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:

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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).

How Not To GO Wrong...

…Buy THIS book: "How Not To Be Wrong" by Jordan Ellenberg


"The lessons of mathematics are simple ones and there are no numbers in them: that there is structure in the world; that we can hope to understand some of it and not just gape at what our senses present to us; that our intuition is stronger with a formal exoskeleton than without one. And that mathematical certainty is one thing, the softer convictions we find attached to us in everyday life another, and we should keep track of the difference if we can."  -- Jordan Ellenberg


To see it on a bookshelf Jordan Ellenberg's new volume looks like a slim, modest read… but, in fact, it's a dense, almost 450-page, surprisingly rich, entertaining, and jaunty math volume. And I'll cut to the chase to say that even though the year is only half over, I won't be surprised if this turns out to be my FAVORITE math book for all of 2014! It will certainly be in the top 2 or 3.

The five parts of Ellenberg's book, are entitled:

Linearity
Inference
Expectation
Regression
Existence

You might infer from that, that it is a volume bent toward statistical, probabilistic, and 'big data' related topics. You'd be right. This is a math genre that has gained great currency in the last few years -- so much so that I'm a bit weary of reading popular (and somewhat redundant) treatments of these subjects. BUT... Ellenberg's text is amazingly fresh, current, and fun to read! So much so, that I initially wondered how much of the final product was Ellenberg's own voice, and how much possibly molded by an expert editor -- but Ellenberg has written a novel before and has a degree in creative writing… moreover, Cathy O'Neil (who wrote a great review of this book, and knows Ellenberg personally) assures us that the book "reads just like Jordan talks" -- so there you have it!

Having said all that, I'll caution that the book, while written for a general audience, does require some minimal interest in, and aptitude, for mathematical discussion if it is to be appreciated/enjoyed. I'll reiterate what I've said before that the only math book I've seen in recent years that I think can truly draw in the naive math-phobic or math-inept is Steven Strogatz's 2012 "The Joy of X." For anyone though who has 'graduated' from Strogatz's treatment, this is a great follow-up, and concentrated on very timely topics, while yet covering a surprising amount of ground.

Let me tell you just how fresh this book is: there is not one chapter, not one section, nor paragraph, or line or word about the Monty Hall problem! Don't get me wrong, I love the Monty Hall problem, and believe it is one of the most interesting, instructive math tales around, but it has become an obligatory, rite-of-passage entry into every popular math book around (especially any involving probability)… Ellenberg just skips it... and I think that's great!  In fact, even when Ellenberg touches upon subjects that are fairly routine in such volumes, he gives them his own engaging spin, his own re-creation, that makes them fresh again. It is a remarkable achievement in exposition. Coming across topics like Monty Hall in other books gives me a sort of yawning 'oh, here we go again' gut reaction… I NEVER had that response reading Ellenberg.

The very first example he uses in the book is a fascinating real-life one I was unfamiliar with, dealing with bullet holes in missing World War II planes: essentially, the question arose how to more efficiently aluminum-plate war-planes to resist being shot down -- too little plating and the planes were more vulnerable; too much and the added weight made them less fast and maneuverable. It was noted that returning planes had the most bullet holes in the fuselage and a smaller number in the engines… implying perhaps that the fuselage needed more protection… but NO, it took statistician Abraham Wald to deduce that the planes getting hit in the fuselage were actually able to return to base, and it was planes being hit in the engines that weren't even returning successfully (to be a part of the sample); i.e. it was the engine compartments that needed more shielding.
The book is full of such clever, sometimes counter-intuitive examples. And throughout, a major theme of Ellenberg's is that mathematics is not so much computation and mechanical procedures as it is the careful application of common sense to pattern and structure.

I'll just list some of the prominent popular subjects he touches upon through these pages:

-- the Laffer Curve (famous, laughable cornerstone of Reaganomics)
-- obesity research
-- prime numbers
-- "the Baltimore stockbroker" -- this is a famous tale (though I've never seen it given this name before) explaining a system for sending out 10 newsletters successfully predicting some stock market movement, and then (with your 100% batting ave.) sending out an 11th letter soliciting new customers for your prescient services.
-- a famous 2009 fMRI study of a dead salmon, that made the rounds (yes, a dead fish scanned by fMRI)
-- the "hot hand" notion in basketball
-- the "crisis" in scientific replication, and John Ioannidis' work
-- the "crappy algorithms" that are now part of business 'Big Data'
-- state lotteries
-- correlation vs. causation and the "slippery" slope between them
-- the nature of "genius" in mathematics
-- opinion polling and elections

And those are just some of the more interesting (popular) topics along the way, while in-between Ellenberg teaches a little calculus, statistics, Bayesian analysis, non-Euclidian geometry, game theory, and an excellent section on regression analysis (although this may also be, for many, the most boring or tedious part of the volume). Somehow Ellenberg manages to go into more depth than others often do, yet remain clear and not too technical. Also mixed in here, some reflective history as well, as Ellenberg relates how the "territoriality" of mathematics has expanded over time, from rather limited areas, to domains where it didn't even seem applicable at one time or another.

And beyond the more usual mathematicians, there is mention of a sundry cast of characters: Daniel Ellsberg, Thomas Picketty, B.F. Skinner, David Foster Wallace, Antonin Scalia, all make appearances in these pages.

Meanwhile, throughout, Ellenberg lobs in his droll humor along the way… rare (and wonderful) to find in a math book. For some reason the simple line that most cracked me up came when he was reporting on Bertrand Russell's famous communique to philosopher Gottlob Frege regarding the latter's magnum opus on math's logical foundations. Russell, almost casually, mentions a single paradox (now famously known as "Russell's Paradox") he has found in Frege's account of set theory , which essentially undid all Frege's hard work. Ellenberg writes, "Despite the respectful tone ('I have encountered a difficulty,' not 'Hi, I've just borked your life's work'), Frege understood at once what Russell's paradox meant for his version of set theory" -- something about even imagining the properly-British Lord Bertrand Russell writing, 'Hi, I've just borked your life's work,' sent me into a cascade of chuckles -- I'll just bet Ellenberg too formed a big Cheshire grin on his countenance when he wrote those words ;-) Anyway, there are many such grin-producing lines.

Another lovely aspect of the book are the hand-drawn illustrations throughout done by Ellenberg himself. In a day of easily-done, precisely-composed graphs and mathematical illustrations, Ellenberg's hand-crafted jottings add another surprisingly delightful element of 'freshness' to these pages (I've seen books where hand-drawn illustrations didn't work well at all, but here they do!).

This book (and its author) is getting widespread coverage right now (#19 on one bestseller list), and sometimes when that happens there's a lot of hype and PR involved… in this instance it's all well-deserved. Cathy O'Neil writes of Jordan having "an infectious positivity," and that is indeed one of the unexpected benefits and appeals of this volume.
Just a splendid book (Fields Medalist Timothy Gowers says of it "destined to be a classic"), especially for the first time out-of-the-box… can't imagine what Jordan will do for an encore… or, if he even needs an encore after this bravura performance!

[Additionally, an excellent review of Ellenberg's book from Alex Bellos here:
http://tinyurl.com/pbsrxl2 ]