...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

Sunday, April 26, 2015

Jim Henle Serves Up Math, Piping Fresh

"The Proof and the Pudding" by Jim Henle

Back in February I called Michael Harris's "Mathematics Without Apologies" perhaps the oddest popular mathematics read I'd ever come across... and in a serious, philosophical and psychological way, it was. But now, just a couple months later I come across Jim Henle's short "The Proof and the Pudding," which is also one of the oddest math volumes I've seen, but in a jaunty, playful, and completely opposite way from Harris's.
This book juxtaposes mathematics, mostly puzzles/games and the like, with cooking recipes and tries to claim the two activities share a lot in common. I don't think he's fully convincing that "Mathematics and gastronomy are practically the same," but he is convincing that they both are fun, and thus successful in his "secret goal... to elevate the status of fun."

Henle's recipes look delicious... but no more-so than his mathematics. His joy from both pastimes nearly jumps off every tersely-composed page, and is contagious. I'm not a cook, but still feel the urge to try some of his gastronomic suggestions. Henle had my mouth watering... and my brain neurons firing from the math puzzles that are reminiscent of Martin Gardner columns. Any fan of Gardner's recreational math (and I hope that includes EVERYone who reads this blog) will enjoy the mathy excursions throughout this small volume.  As to how useful these games are I'm not sure, but as Henle quotes a colleague at one point:
"There are two kinds of mathematics: applied mathematics and mathematics that is not yet applied." ;-)

Most of Henle's math fun is connected to the paths traveled by 'bouncing dots or balls' inside rectangles or boxes, and I even wonder if Henle's book might do for these little games what Gardner's presentation of John Conway's "Game of Life" did for the obsession with that game -- on a side-note, Conway's less famous recreational creation called "Phutball" or "Philosophers' football" also gets some mention herein, along with brief forays into Sudoku variations and card tricks. None of it is overly deep or complicated; as Henle says, he is trying to show "features of mathematics" without really "doing math." And he does so in a stimulating way. Toward the end he also pays homage to both Julia Child and Gardner as inspirations for the volume.

Vanity, gluttony, parsimony, elegance, playfulness, creativity, and even ethics, are just some of the features that Henle argues are found in both cooking and mathematics. One section also talks about the importance of "messing up" in both endeavors and trying things out that fail... very reminiscent of advice I've seen from both Keith Devlin and Paul Lockhart (and perhaps others) in the past.

If I was an editor at a publishing house, and someone came to me with an idea of combining the disparate contents of this book I think I would've said, 'Thanks, but I'll pass on that'... so am very glad that the editors at Princeton University Press are far wiser than I, because this book is a charmer. Henle does such a great job of pulling you into his world and his passion, that you enjoy the alternation of topics as much as intended; probably even more-so if you yourself seriously like dabbling in the kitchen.

The volume is a fun, short romp (~160 pgs), but a review won't give the full flavor of it... you need to just pick it up and begin reading on your own to get sucked into Henle's idiosyncratic delights. And how often do you get to salivate while reading a math book?! You will here. Try not to drool on the pages.

Friday, April 24, 2015

Weekly Potpourri

Lest you missed any of these:

1)  Hmmm... following the viral success of the 'Singapore problem' saw lots of folks putting up puzzles this week of various sorts. Will only mention a few:
Futility Closet ran 3 humdinger brain twisters last weekend:
and then also posted this lovely "quickie" the next day:

the io9 site conjured up an old classic puzzle:

Mike Lawler brought home a good discussion problem for youngsters from the Wash. DC. MathFest (among his many weekly offerings):

and from Presh Talwalkar this one (with some now-familiar names):

Christian Perfect at The Aperiodical also goes over a lot of puzzle ground, including throwing in some other classics from recent times:

...anyway, I like the name "Cheryl" but if I don't hear it again for awhile, well that'll be just fine with me!! ;-)
Also from  Mike Lawler...  I think this NCTM-related post of his from the week ought be read by EVERYone, simply for all the great links he provides in it (including some more problems):

