...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, June 23, 2017

The Friday Math-mix

Week #21 of the Trump/Putin takeover:

1)  Something different from the unpredictable James Propp this month:

…speaking of Jim, he recently won a noble prize (well, seems noble to me anyway), writing about dinosaurs:

2) The tale of a ranking (guest post at mathbabe.org):

3)  A little mix of statistics, science, and philosophy (via Daniel Lakens):

4) Robert Talbert gives an overview of flipped learning and self-regulated learning:

5)  The double life of mathematician/football-star John Urschel (h/t Egan Chernoff):

6)  Tiling with Koch snowflakes (h/t John Baez):

7)  Followup to the Anna Haensch “refrain-from-discussing-mathematics” sign/tweet that went viral last week:

9)  A highlight of my week was interviewing professor/author Ed Scheinerman:

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

All I got for ya:

Tuesday, June 20, 2017

Ed Scheinerman.... Seeing Masterpieces In Mathematics

Math-Frolic Interview #42

I fear that too many people’s mathematics education is devoid of joy. Imagine if children’s reading education focused primarily on  spelling and punctuation, but not on delights such as Harry Potter or creating stories of one’s own; that approach would hardly instill students with a love of literature.
-- Ed Scheinerman

Thus far, Dr. Ed Scheinerman's "The Mathematics Lover's Companion" is my favorite popular math book of this year. It's a buffet of somewhat typical math topics that are well-worn in other volumes, but Ed's specific mix and engaging writing style about what he views as "masterpieces" of math-thought, help raise the volume above most of its counterparts. The 23 chapter headings from the Table of Contents give you a hint of the content, but not of Ed's fresh, clear writing style (he has previously won awards from MAA for his expository writing):  

I definitely recommend the volume to budding math enthusiasts, and seasoned ones as well!
I was happy to get Dr. Scheinerman's responses to a few questions:


1) Just by way of introduction can you briefly recount your own path to becoming a professional mathematician?

From about grade 7 on I was very fortunate to have had excellent mathematics teachers. Geometry was almost entirely doing proofs; proof was a wholly unexpected concept for me and greatly sparked my interest. Of particular importance though was my 10th grade mathematics teacher, John Wells, who emphasized mathematics as a creative subject. He encouraged and supported my mathematical interests, including advocating my application to the Hampshire College Summer Studies in Mathematics led by David Kelly. Attending that program was undoubtedly the most important catalyst in my path to becoming a mathematician.

[...currently, Dr. Scheinerman is a mathematics professor at Johns Hopkins University]

2)  Your prior writing seems to be mostly technical or academic in nature… what made you decide to write a “popular” math book, and who would you say the book is primarily written for?

I find that most people do not have a good sense of what mathematics is about. It seems to me that all the “good stuff” is left out of a typical high school curriculum. It is not unusual for me to meet people that know what a prime number is, but have no idea (and likely never considered) that there are infinitely many or how one can prove this. Showing that there are infinitely many primes is certainly accessible to high school students. 

We don’t teach English to students just so they can read instructions and write advertising copy. Were we to teach English the way we teach mathematics, we’d omit reading any Shakespeare and students would conflate spelling and literature, just as most people conflate arithmetic and mathematics. I recall (with horror) attending a presentation by a highly distinguished journalist who quipped that he “could never understand what an isosceles triangle was” and the audience laughed in agreement. 

My goal therefore is to provide a bit of an antidote: to present exciting mathematical topics that are accessible at the high school level that readers can enjoy.

3)  What might you say sets your book apart from many other volumes that cover similar topics… or why might someone familiar with these topics still enjoy reading your volume?

I tried in this book to “get to the point” for my reader. One can purchase entire books on (say) the number π but I sought to give my reader a “tasting menu” of great mathematics in which each chapter stands independent of the others. That way the reader can skip around, or put the book aside for a while to return later for another round of fun.

4)  What were some other subjects you considered for inclusion in the book, but in the end didn’t make the cut as math "masterpieces”?

I struggled mightily to write a chapter about the Axiom of Choice. I was not able to present it in a way that I thought my readers would find intelligible and interesting. I think it’s just too technical and the path to interesting consequences (e.g., nonmeasurable sets) too difficult for my intended audience.

5)  Who have been some of your own favorite “popularizers” of math over the years?

Without doubt one name stands above all others: Martin Gardner. I avidly read his Scientific American column and his many books.

[...Martin, a non-professional-mathematician, would no doubt be heartened, yet surprised, at how often his name comes up in this context!]

6)  The first two parts of the book essentially cover elements of algebra and geometry, fitting topics for a math volume, while Part 3 is about “Uncertainty” (a favorite topic of mine). Can you say a little about how that came to be the third big subject area of the book?

