...a companion blog to "Math-Frolic," specifically for interviews, book reviews, weekly-linkfests, and longer posts or commentary than usually found at the Math-Frolic site.

"Mathematics, rightly viewed, possesses not only truth, but supreme beauty – a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show." ---Bertrand Russell (1907) Rob Gluck

"I have come to believe, though very reluctantly, that it [mathematics] consists of tautologies. I fear that, to a mind of sufficient intellectual power, the whole of mathematics would appear trivial, as trivial as the statement that a four-legged animal is an animal." ---Bertrand Russell (1957)

******************************************************************** Rob Gluck

Friday, July 25, 2014

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:

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:

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:

4)  Vi Hart explains transcendental numbers, the number line… and darts, as only she can:
...and h/t to Evelyn Lamb for pointing out this arXiv contribution from Vi Hart (and Henry Segerman) on the symmetry of quaternions:
(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):

6)  Another teacher reports their experience flipping the classroom (geometry):

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:

8)  A little bit of Boolean algebra history:

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

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

11)  In honor of the Martin Gardner centennial this year, interviews with Martin Gardner (accessible online); always good stuff:
In case you missed it, you can also visit the little carnival game of Martin Gardner's I offered at Math-Frolic this week:

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:

13)  A Forbes writer summarizes Keith Devlin's view of the future of math (good overview!):

14)  MathMunch honors Bill Thurston's creative math mind in their latest post:

15)  Of airplane crashes and statistics:

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):
(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, July 18, 2014

Friday Potpourri

 A smallish bowl of math ghoulash from this week:

1)  Ed Frenkel's recent public talk at Oxford (GOOD stuff):

2)  The Fourier Transform (from The Guardian):

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:

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 ;-):

6) Mike Lawler and the boys teach some combinatorics:

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):

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):

Sunday, July 13, 2014

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:


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


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.


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. 

[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.



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, July 11, 2014

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:

2)  From The Guardian, the statistics of medical tests:

3)  The Pigeonhole Principle made it into some popular press this week:

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):
…a little more background on this speech here:  http://tinyurl.com/nrf3rvk

5)  Fascinating NY Times portrait of billionaire mathematician/philanthropist James Simons:

6)  Mathematicians and the NSA…  discussion in AMS Notices:

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


8)  Evelyn Lamb writes about infinity here:

And, if you missed it, my own prior posting right here at MathTango also dealt with infinity... and award-winning writer David Foster Wallace:

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:

Sunday, July 6, 2014

Infinity and Angst (David Foster Wallace)

I've moved this Sunday reflection, which grew longer-than-usual, to here from its customary spot at Math-Frolic:
"Here is a quotation from G.K. Chesterton: 'Poets do not go mad but chess players do. Mathematicians go mad, and cashiers; but creative artists very seldom. I am not attacking logic: I only say that this danger does lie in logic, not in imagination.' Here also is a snippet from the flap copy for a recent pop bio of Cantor: 'In the late nineteenth century, an extraordinary mathematician languished in an asylum… The closer he came to the answers he sought, the further away they seemed. Eventually it drove him mad, as it had mathematicians before him.'
"The cases of great mathematicians with mental illness have enormous resonance for modern pop writers and filmmakers. This has to do mostly with the writers'/directors' own prejudices and receptivities, which in turn are functions of what you could call our era's particular archetypal template….

"Chesterton above is wrong in one respect. Or at least imprecise. The danger he's trying to name is not logic. Logic is just a method, and methods can't unhinge people. What Chesterton's really trying to talk about is one of logic's main characteristics -- and mathematics'.  Abstractness.  Abstraction."

-- From "Everything and More" by David Foster Wallace

 I've lately been re-reading parts of David Foster Wallace's "Everything and More: A Compact History of Infinity."
I don't read fiction, but that doesn't stop me from sometimes being intrigued by fiction writers, or in this instance one who additionally wrote non-fiction. And I have other reasons to be fascinated by Wallace:
He spent much of his childhood in Champaign/Urbana, Illinois, very near my own hometown, and died tragically in 2008 while teaching at my alma mater, Pomona College, in Claremont, California. In-between his brain seemed to gallop effortlessly all over the place.
Of course it's not his widely-acclaimed, award-winning fiction that interests me; it's his, slightly-lesser-known, non-fiction. That a person of the humanities with an English degree, who poured himself into long, involved, complex novels and wordplay, was capable of also writing about deep mathematics is fascinating. It's a little less strange given that Wallace did deeply study philosophy, logic, and mathematics at the college level... but still amazing to me that "Everything and More" could be born in the same mind that authored "Infinite Jest"(…interesting that "infinite" makes its way into this title as well).

