there for ya:
http://blogs.scientificamerican.com/roots-of-unity/2014/08/31/look-ma-no-zero/

2)  One of my favorites, James Grime, opened a brand-spanking new website recently (good stuff):
http://www.jamesgrime.com/

3)  Math, logic, Buddhism, and more from interview with Chris Mortensen here:
http://tinyurl.com/pdmnlp9

4)  Interesting guest post on Mathbabe this week from someone who is, ahem, a generation older than Mathbabe:
http://mathbabe.org/2014/09/03/guest-post-bring-back-the-slide-rule/

5)  Mathematics and gerrymandering:
http://www.ams.org/samplings/feature-column/fc-2014-08
(h/t to Steven Sltrogatz for this one)

6)  Statistician Andrew Gelman takes both Alan Turing and Daniel Kahneman to task:
http://tinyurl.com/mcq2wa2

7)  Mark Chu-Carroll finishes up his series on Gödel Incompleteness here:
http://www.goodmath.org/blog/2014/09/03/godel-part-4-the-payoff/

8) Back to "Mathbabe" who recounts the noisiness of student evaluations here:
http://mathbabe.org/2014/09/04/student-evaluations-very-noisy-data/

9)  I'm not sure that "sampling error" gets discussed enough, but here's a start:
http://learnandteachstatistics.wordpress.com/2014/09/04/sampling-and-non-sampling-error/

10)  Finally, probably worth noting (for any science-buff who's been living under a rock the past week) that xkcd's proprietor Randall Munroe's new book, "What If?" is now out and getting fab reviews:
http://tinyurl.com/ohkuakh

(and be sure to check out the blog "meme" I've casually pitched out to all math bloggers over at Math-Frolic...)

Robin Williams Redux... (background of a tweet)

Now for something completely different (for MathTango)…

I've written before how much I admire Cathy O'Neil's keen ability to touch on varying topics over at her blog. Despite coming from a mathematics academic background and titling her blog "Mathbabe," Cathy writes on a wide range of topics that rattle around in her head. So I'll sorta take that cue today to veer off and relate an odd, completely NON-mathy episode from my weekend…

I tweet under some different accounts, but lay low on Twitter, and neither expect nor have many of my tweets re-tweeted.  Saturday I posted a simple tweet linking to someone else's tweet about Robin Williams, which I thought was interesting, then went on about my way....

(the original tweet I was re-tweeting here): https://twitter.com/JessieJessup/status/505463065089830912/photo/1 which included this commentary:

When I returned five hours later, the tweet, to my astonishment, had taken on an incredible life of its own. By the following day the response blew me away! (eventually almost 6000 retweets). Clearly, Robin Williams is beloved, and concern over mental health issues touch a nerve for lots of folks in this country!  Most people seemed positive about the passage above, and quite sure of what it said (often, the response was along the lines of, 'YES! this needs to be said more often').

SO, here's the weird thing! -- I wasn't at all sure in my own mind, what exactly the above anonymous poster was trying to say!? I just thought it was an interesting take, but with two completely opposite interpretations possible, so am asking now for any clarification anyone may choose to offer.
Here were my two interpretations:

1) on the first quick read I thought the individual was noting how weak and inadequate our mental health system is, because here was Robin Williams, who did everything right (accessing the system) and yet stiiiiill killed himself at age 63.

BUT, upon further readings (and some of the Twitter comments) I concluded, that actually the writer was saying, just the opposite:

2) that this is an instance where the system DID WORK, because Robin DID access the system, got help, and we had him around, as a highly successful, productive individual, for decades longer than we might have IF the system had failed.

In short, I think the writer is saying that despite how things look and feel, Robin's case is more a success story than a tragedy, and needs to be viewed that way… BUT, I'm still not completely certain!??? (or maybe there's a more-nuanced in-between interpretation?).
(I should quickly add that another clearer, less ambiguous message the writer conveys is that mental illness still unfortunately carries a stigma associated with it that other long-term illnesses do not have.) 

Thoughts from others?....