2) moving on,  a video interview with Devlin... Keith Devlin (mostly about his Stanford MOOC)... while some are increasingly negative or pessimistic about the future of MOOCs, Keith continues to tout their value... very worthwhile:

3)  Here was one teacher's wrap-up of the recent NCTM conference:

4)  Aeon has offered a series of essays, from an odd mix of folks, on the mystery of mathematics, of which I think Scott Aaronson's is the best:

  "Mathical" children's math book winners were announced last weekend:

6)  Ian Stewart and Steven Strogatz received the 2015 Lewis Thomas Prize for Writing about Science
(you can start at about the 10-minute point if you want to skip the introductory stuff)

7)  "Mathematics Rising" blog looks at the re-issue of John Horgan's "The End of Science":

8)  Heavily philosophical review (from Massimo Pigliucci) of Lee Smolin's latest discourse on mathematics:

9)  Imprecise language in the New York State Regents Exam gets the attention (a-a-a-again) of Patrick Honner:

10)  A quick note from John Cook on experiments versus reality!:
(I think this has a LOT more generalizability than Cook is referencing; i.e. it applies well beyond economics and business)

11)  Longish piece on college-level math/calculus for the life sciences:

Potpourri BONUS! (extra NON-mathematical links of interest):

 One of the laws of life is that you can never see enough nesting birds!... so a couple of addictive Web nestcams (WARNING: NSFW... because you'll get NO work done):

Allen's Hummingbirds:   http://www.bellahummingbird.com/
Barn Owls:   http://cams.allaboutbirds.org/channel/42/Barn_Owls/


Friday, April 17, 2015

Big Bag of Weekly Links

The math bits I didn't much cover at Math-Frolic this week (and quite a varied selection I must say!)...

1)  Only one topic to start a wrap-up of this week with: that Singapore logic conundrum...

Ever-instructive and smiling James Grime covers the possible answers (depending on semantics) in this video:

And among his multiple postings for the week, Mike Lawler talked through the puzzle with his two young logicians:

It's been fascinating (sometimes exasperating) reading the comments at various sites regarding this interesting, if not greatly-worded problem, which has different sticking points for different people. I wish I'd kept a list of the sites that did a good, clear job (many didn't) explaining the tricky reasoning involved.

Anyway, if by now you're bored with the Singapore problem, you're free to move on to the next level:

A-A-AND, even Fields Medalist Timothy Gowers gets into the act here:

2) moving on, +Plusmaths Magazine discusses the nature of proofs:

3)  Steven Strogatz pointed to 40 math modules developed at Cornell for middle and HS teachers & students... he calls them "fantastic"... that's enough to get MY attention:

4)  Also, this week Math Munch took all of its inspiration from Strogatz:

5)   The "Texas sharpshooter fallacy" and big data:

6)  If you missed this week's PBS Nova episode, "The Great Math Mystery," you can view it online:
One blogger reviewed it here:

7)  Some followup, from Regina Nuzzo, to one psychology journal's "cold turkey" decision to drop p-values from their pages:

8)  An interview (about books) with Freeman Dyson... only slight mathematical content, but always interesting to hear from him (h/t to Jordan Ellenberg for this one)... though disappointing he's unable to name a single math book of recent times as a good book for lay readers... c'mon Freeman get with the times, there's some GREAT stuff out there!:

9)  Brian Hayes' first encounter with the algorithm of the IRS's Schedule D form... oh what joy!:

10)  Futility Closet looks at a card game you have a 50/50 chance of winning and can't improve upon (...unless of course you're psychic):


11)  For math teachers LOTS of reporting at the #NCTMBoston and #Shadowcon15 Twitter conference hashtags this week.

12)  And for 13 more mathy links check out the newest (121st) "Carnival of Mathematics":

13)  Lastly, for my recursive page of the week, a publisher finally gets it right:

...Hope everyone finds at least a couple links suiting their interests among the above.