Wallace called his 300+ page volume ("Everything and More") on infinity a "booklet," and he no doubt genuinely considered it but an introduction to the whole subject; scratching the surface of a topic that so often baffles undergraduates, even leading to incredulity or heated arguments, amongst young math majors. Yet the book is a meticulous parsing of the subject as virtually never found in a popular work. In fact, I suspect it falls into that category of 'widely-bought, least-read books ever,' with a large percentage of buyers never completing it; purchasing it solely based on the author's reputation, and then abandoning it after the first 30-50 pages.

The book received a number of favorable reviews upon release, but several professional mathematicians also harshly critiqued it, finding it peppered with technical errors… I s'pose that I, as a non-professional, tend to be more forgiving, spellbound as I am by Wallace's ability to even approach these strenuous subjects innovatively… not that that justifies inaccuracies, but just that my joy with the volume stems not simply from the mathematics/philosophy entailed, so much as from the sheer audacity of a renowned novelist crossing boundaries to tackle such matters. I can't even imagine who this book was intended for… surely not the same audience who loved Wallace's fiction; but nor for professional mathematicians who would find faults in it. And not just for me, an audience of one ;-) Somewhere out there must be other "mees," I guess, who stand almost in awe of what Wallace accomplished: the mix of language and math, of thought and meta-thought, of narrative and cerebral-wrestling, while attempting to communicate it all to a mass(?) audience. As I wrote once before, this volume is "written in an informal and conversational tone about ideas that are utterly UN-informal and UN-conversational (...and the multitudinous footnotes are virtually as fascinating as the main text)."
And Wallace's prose isn't just deep, but in some ways, prescient... anticipating something we now commonly hear about high school math education, here's what he said in 2003 about college-level math:
"The trouble with college math classes -- which classes consist almost entirely in the rhythmic ingestion and regurgitation of abstract information, and are paced in such a way as to maximize this reciprocal data-flow -- is that their sheer surface-level difficulty can fool us into thinking we really know something when all we really 'know' is abstract formulas and rules for their deployment. Rarely do math classes ever tell us whether a certain formula is truly significant, or why, or where it came from, or what was at stake. There's clearly a difference between being able to use a formula correctly and really knowing how to solve a problem, knowing why a problem is an actual mathematical problem and not just an exercise."
This remains one of the quirkiest, both convoluted and semi-profound, volumes on my math bookshelf, from one of the quirkiest, most imaginative minds America has produced. Possibly there is some irony, some stinging irony, that Wallace, a long-time sufferer of depression, died tragically at his own hands, via hanging at the young, fertile age of 46... possibly even suffering mental demons not altogether dissimilar from Georg Cantor, a century earlier; died perhaps an example of the same stereotype or "archetypal template" he points to in the opening passage above ("the closer he came to the answers he sought, the further away they seemed").

One of the endorsement blurbs on the back of my copy of the volume says, "...David Foster Wallace is the perfect parachute buddy for a free fall into the mathematical and metaphysical abyss that is infinity." I think "abyss" may be too strong a word, but I do like the imagery of 'freefalling' into infinity... with an English major no less!
This volume won't suit a lot of people's taste, but reading it more as a treatise on human thought/genius and psychology, than a math treatise, I return to it... in wonderment and reflection... each year.

Friday, July 4, 2014

Friday Potpourri

Another week's mix of mathy selections:

1)  Evelyn Lamb reviews "Really Big Numbers" by Richard Schwartz (children's book):

2)  You undoubtedly heard this week of Facebook's mass study in emotion-manipulation; be sure you've read Jordan Ellenberg's take:
And several more links re: the Facebook study here:

3)  A little introduction to the quaternions:

4)  Another teacher weighs in on the new volume, "Playing With Math," from Sue VanHattum:

5)  Doing calculus employing masses instead of area:

6)  Statistics as an underpinning of science and society:
But then, this non-confidence-instilling piece on confidence intervals:

7)  I blog-posted this one but it's so much fun I'll re-link to the "Painter's Paradox" of Gabriel's Horn, in case you missed it:

8) Look Ma, no numbers!... a pictorial geomagic square from the ever-inventive Lee Sallows (via Futility Closet):

9) Anyone know if a P vs. NP proof that appeared this week is being taken seriously??? I'm certainly in no position to judge, though just the fact that it concludes that P = NP, and does so in essentially just 3 pages, gives me cause for doubt:

10) And just up from Sol Lederman another new "Inspired By Math" podcast, with Richard Rusczyk and a focus on math competitions:

11)  Lastly, my own take on Alex Bellos' latest book, "The Grapes of Math":