Friday Wrap-up

Another week from the world of math:

1)  Article touting the role of rote memorization in early math education:
http://tinyurl.com/lj759wd

2)  Fawn Nguyen describes the beginning of her classroom school year, as perhaps only she can:
http://fawnnguyen.com/first-two-days-school/

3)  LA Times op-ed on the gender-gap in mathematics:
http://www.latimes.com/opinion/op-ed/la-oe-su-women-in-mathematics-20140826-story.html

4)  Of sheepdogs, herding, and mathematics:
http://www.bbc.com/news/science-environment-28936251

5)  For some reason I've never much cared for Sudoku but do enjoy Ken-Ken, and apparently someone finds the latter useful as a classroom tool as well:
http://www.mrlsmath.com/free-teaching-tool-kenken-classroom/ 

6)  Evelyn Lamb promotes proofs by contradiction this week at "Roots of Unity":
http://tinyurl.com/p7dogqr 

7)  Week wouldn't feel complete without linking to at least one Common Core-related post:
http://www.mathforgrownups.com/common-core-common-sense-myths-about-the-standards-part-4/

8)  And in the more-physics-than-math category I'll toss in another fascinating read from Natalie Wolchover and Quanta Magazine on recently discovered "tetra quarks" (particle physics just goes on and on and on!):
http://www.simonsfoundation.org/quanta/20140827-quark-quartet-fuels-quantum-feud/

9)  Lastly, I'll re-cite a couple of Math-Frolic posts from the end of last week for any who missed them, because I thought the short video "Prime Verite" was cool (and it involves the Freeman Dyson/Hugh Montgomery interaction I've referenced before):
http://math-frolic.blogspot.com/2014/08/short-film-about-prime-numbers.html

…and the James Tanton video from the day before the above relates to the same notion:
http://math-frolic.blogspot.com/2014/08/epiphanies.html

Another Friday Collection

From this week's wonderful world of math:

1)  Shortly, after last week's potpourri came out the 113th Carnival of Mathematics went up; if by any chance you missed it, a lot more mathy links there:
http://www.walkingrandomly.com/?p=5537

2)  I've referenced this research before, but just last week NPR covered findings that indicate winners of the Fields Medal (and other prizes) actually lowers one's future professional productivity:
http://www.npr.org/2014/08/18/341283394/how-does-winning-fields-medal-effect-mathematicians-productivity

3)  More Deborah Mayo on p-values:
http://errorstatistics.com/2014/08/17/are-p-values-error-probabilities-installment-1/

4)   A post from the always-thoughtful mathematician Robert Talbert (on goals):
http://chronicle.com/blognetwork/castingoutnines/2014/08/18/the-four-things-i-am-really-working-on-this-semester/

5)  In a 'good news' story, the first five winners of the "Breakthrough Prize" for mathematics have agreed to donate a portion of their awards to support math graduate students in the developing world:
https://breakthroughprize.org/?controller=Page&action=news&news_id=19

6)  Peter Woit reports from a conference with a focus on number theory relating to unification in physics:
http://www.math.columbia.edu/~woit/wordpress/?p=7114

7)  Much of the recent ICM conference in Seoul has now been uploaded to YouTube:
https://www.youtube.com/user/ICM2014VOD/feed
Also, for the pros out there, Terry Tao has put up a blog post covering a finding announced at the conference ("Large Gaps Between Consecutive Prime Numbers"):
http://terrytao.wordpress.com/2014/08/21/large-gaps-between-consecutive-prime-numbers/


8)  The 3 Lawler boys work out the symmetries of a cube:
https://www.youtube.com/watch?v=gN86FeO_Lmg&feature=youtu.be

9)  Nassim Taleb takes this stab at what probability is (pdf):
http://ow.ly/AAxAO 

10)  What better way to round out 10 offerings than with another excellent podcast from the "7th Avenue Project," this time with Jordan Ellenberg (make time for this if you can; it's 67 mins.):
https://soundcloud.com/7th-avenue-project/jordan-ellenberg-radio-interview-how-not-to-be-wrong 
(h/t again to Dr. Noson Yanofsky for pointing me to this)

Friday Bonanza

ICYMthem:

1)  Fun li'l anecdote about topologist Egbert Rudolf van Kampen from MathOverflow.net last week:
http://mathoverflow.net/questions/178104/a-topologist-is-not-a-mathematician-a-small-question