Potpourri BONUS! (extra NON-mathematical links of interest):

1)  Cats... and prisoners together:

2)  And in one of those oddball human stories that are hard to fathom, the 61-year-old postal worker who invaded Capitol Hill this week in a gyrocopter, with the best of intentions, explained what his purpose was via YouTube:
(The fuller story here:  http://tinyurl.com/lpvb65b )

[...meanwhile, flying a gyrocopter to the Capitol must now be added to my lifetime-bucket list ;-) ]

Sunday, April 12, 2015

Erica Klarreich... Journalist/Mathematician/Ray Smullyan Fan

Math-Frolic Interview #30

"A mathematician before I became a full-time journalist, I try to convey the essence of complex mathematical ideas to non-mathematicians, and give them a sense of the beauty and depth of mathematics.

"At the same time, I also enjoy plunging into topics far from my mathematical roots, and have written about fields such as economics, computer science, medicine, and biology -- often as these fields relate to mathematics, but often simply for their own sake."  -- Erica Klarreich (from her Web homepage)

After I interviewed science/math writer Natalie Wolchover a bit ago, it occurred to me I should interview her Quanta colleague, Erica Klarreich, who actually specializes even more-so in mathematical pieces.  I imagine most readers here are likely familiar with Erica's excellent writings, but if not, you can check them out HERE (or via some of the links below).


1) How and when did your interest in mathematics begin? And when did you know you would pursue mathematics professionally?

I grew up in a math family, so I can’t remember a time when I wasn’t interested in math. My grandfather and my father were math professors, and my mother was a high school math teacher before she had children. I have happy memories of us reading Raymond Smullyan’s books of logic puzzles around the dining room table (now I read them with my own son!). My parents certainly didn’t force math down our throats, but it did feel like the family business. My older sister and I both ended up getting PhDs in math, although my younger sister said a polite “Thanks, but no thanks.”

[ahhh, another Ray Smullyan fan... in your honor I re-ran one of my favorite puzzles from him over at Math-Frolic on Friday.]

2)  Though math is your specialty, you've written across the board on many scientific subjects -- do you just have a lot of disparate interests, or is there some thread that unites all the topics you explore and write on?

I really like writing about areas of science other than mathematics, because I learn so much in the process (although that’s true of my math articles as well). I’d say, though, that most of my articles do have a math slant. Math is the language of science, which is what makes it such a great specialty—I can use it as a springboard to explore such a wide range of topics.

3)  In that same vein, it seems to me you write about some of the most fascinating, perhaps deep and dare I say almost mystical, aspects of mathematics... do you see it that way, or how would you characterize the subjects you're drawn to?

Actually, some of my favorite topics to write about, such as game theory and theoretical computer science, are quite pragmatic. But it’s true that when I’m writing a pure math story, I look for story elements that I guess you could describe as “mystical.” I think people read pure math stories for the same reason they read about, say, astronomy — because our explorations of the Platonic world of mathematics say something fundamental about who we are as human beings. When mathematicians push past the border of what we previously knew about prime numbers, say, or discover a connection between two seemingly distant parts of the Platonic world, they’re telling us not just about mathematics but also about ourselves, and our relationship to truth and beauty.

4)  What was the subject of your doctoral work in mathematics, and at what point did you decide you'd rather be a math/science journalist than a professor or applied mathematician?

I did my PhD in three-dimensional hyperbolic geometry, which I later got to write about in one of my favorite articles for Quanta Magazine

I still love hyperbolic geometry (although my knowledge has gotten pretty rusty), but already in graduate school I was starting to question whether the academic life was right for me. Hyperbolic geometry is a field that sits on the cusp of several other big fields of mathematics, so there was a huge amount of mathematics to learn, and I never felt that I understood those related fields enough to be able to make the deep connections that would lead to really exciting new mathematics. I probably could have worked in some small corner of the field and done decent work, but I knew that wouldn’t feel meaningful to me. Still, I didn’t know what else I could do, so I finished my PhD and went on to a three-year position at the University of Michigan.