I must admit that the organization of the book arose after the chapters were written. I had (nearly) two dozen independent chapters and sought a way to arrange them. The broad headings of number, shape, and uncertainty worked.

7)  Do you have any further “popular” math books in mind to write?

Both I and my editor are encouraged by the positive reception this book has been getting (including a shout-out in the New York Times Review of Books) so I’m working on a Mathematics Lover’s Companion, Volume 2. My first chapter is written and it’s a “do it yourself” introduction about mathematical research that will demonstrate the process (including some of the frustration and then the joy) of mathematical discovery. It should be widely accessible even to folks whose algebra has completely rusted.

[...this is great to hear about!]


Thanks for the answers here Dr. Scheinerman; very much looking forward to your next volume (and hoping you find a way to include the Axiom of Choice! ;)

Friday, June 16, 2017

Potpourri of the Week

During week #20 of Donald Trump’s Emperorship:

1)  A new math/statistics blog from a graduate stats couple:

2)  What are complex numbers… I mean, really? (h/t to Jim Propp for this one):

3)  “The illegitimate open-mindedness of arithmetic”… (h/t to Joselle Keyhoe):

4)  Coordinate planes as only Ben Orlin would fancy them:

5)  Another commentary on math giftedness (h/t Cathy O’Neil):

6)  Another post on p-values and fake science results (h/t Stephen John Senn):

7)  Correlation vs. causation in “genome-wide association studies” (h/t Daniel Engber):

9)  I blurbed about a new book anyone into cryptograms will want to have:
…and on Wed. I passed along some puzzles:

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

1) The fascinating case of a former polygraph operator last week on This American Life:
This story actually comes from another great Web podcast series: Love + Radio 

2)  Last week’s TED Radio Hour included a replay of a favorite old segment with Mike Lowe explaining people’s success with “dirty jobs”:

And as long as I’m pushing podcasts, may as well remind folks that NPR’s wonderful “Invisibilia” is back for its third season:

Monday, June 12, 2017

For Alan Turing Wannabes

Newly showing up in bookstores, “Unsolved” by Craig Bauer will likely appeal to a wide audience — didn’t  ALL of us math-lovers at some time play with cryptograms as a kid… and many carried that interest into adulthood. And even many others, without a direct interest in math, carry a fascination with the mystery, game-playing, and intrigue of ciphers.
This is a 500+ page imposing volume from Princeton University Press.  Though I’m not particularly fascinated by cryptography in general, I found the chapters on some of the most famous/familiar cases (the Voynich Manuscript, the Zodiac killer, the Cicada internet ciphers) quite gripping. There’s hardly any actual math in the volume, but of course solving cryptographic messages is very much an activity of thinking mathematically, so I feel justified to speak of the book in the popular math category, and don’t doubt mathematicians will find it interesting (the author is a mathematician himself).

Included are a few ciphers that have been solved, as examples, but the book very much concentrates on UNsolved ones. So for those who like working on such things there’s loads of work/play here (and the volume has an associated website for even more followup; also toward book’s end the author casually mentions the possibility of an eventual 2nd volume coming out).  Most of these ciphers were new to me, though I suspect for those really plugged into this subject many will be very well known.
I found myself more engrossed in the contents of the volume than I’d expected because unsolved cryptographic messages (and the minds that create them) are so inherently interesting, and come in so many different forms/contexts; and they stretch across centuries right up to modern times and modern technologies. The book ends with a chapter on potential communication with extraterrestrials, and description of RSA cryptology. Worth noting also, that it is possible some of the ciphers included are hoaxes and utter nonsense, but even figuring that out would require great effort/detective work.

It will be interesting to see if a book like this, offering up these mysteries to a new hive-mind of readers, may produce some solutions in the near future to long-unsolved cases. And if you do solve any of them, the NSA may wish to talk with you about job opportunities ;)

 Here are a couple of older YouTube videos of author Bauer speaking on his topic:

Friday, June 9, 2017

The Math Keeps Comey, er, I mean Coming

Some of the math bits from week #19 of Donald Trump’s attempted lockdown of democracy:

1)  The latest Carnival of Math is ready to entertain and elucidate you here:

2)  Lie groups, E8, and communicating cutting edge math to the public:

3)  Squared squares from Numberphile and James Grime:

4)  An intro to Zipf’s Law:

5)  A new social media (“Mathstodon”), specifically for math buffs:

6) statistical evidence for research misconduct,” via Andrew Gelman:

7)  Here’s another review of what is so far my favorite popular math volume of the year:

8)  Mathematics and the real world of near-misses (yet another fun read from Evelyn Lamb):

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

1)  The always-interesting physicist Brian Greene with Krista Tippett on “On Being” last week:

2)  Some heavy discussion from Scott Aaronson and a sh*tLOAD of commenters on reductionism/causation/emergence:

Friday, June 2, 2017


It’s week #18 of America-held-hostage by Donald Trump (...or Steve Bannon?), and here are some math bits:

1)  Good interview over at Math Blog with some bloke named Keith Devlin:

2)  John Baez on set theory, forcing, and “set-theoretic geology”:

3)  A puzzle of Erdös’ revisited:

4)  Marcus du Sautoy with a very basic intro to Gödel’s Incompleteness Theorem (via Numberphile):

5)  And another video... haven't carved out time to watch this yet, but if Mike Lawler recommends it I know it'll be good (from PBS's "Infinite Series"):

6)  A few connections between math and music:

7)  ICYMI, yesterday I noted some of the recent offerings from Princeton University Press of interest:

8)  Luckily Evelyn Lamb has come to the rescue of my short potpourri by putting out her latest “Tinyletter” edition yesterday with several more links (…but hopefully by now you get her monthly letter in your own email and don’t need me to remind you of it!):

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

1)  In follow-up to the recent hoax paper that made the rounds Jerry Coyne has now posted about another paper, from 2006, that reads like a (postmodern) hoax… but no indication it was:

2)  And this from the “language is awesome” category:

Sunday, May 28, 2017

Mathematician, Gambler, Hedge Fund Chief…

“A fascinating insight into the thought processes of someone with little interest in fame, who has mostly stayed under the radar, but who has followed his inquisitive mind wherever it has led him, and reaped the resulting rewards. There is nothing more important than knowing how to think clearly. Read this book and learn from a master.” — Paul Wilmott

A further look today at a volume I mentioned a short while back, “A Man For All Markets” by (and about) Edward O. Thorp.  It may not be thought of as a popular math read, but I think there is just enough math in it to qualify.

For any who don’t know, Ed Thorp is a trained mathematician, who taught for awhile, before following his heart and delving into games/gambling/Las Vegas and later the stock market and Wall Street… with, one should quickly add, remarkable success! This book tells the autobiographical story of his incredible life. 
Thorp started by figuring out (mathematically) winning strategies for gambling endeavors like blackjack, roulette, and baccarat before moving on to run very successful mutual/hedge funds on Wall St. If you have no interest in the financial markets than this bio may not grab you, but as most people do have some interest, it contains pages that will draw in most readers. His many life accomplishments make it seem easy to just apply basic logic to various situations, including the stock market, and succeed, yet most people consistently fail at such efforts.

The book reminds me slightly of Siobhan Roberts’ account of John Conway, "Genius At Play," from 2015 (my favorite volume of that year), but it is not nearly as fun a read. The similarity comes from two iconoclastic and brilliant figures telling the anecdotes of their lives. But Roberts’ lively, engaging writing and Conway’s antics lifts her excellent portrayal to  another level. In comparison, much of Thorp’s volume is duller, the writing often more stilted or bland, but still his anecdotes are fascinating enough to pull you in. Stories around his gambling pursuits, the rise and fall of his own hedge fund (Princeton Newport Partners), the Black-Scholes options-pricing formula, his take on the Bernie Madoff affair, his contrarian analysis of the traditional “Efficient Market Hypothesis,” and take on the 2008-9 market crash, are among many interesting passages sometimes couched within more stodgy, matter-of-fact material. I especially enjoyed the last few chapters and "thoughts."

One thing I also liked about the volume is the way it portrays an individual who relied heavily on “intuition” to launch most of his successful ventures, before his technical brilliance fleshed out all the details required. The central importance of intuition, passion, and curiosity sometimes gets lost in the focus on logical deduction among mathematicians, and Thorp implies that he succeeded where others failed because of his greater intuitive grasp of situations more so than keener logic.

A longer, more detailed review of the volume available here:

I do recommend the book, especially to anyone with an interest in the many machinations of Wall Street, but it’s not the most riveting read around, despite many entertaining parts.

Friday, May 26, 2017

Another Friday, Another Math-mix

Week #17 of Trump’s looting-and-dismantling of America….

1)  From Quora last week, “What’s the most important thing happening in mathematics right now?”:

2)  Futility Closet presented the Thue-Morse sequence:

3) Pi Hiding In Prime Regularities”… another phenomenal presentation from Grant Sanderson:

4)  Eugene Stern, guest-posting at Mathbabe blog, has some thoughts on value-added models for teachers:

5)  R. Talbert once again on flipped learning and his new book:

6)  A big “Math Teachers At Play” blog carnival for May:

7)  “One of the real old chestnuts of mathematics,” the Goldbach Conjecture, newly presented by Numberphile:

8)  Getting to the point that a potpourri without something from Evelyn Lamb is a rare event… and it won’t happen this week:

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

1)  ICYMI, Jerry Coyne on the latest ‘Sokalized’ effort to make the rounds:

2)  Terry Gross had a fascinating interview with Pulitzer writer Tom Ricks this week:

…lastly, I’ll just leave this here for any who’ve missed it along the way:

Friday, May 19, 2017

The Week Gone By

Some mathiness during week #16 of the Trumpian Debacle…

1)  Grant Sanderson has completed his “Essence of Calculus” series on YouTube:

...help Grant continue such wonderful work by contributing to his Patreon account here:

2)  For those deeply into set theory here’s a recent paper by philosopher Penelope Maddy on foundations of set theory:

I interviewed Dr. Maddy here about 2 years ago:

3)  The simplicity of social psychology research:

4)  Fawn Nguyen teaching mathematical thinking:

5)  Don’t know if this will take off or not, but a math book swap via internet is being tried out:

6)  Re-thinking geometry to re-think time (via Quanta Magazine):

7)  Robert Talbert interviewed about ‘flipped learning’:

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

1)  In case you’ve somehow missed it, some discussion of the Dunning-Kruger effect (competency/overconfidence):

Friday, May 12, 2017

Potpourri (...such as it is)

A short potpourri from week #15 of the Trump Apocalypse:

1)  Yet another review of my favorite popular math book from last year, Cathy O’Neil’s “Weapons of Math Destruction”:

2)  Pat Ballew has amassed a lot of great historical material with his “On This Day In Math” blog and Twitter feed. I suggested earlier this week that with some organizing effort the material could probably make a great calendar or book for math fans. 
Any publishers interested ought to check with Pat:

3)  Presh Talwalkar on Viviani’s Theorem, Sperner’s Lemma, and more:

4)  An ‘intrepid’ interview with Barry Mazur:

5)  Brian Hayes points out this mathematical approach to the question “What is life?”:

6)  Today I blurbed briefly about 3 recent books:

...and just a couple of decades-old quotes to close out the week (...you know, for those too young to remember history, and thus subject to repeating it):
“Just remember that once the toothpaste is out of the tube, it is going to be very tough to get it back in.”  -- John Haldeman (1973)
"We have a cancer within, close to the presidency, that is growing. It is growing daily.”   -- John Dean (1973)

Friday, May 5, 2017

More Mathy Stuff

Math-Frolic was distracted by other things this week, so here's some of the mathy things it didn't report on:

1)  Intransitive dice provide the basis for a possible Polymath Project:

2)  And from Evelyn Lamb this week.…
Here, she’s smiling over tiling:

…and here playing with the Douady Rabbit fractal:

…and finally her newest monthly “tinyletter” with a lot more than just math in it:

3)  A new “Math Teachers At Play” blog carnival posted last weekend:

4)  And the 145th Carnival of Mathematics is here:

5)  I liked the 2 puzzles served up by The Riddler this week… but could only solve one of them :(

6)  The ‘Chaos game” from Numberphile:

7)  I’ve enjoyed Marcus du Sautoy’s encyclopedic new book (especially the last few chapters), “The Great Unknown,” which is more physics than math but still worth mentioning here. He was on NPR this week discussing it:

8)  Art Benjamin and Siobhan Roberts win math communication awards (h/t S. Strogatz):

9)  Nicely-written essay on prime numbers from a relatively new blog:

10)  Latest edition of the Saskatchewan Mathematics Teachers’ Society newsletter (The Variable) including a new column from Egan Chernoff:

11)  Andrew Gelman offers up his view of what hypothesis testing is all about:

12)  I will RE-mention Grant Sanderson’s incredible new “Essence of Calculus” series (YouTube) as he keeps adding new videos:

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

1)  A VERY powerful “On Being” episode (especially for parents, or those with family tragedies) last weekend with Sheryl Sandberg and Adam Grant:
(…there are so many “On Being” episodes I love, and this one quickly becomes one of them!)

2)  Just an interesting, curious bit of news from the week (in the event you're preparing to be buried):

Friday, April 28, 2017

Some Friday Math Picks

1)  James Tanton interviewed:

...and here, an experiment proposed with logarithms from by Dr. Tanton:

2)  Colm Mulcahy on the “Mathematics Genealogy Project”:

3)  Mark Chu-Carroll offers up an intro to “type theory”:

4)  Anna Haensch writes about “Gifted,” the movie and the trait:

5)  Series, as only Ben Orlin could explain them:

6)  Mike Lawler offered up a challenge to “everyone in and around math.” Care to take him up on it:

...Mike's been on fire this week with interesting posts/problems, so check 'em out if you get the chance.

7)  "What Is a Manifold?":

8)  Andrew Gelman (and a lot of commenters) on "evidence-based design":

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

1)  In case you've somehow missed it, Jimmy Wales of Wikipedia is launching a new project to fight fake news, called “Wikitribune”:

2)  John Horgan interviews Peter Woit (mostly on physics):