2)  New popular statistics (…I know, that sounds like an oxymoron! ;-)) book out from Gary Smith, "Standard Deviations":
http://tinyurl.com/poefeew
(haven't read it, but it's from a professor at my alma mater, so oughta be good)

3)  Another nice geometry puzzle from Presh Talwalkar this week:
http://tinyurl.com/m6pefvp

4)  Thoughts on problem-solving from Mike Lawler:
http://mikesmathpage.wordpress.com/2014/08/12/problem-solving/

5)  Not as much 'meat' here as I'd like, but still happy to see "recursion" (one of my favorite topics) wiggle its way into the popular press:
http://phenomena.nationalgeographic.com/2014/08/12/to-infinity-and-beyond/

6)  A little something from Vanderbilt on learning math and cognitive development:
http://news.vanderbilt.edu/2014/08/math-teaching/

7)  Again, Common Core; this time, division of fractions:
http://tinyurl.com/mnwqyu4

8)  In the math-editorial genre, Doron Zeilberger is characteristically annoyed with something… and this time it's Max Tegmark:
http://www.math.rutgers.edu/~zeilberg/Opinion138.html

9)  Meanwhile, Cathy O'Neil points us to a new information/assistance site, stemforums.com, that many may find useful:
http://tinyurl.com/m3qu2da

10)  Just notified that Alfred Posamentier and Ingmar Lehmann have a new book out, "Mathematical Curiosities" -- I feel fairly safe in predicting, it's GOOOD!:
http://tinyurl.com/o4glt93

11)  Will close out with a simple, fun Martin Gardner riddle tweeted by @WWMGT this week ;-):

"A bus leaves M for T at noon. An hour later a cyclist leaves T for M, moving slower. When bus and bike meet, which will be further from M?"


==> On a sidenote, CONGRATULATIONS to Numberphile for reaching 1 million subscribers on YouTube this past week… pretty impressive for a math site (and well-deserved)!!!
https://www.youtube.com/user/numberphile

Friday Potpourri

Another week's-worth of schtuff:

1)  Sue VanHattum has started a new "Math Mama's Gazette" for students and teachers. First issue here:
http://mathmamawrites.blogspot.com/2014/08/math-mamas-gazette-issue-number-one.html

2)  Stephen Stigler's 7 pillars of statistics:
http://blogs.sas.com/content/iml/2014/08/05/stiglers-seven-pillars-of-statistical-wisdom/

3)  The fifth run of Keith Devlin's "Introduction to Mathematical Thinking" (10-week) MOOC course begins around end of September:
https://www.coursera.org/course/maththink

4)  A follow-up to last year's claimed proof for the Millennium Prize Navier-Stokes equations (now being re-worked):
http://tinyurl.com/ohm44q9

5)  No doubt, inevitable, a "Common Core Math For Parents For Dummies" is now on the way:
http://christopherdanielson.wordpress.com/2014/08/05/news-a-new-project/

6)  Frequentist and Bayesian interpretations of statistics (side-by-side):
http://www.workinginuncertainty.co.uk/probtheory_axioms.shtml

7)  Mike Lawler offers this follow-up take to a Keith Devlin blog piece:
http://tinyurl.com/leffaq5

8)  Popular science writer Carl Zimmer ventures into the land of statistics with a piece for Nautilus on the 'null hypothesis' (interestingly placed under the heading of, "Epistemology," and using Bigfoot as a working example):
http://nautil.us/issue/16/nothingness/why-we-cant-rule-out-bigfoot 

9)  And for those who just like to play with crunched numbers, here's an oddball look at taxi-driver tipping in NY City:
http://www.businessweek.com/articles/2014-08-07/tipping-taxi-drivers-data-analysis-cant-explain-these-puzzles

10)  Lastly, not math, but I'll plug a small volume I just finished and enjoyed: "The Universe" edited by John Brockman. I assume a number of readers here, fancy, as I do, reading popular cosmology/physics books, though I find few I can wholeheartedly endorse for lay readers. This volume though is a wonderful compendium of many different thinkers ranging over a variety of topics/debates within cosmology, and very readable -- if you're familiar with the sorts of compendiums Brockman puts out, then you already know that you do or don't enjoy this sort of thing. Some of the essays are already dated a bit, but still a splendid collection, if this is an area you have some familiarity with.

Friday Potpourri

In case you missed 'em:

1)  Who doesn't love the Mandelbrot Set. As if enough hasn't already been written/presented about it on the Web, Numberphile comes along with another GREAT instructive piece:
https://www.youtube.com/watch?v=NGMRB4O922I&feature=youtu.be

2)  An extensive guide (pdf) for teaching secondary-level mathematics from a Brit educator:
http://education.lms.ac.uk/wp-content/uploads/2014/07/DMG_6_no_1_2014.pdf

3)  It's reported that reclusive math genius Gregori Perelman and his mother have left their digs in Russia for a small town in Sweden (where he can continue to turn down awards for his math work):
http://www.themoscowtimes.com/news/article/eccentric-math-genius-ditches-russia-for-sweden/504076.html

4)  Tackling math, the James Tanton way:
http://headinside.blogspot.com/2014/07/tackle-that-math-problem.html

5)   Film based on the life of Ramanujan going into production first week of August in UK:
http://tinyurl.com/klzfnzn

6)   Some student math favorites from Dan Anderson (h/t to Mike Lawler for calling attention to this):
http://blog.recursiveprocess.com/2014/07/29/my-favorite-for-the-students/

7)  Likely useful for teachers: a new "open curriculum" site for lessons supportive of Common Core (h/t to Fawn Nguyen):
http://opencurriculum.org/browse/common-core/mathematics/

8)  A brand new, and once again, great, great column this morning from Keith Devlin, concerning people's misconception of mathematics, while continuing his crusade for "mathematical thinking," and against some of the "off-the-wall" parental conclusions regarding Common Core (he gives a big hat tip to Jordan Ellenberg as well). This is required weekend reading ;-) :
http://devlinsangle.blogspot.com/2014/08/most-math-problems-do-not-have-unique.html

9) Lastly, if you want a mental workout, here is Richard Wiseman's puzzle for this Friday:
"Can you create a 10-digit number, where the first digit is how many zeros in the number, the second digit is how many 1s in the number etc. until the tenth digit which is how many 9s in the number?"

Friday Picks

A big juicy helping of potpourri this week:

1)  Quantum mechanics now violating the pigeonhole principle? It's oft-said that if you think you 'understand' quantum mechanics, then you don't, because it isn't comprehensible; and now this adds to the confusion:
https://www.sciencenews.org/blog/context/you-shouldn%E2%80%99t-try-pigeonhole-quantum-physics

2)  Long, interesting post from Tim Gowers… math over my head, but still interesting just for the glimpse it gives of how his mind operates:
http://gowers.wordpress.com/2014/07/19/mini-monomath/

3)  I'll give another plug to these folks, who are trying to make a documentary around the topic of networks and Bacon-Erdös numbers:
https://www.kickstarter.com/projects/395786474/erdos-bacon

4)  Vi Hart explains transcendental numbers, the number line… and darts, as only she can:
https://www.youtube.com/watch?v=Swm8tTLWirU&feature=youtu.be
...and h/t to Evelyn Lamb for pointing out this arXiv contribution from Vi Hart (and Henry Segerman) on the symmetry of quaternions:
http://arxiv.org/pdf/1404.6596v1.pdf
(does Vi have other publications/submissions?)
Evelyn's own take on the work, btw, is here (from May): http://tinyurl.com/lrfqd6m

5)  A survey is being conducted to study the philosophical intuitions of mathematicians "relating to the objects and methodology of mathematics." If you are a mathematician and can take time to participate please go here (they'd like as large a sample as possible, so feel free to pass on to others also):
http://goo.gl/Gu5S4E

6)  Another teacher reports their experience flipping the classroom (geometry):
http://www.siemensstemacademy.com/index.cfm?event=showBlogPost&c=&postid=2240

7)  Not for the first time, the argument that we ought drop calculus from high school curricula to make room for computer programming and statistics courses, is made:
http://www.forbes.com/sites/stevensalzberg/2014/07/17/should-we-stop-teaching-calculus-in-high-school/

8)  A little bit of Boolean algebra history:
http://www.businessinsider.com/boolean-algebra-computers-2014-7

9)  "Why Do Americans Stink At Math?" …more math education debate from the NY Times:
http://tinyurl.com/n76cl6v
Meanwhile, in the Common Core debate, a California teacher pleads with parents to come view her classroom, before making up their minds:
http://fawnnguyen.com/come-observe/

10)  Cliff Pickover's newest offering, coming out in time for Christmas, looks like a pleaser for readers here, "The Mathematics Devotional":
http://tinyurl.com/m42v7eq

11)  In honor of the Martin Gardner centennial this year, interviews with Martin Gardner (accessible online); always good stuff:
http://martin-gardner.org/Interviews.html
In case you missed it, you can also visit the little carnival game of Martin Gardner's I offered at Math-Frolic this week:
http://math-frolic.blogspot.com/2014/07/lil-game-from-martin-gardner.html

12)  There's a film based on Alan Turing's life, "The Imitation Game," on the way, and James Grime (for The Aperiodical) has it covered:
http://aperiodical.com/2014/07/an-alan-turing-expert-watches-the-the-imitation-game-trailer/

13)  A Forbes writer summarizes Keith Devlin's view of the future of math (good overview!):
http://ow.ly/zy5gS 

14)  MathMunch honors Bill Thurston's creative math mind in their latest post:
http://mathmunch.org/2014/07/23/zippergons-high-fashion-and-really-big-numbers/ 

15)  Of airplane crashes and statistics:
http://understandinguncertainty.org/another-tragic-cluster-how-surprised-should-we-be

16)  Finally, great new (90-min.) interview from "7th Avenue Project" with Stanford mathematician Persi Diaconis this week (thanks to Noson Yanofsky for passing it along to me):
http://7thavenueproject.com/post/92353298895/persi-diaconis-magic-mathematics
(includes talk of Steve Martin, magic, James Randi, Ricky Jay, stealing, and oh yeah, a smidgen of math, but really more magic)
 In fact what better way to head into the weekend than by re-visiting Steve Martin as "The Great Flydini," an act it turns out Persi, believe-it-or-not, was partially responsible (or to blame) for:

Friday Potpourri

 A smallish bowl of math ghoulash from this week:

1)  Ed Frenkel's recent public talk at Oxford (GOOD stuff):
http://podcasts.ox.ac.uk/love-and-math

2)  The Fourier Transform (from The Guardian):
http://www.theguardian.com/science/2014/jul/13/fourier-transform-maths-equations-history

3)  Another interesting (in a nerve-wracking way) puzzle from Presh Talwalkar (Zeckhauser’s Paradox):   http://ow.ly/z7Jx2

4)  John Allen Paulos talks attraction, statistics, and Bayes Theorem in the NY Times:
http://www.nytimes.com/2014/07/15/science/the-advanced-metrics-of-attraction.html?ref=science&_r=0

5)  Vi Hart, being her cool self again (when she's not doing microwave countdowns!), takes a look at reverse Cantor diagonalization -- now if she could just add a 1/2 speed button to her vids ;-):
http://ow.ly/zaEDC

6) Mike Lawler and the boys teach some combinatorics:
https://www.youtube.com/watch?v=lqbduReiKvw&feature=youtu.be

7) These two links just showing up in my Twitter feed (h/t to Alex Bogomolny and Gary Davis) on Bill Gates and Common Core (good reads):
http://t.co/sxXQOJp2un 
http://tinyurl.com/o3cybpu

8)  And it was a hugely oddball week over at Math-Frolic with talk of Richard Feynman, Sally Ride, Comcast, but little math. Maybe back-to-normal next week...


--- It feels impossible to even put up a blog post today, without acknowledging the horrific news of yesterday, a very dark day. Sympathies (...despite what little potency they have) to any/all directly affected by the tragedies... NOT proud to be part of the human race today. 
A peaceful, contemplative weekend to all... somehow.

ADDENDUM: now have to add this ;-) just appearing in my Twitter feed (h/t Sam Knight):

Jordan Ellenberg... Getting It Right

 Math-Frolic Interview #25

"Mathematics as currently practiced is a delicate interplay between monastic contemplation and blowing stuff up with dynamite."
               -- Jordan Ellenberg in "How Not To Be Wrong"

"He’s really somewhere between a mathematician and a stand-up comedian, and to be honest I don’t know which one he’s better at, although he is a deeply talented mathematician."
-- blogger Cathy O'Neil on Jordan Ellenberg

 I feel like I'm the last person on the planet to interview Jordan Ellenberg :-( so busy has he been since his book, "How Not To Be Wrong" appeared (...but better last, than never!). As a fan of his Web writing I'd requested an interview months before his book was released, and, luckily since most of my questions don't pertain specifically to the book, they still have at least some freshness, despite his recent whirlwind tour and almost over-exposure!
For any who missed it, I reviewed Dr. Ellenberg's book a month ago, and already pegged it as likely my favorite math book for all 2014. Anyway, hopefully you can learn a little bit more about the young Wisconsin professor/author/blogger from his answers below:

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

1) To start, can you tell readers how your interest in math began, and when you knew you wanted to pursue it professionally?

I was interested in math from the time I was a very small child.  (I think there’s a prevailing stereotype that all mathematicians show a special interest in math very early, but that really doesn’t seem to be the case.)  I always thought I was going to be a mathematician, but I tried other things.  Whenever I wasn’t doing math, I found I missed math.  Having this knowledge was very useful!

2) You have a book out… tell us what it's all about, and do you foresee more books in the future (you also wrote a novel about a decade ago; any more fiction in your future, as well)?

The book is called "How Not To Be Wrong" and it makes the case that mathematical thinking is naturally woven into all of our thinking.  We shouldn’t think of it as an alien habit we have to acquire, but a pre-installed part of our cognitive toolkit, which everybody can get better at using.  I hope a lot of people who don’t ordinarily buy math books will read it — but I think it has a lot to offer to people who know a lot of math as well!  I certainly learned a lot writing it.

3) From what I've read, you were a child prodigy…  how difficult was it growing up, being so far ahead of your own peer group, and do you have siblings that were similarly gifted? …also, any other mathematicians in the family?

I know lots of people who found it very difficult to be academically advanced as a kid.  I didn’t.  I didn’t find that being many grade levels ahead in math made it harder for me to relate socially to other children, and I never had any desire to leave school and go to college early.  In fact, I used to think it was a bad idea to do that; but now, as an adult, I know lots of people who started college very young and are glad they did.  My parents are both statisticians, which made things easier; they knew very well what I needed to learn and where the resources were for learning those things.

4) Up to this point in your life what math-related achievements are you most proud of?

You’re always proudest of the things that push you to learn new things and acquire new skills.  I have two big interdisciplinary projects going on, with a bunch of collaborators, a project in “stable topology” and a project in “FI-modules” — both mix number theory (my main specialty) with other subjects that I’ve had to learn a lot about as I go.  I tend to be more attracted to projects that involve things I don’t know how to do.  The book itself is like that; I’ve done a lot of popular writing  but I didn’t know what would happen when I tried to do it at length.  And I’m pleased with the results!

5) Your math blog is titled "Quomodocumque" -- if you're not too sick of answering this question ;-), want to tell readers where that title comes from and why you chose it?

It means “in whatever fashion” and is meant to suggest a sort of eclecticism.  I went to a history-of-math talk that I didn’t understand at all, but at some point there was a slide of a Latin mathematical manuscript, which contained that word, and I said to myself, well, even if I get nothing else out of this talk, that’s a hell of a word.

6) What have been some of your favorite posts over the time you've been blogging… either your own personal favorites, or ones that generated a lot of reader interest?

Thanks to counter stats I know exactly what people like to read and what they don’t.  Nobody cares about the Orioles.  Lots of people like math posts, including technical math posts.  Posts about politics and controversies within the profession are by far the most popular:  hiring practices, women in math, professional ethics, etc. 
One of my most popular posts was an argument against a paper published in Science, which I think falls victim to an interesting mathematical mistake:

http://quomodocumque.wordpress.com/2013/01/05/do-we-really-underestimate-how-much-well-change-or-absolute-value-is-not-linear/

I also like this older one, about a math puzzle said to have been used as a Google recruitment tool;

http://quomodocumque.wordpress.com/2011/01/10/the-google-puzzle-and-the-perils-of-averaging-ratios/

7) What are your favorite digital resources for assisting in teaching mathematics?

People love to make fun of it, but Wikipedia is an immensely valuable resource for mathematics.  I assume all the math pages are written by procrastinating graduate students.  They’re very good.  Of course, the more technically minded blogs, especially Terry Tao’s, do a huge amount of work at the research level, spreading news not only about new theorems but about new ideas, techniques, and strategies.  MathOverflow is wonderful for people who already know enough to ask and answer questions there.

[Well, that's interesting/unexpected to hear... I've always been impressed with Wikipedia's math pages, but was almost afraid to say so, since it seems uncouth to say out loud! :-/  thus, good to hear the confirmation.]

8) You write for Slate and various other media outlets… if someone isn't familiar with your writing, can you point to 2-3 (Web-accessible) pieces that are a good introduction to your writing?

Here’s a recent piece from the Wall Street Journal, drawn in part from the book, where I talk more than there’s room for here about the idea of genius as applied to Ramanujan, Hilbert, Minkowski, and football.

http://online.wsj.com/articles/the-wrong-way-to-treat-child-geniuses-1401484790

This old piece from the Believer, a joint review of books about the Riemann hypothesis and books about mountain climbing, is probably my favorite of the magazine pieces I’ve written.  The crazy idea of the piece is entirely due to my editor, Heidi Julavits, who somehow knew it would work. 

http://www.believermag.com/issues/200311/?read=article_ellenberg
[This is a long, but very interesting piece for those specifically interested in the Riemann Hypothesis, or who have read the books involved.]

This one’s not about math at all, but about my son and baseball.

http://www.slate.com/articles/sports/sports_nut/2013/10/kids_and_baseball_you_may_think_it_s_slow_and_boring_but_my_8_year_old_son.html

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Thanks for the responses Dr. Ellenberg! Jordan has been all over the place of late, both physically and in cyberspace, so I won't attempt to give all those links here, but Google him if the links above make you thirsty for more! And by all means buy his book -- I'm not exaggerating when I say it is one of the best pieces of mathematical writing (for a general audience) I've ever seen... amazing for a first-time effort. As I recently wrote, it made my heart feel good to walk inside a bookstore and see TWO attractive MATH books (Jordan's and Alex Bellos') sitting right up front on the bestseller table greeting people's eyes (and hopefully, with high Hawking Index scores! -- see this Ellenberg WSJ piece).

Friday Selections...

A few more mathy links for the weekend:

1)  If you missed Ed Frenkel on NPR's "Science Friday" a week ago, catch it here:
http://tinyurl.com/lsb6oxo

2)  From The Guardian, the statistics of medical tests:
http://www.bbc.com/news/magazine-28166019

3)  The Pigeonhole Principle made it into some popular press this week:
http://io9.com/why-the-pigeonhole-principle-is-one-of-maths-most-power-1601025172/+estheringlis-arkell

4)  H/T to Steven Strogatz this week for tweeting a YouTube link to a U.S. Congressman (and mathematician) talking about the prime number gap problem to the House of Representatives (the audience isn't shown, so one has to imagine the yawns):
https://www.youtube.com/watch?v=uh6GCY9i6tY&list=UUlUOx6F8GKshxGBUBLkisug&index=13
…a little more background on this speech here:  http://tinyurl.com/nrf3rvk

5)  Fascinating NY Times portrait of billionaire mathematician/philanthropist James Simons:
http://www.nytimes.com/2014/07/08/science/a-billionaire-mathematicians-life-of-ferocious-curiosity.html?_r=0

6)  Mathematicians and the NSA…  discussion in AMS Notices:
http://www.ams.org/notices/201406/rnoti-p623.pdf

7)  Patrick Honner introduces his "Grand Challenge For Mathematics Education" here:

http://mrhonner.com/archives/13828

8)  Evelyn Lamb writes about infinity here:
http://blogs.scientificamerican.com/roots-of-unity/2014/07/10/the-fault-in-our-stars-infinities/

And, if you missed it, my own prior posting right here at MathTango also dealt with infinity... and award-winning writer David Foster Wallace:
http://mathtango.blogspot.com/2014/07/infinity-and-angst-david-foster-wallace.html

9)  Finally, when you're finished with this li'l math potpourri, the brand new 112th Carnival of Mathematics beckons with plenty more good stuff ready-and-waiting for you:
http://www.theoremoftheday.org/SpecialEvents/CoM112.html