During the years at Michigan, I started reading a lot of popular science writing, which for some reason I had never done much before, and it occurred to me that writing about science must be one of the coolest jobs around. I had always liked to write, so I started digging around online, and came upon the website of the science writing program at UC Santa Cruz. At the time, there were a bunch of questions on the website along the lines of: Do you like explaining your research to friends even more than doing the research? (Yes!) Do you enjoy taking in the full sweep of science more than specializing narrowly? (Yes!!) Were you one of those weird people who actually enjoyed writing term papers in college? (Yes!!!) As the number of exclamation points in my answers grew, I realized that I had found a possible new career. The Santa Cruz program is (or at least back then it was) the only science writing program aimed primarily at scientists, not journalists, so it was perfect for me. I applied, and at the end of my three years at Michigan, I went there.

5)  How long does it generally take you to write the typical article you do for, say, Quanta (if you can even generalize), and how many editors/fact-checkers must review it before we readers see it in publication?

There’s a lot of variety. I discovered early in my career that I don’t like to write news stories. Those often take just a day or two to complete, and I always found it stressful trying to fit in all my interviews that quickly. Besides, I just like going deeper than a news story permits. So I almost always write feature articles. Occasionally, these can be newsy, in which case we try to turn them around quickly. For example, a couple of years ago I wrote for Quanta about some breaking news connected to the twin primes conjecture , and my recollection is that we turned that story around in just a week. What’s more common for me is to spend several weeks researching and writing a story (or sometimes longer than that, if I’m working on several stories in parallel). Once I’ve written my draft, what happens next depends on the publication. Pretty much all the places I write for do a top edit and then a copy edit; some use fact-checkers, some ask me to fact-check the article myself, and some show the article to a panel of reviewers.

6)  Among all the articles you've written, do you have a few Web-accessible favorites you'd point people to who aren't familiar with your work? 

The Quanta article about the twin primes conjecture really resonated with readers, partly because the question of patterns in the prime numbers is so compelling, and also because it was an amazing story of an unknown mathematician making good. Another Quanta story that attracted a lot of readers was my profile of Maryam Mirzakhani, the first woman to win the Fields Medal.

I’ve also written some fun pieces lately for Nautilus: one about optical illusions and one about how to divide things fairly.

7)  What popular (or technical) math writers do you especially like to read? And what are some of your other main interests/hobbies/activities?

I’m a big fan of Steven Strogatz’ writing, and I really liked his math series in the New York Times. I also greatly enjoyed Jordan Ellenberg’s book, How Not to be Wrong. I have to confess, though, that when I’m reading for pleasure, I’m more likely to pick up a novel than a popular science book. I’m in a book group that specializes in nineteenth-century English novels; we just finished reading Martin Chuzzlewit, which is a giant doorstop of a book, but my idea of fun!

I like solving cryptic crossword puzzles, which are crosswords in which the entries are clued by wordplay instead of ordinary definitions. Two of my friends are the creators of the cryptic crossword that appears weekly in The Nation magazine, and a small group of us meet over breakfast to solve their puzzles before they go into print and critique the clues.

During the last two years I’ve been working on a passion project: a children’s novel that I’m writing together with my younger sister. It’s been huge fun, and now we’re getting ready to start the submission process.

...Good luck with the children's novel; that can be a hard genre to break into, and I often don't fully understand what makes one children's novel a huge success, and another one less so.

8)  Finally, you and Natalie Wolchover are two of a great band of writers for Quanta Magazine -- just curious if you guys all know each other well, socialize, collaborate at all, or do you all lead separate lives, just writing for the same outlet?

We lead separate lives, unfortunately. I’m just a freelancer for Quanta, and since I live in Berkeley and Quanta’s offices are in New York City, I’ve never actually met any of the Quanta staff face-to-face, even the ones with whom I work quite closely. They have very nice voices, though!

Thanks Erica; we're fortunate to have writers like you putting out such a great variety of in-depth, mathematical content on the Web on a regular basis.
And if you want to hear Erica's voice, Sol Lederman interviewed her for his podcast series about 2 years ago (she covers much of the same ground I asked about above, in even more detail):
Also, another transcribed interview with Erica here:

Friday, April 10, 2015

Another Veek of Math Links... You're Velcome

Lest you missed them:

1)  A message from an Iowa teacher... that some others can probably relate to:

2)  "Solve My Maths" blog wants to 'take back the F-word':

  A John Conway puzzle via Futility Closet:

4)  Mathematician Jason Rosenhouse looks at good, and not-so-good, writing:

  Interviews with a couple of math-crowd favorites from last week:

a)  A brief transcribed interview with Steven Strogatz here:

b) ...and a 30-minute podcast interview with Jordan Ellenberg at ACME Science:

AND, in more good news for Jordan, he was just awarded a Guggenheim Fellowship! CONGRATS and well-deserved! -- one of only two mathematicians, the other being Tatiano Toro, to receive the award, which more heavily goes to recipients in the arts/humanities.

6)  Another review/update of the twin-prime conjecture proof (which, if one other conjecture is assumed true, is now down to a gap of 6):

7)  And thoughts, from Minhyong Kim, about Mochizuki's ABC conjecture proof, via John Baez:

8)  Uhhh, "prime number magnitudes" are kinda big:

9)  The future of big data????

10)  I'll bet Mike Lawler worked on some math this week:   

11)  And heads-up for  PBSNova show, "The Great Math Mystery" (math, invented or discovered?) coming up this Wednesday:


Meanwhile, Sunday morning, right here, Math-Frolic Interview #30 will be posted, and appropriately for such an auspicious #, it will be with one of the premier math writers currently on the Web.

Potpourri BONUS! (extra NON-mathematical links of interest):

1)  Eric Meade, in a segment from last week's TEDTalkRadio, on the art of magic:
Reminds me of this older Ricky Gervais/David Blaine clip (not necessarily for the squeamish):

2)  And to close out the week, a feel-good animal story:

Friday, April 3, 2015

Good, Friday Potpourri

Here's part of the week that was, in math:

1)  April is "Mathematics Awareness Month" (I'd say Jan. thru Dec. pretty much qualify too, but whatever):

2)  A new "Math Teachers At Play" blog carnival brought to us beautifully by John Golden:

  Some pure coolness (by way of a "nerdy math wallet") from mathbabe.org this week:

4)  Evelyn Lamb continued her Cantoresque focus from last week, with a look at the 'Cantor function' this week:

5)  Ben Orlin offered a nice introduction to Newcomb's Paradox, that young people (AND adults) can argue over unendingly:

  Mark Chu-Carroll discusses a paper that looks at the mathematics of the FedEx hub system for delivering packages:

7) "Mathematics Rising" blogged on what the Chaitins say about creativity, both biological and mathematical:

8)  Research replication as "a quiet crisis" in science, perhaps:

9)  I've never been terribly keen for "Which one doesn't belong" type problems, but they've been in the blogosphere lately (in part due to one instructor's different approach), and I'll pass along this post on them:

10)  A new, and once-again thought-provoking post from Keith Devlin... on computer science and mathematics... and, the reasoning that links them:

11)  From +plus Magazine, too late for Valentine's Day, but just in time for Easter and Passover :-/, "Sexual Statistics":
article here:  https://plus.maths.org/content/sexual-statistics
podcast here:  https://plus.maths.org/content/sexual-statistics-podcast?src=aop

12)  From Quanta, another nice interview with that unexpected math celebrity, Yitang Zhang:

13)  From the NYTimes, 'The problem with math problems...' (good discussion and links):

14)  Mike's math page usually does a bit of math during the week ;-):  https://mikesmathpage.wordpress.com/

15)  Who knew sandpiles were so interesting? Jordan Ellenberg did, as he explains for Nautilus Magazine:

And maybe we'll end the week with this little thought-exercise, also from Ellenberg:

Potpourri BONUS! (extra NON-mathematical links of interest):

1) The amazing, blind Daniel Kish gives a recent TEDTalk explaining his use of personal sonar for navigating his dark world:

2)  And in case you missed it, this viral feel-good story about parenting from the week: