...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, November 19, 2017

Thanksgiving Approaches

End of year is always a good time for lists (which make for good space-fillers too) ;)
So here a list of some websites I'm especially thankful for -- the math-related writers that excite me most when they show up in my RSS feed (in alphabetical order):

Scott Aaronson — love Scott’s unpredictable topics, his honesty, and step-by-step thought processes (even when I don’t understand half of what he’s laying out). Primarily a computer scientist, he also blogs about math, physics, philosophy, culture, politics, and more:

Keith Devlin — NPR “math guy” (and Stanford professor); love his ability to write about math expertly for a mass audience; long-time favorite at my blog; he has several writing venues, the one below being a main one:

Brian Hayes — award-winning essayist; unpredictable what and when he’ll post; a non-mathematician writing often about quirky, math-related subjects, but crisp and interesting whatever topic he chooses:

Evelyn Lamb — has developed into one of the finest math expositors on the Web, suitable for students and professors alike; again with several outlets, but perhaps the main one below for Scientific American:

Fawn Nguyen — what can I say about Fawn that hasn’t been said long before! I don’t follow a lot of primary/secondary education blogs but always perk up when I see she’s posted a new piece for her “Finding Ways” blog; it’s not even the math I enjoy so much, as her passion and wit! (made all the more delicious, knowing that English wasn’t even her native tongue):

Ben Orlin — never would’ve guessed math could be this funny, let alone cartoonish. Have grown to love Ben’s simple, round-faced offspring; but the amazing thing is not how much they make me laugh, but how regularly they make me think!:

Jim Propp — more strictly mathematical, but often on topics I don’t see elsewhere or at least with a different approach; richer and longer posts than most popular blogs, and almost always including ideas one could use in a classroom:

Quanta Magazine — not a blog, and not exclusively math, but some of the best doggone consistent popular science and math writing anywhere on the Web from a stable of great writers (sometimes I shake my head that we get this for free!):

I hope every one of these is already among your favorites, but if not, be sure to check 'em out. Wish I'd had some of these folks as teachers when I was growing up!
[...And feel free to mention below the Internet blogs/writers you are especially grateful for, or excited by, at this thankful time of year.]

Friday, November 17, 2017

The Last Potpourri Before The Thursday When I Give Thanks For A Constitution Which Includes Provisions For Impeachment

Delusional Donald the Democracy-Subverter has returned from Asia, somehow confusing being laughed-at-behind-his-back with respect, and now re-opening the African elephant trophy trade (because assuredly who among us doesn't need more elephant parts adorning our living rooms)... but oh well, onward:

1)  Not sure that there’s any math in this (…you be the judge), but the latest from Scott Aaronson:

2)  A week ago 3 mathematicians got 30 minutes on NPR’s “Science Friday”:

3)  Gender-bias evolution via Tanya Khovanova:

4)  Quite a story (video) from Simons Foundation:

5)  Cathy O’Neil in the NY Times, on algorithmic accountability:
…and she received a little pushback on Twitter:
…and on Medium:

6)  Andrew Gelman points to 3 more new papers on the ‘replication crisis’:

7)  Still trying to understand blockchain? This piece may help:

8)  The latest (and one of my favorites) from Jim Propp at Mathematical Enchantments, about things we've all experienced, and why "the errorists" may be winning:

9)  And I'll end with a little mathematician-generated humor from Futility Closet today:

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

1)  “Your reckoning. And mine”… long, nuanced, fleshed-out piece from Rebecca Traister on recent events:

2)  Internet scammers got you down?… maybe this site can help: 

[...next week being a major/busy Holiday week, I'll forego doing a Friday potpourri]

Sunday, November 5, 2017

A Little Catch-up on Books

Won’t have time to do adequate blurbs (let alone full reviews) of all the books I’m reading now but will mention just a few of those I’m enjoying most, for a general audience. 
Volume I last finished was Ian Stewart’s Significant Figures,” his new compendium of biographical sketches of a couple dozen famous mathematicians — the writing is not as scintillating as some of Stewart’s other offerings, but adequate, especially if you’re looking for succinct profiles of mathematicians from ancient through William Thurston. The first half of the bios (and they’re in chronological order), had an almost cut-and-paste feel to it (to me), while the writing for the more modern half was more interesting/engaging. 
Oddly, after finishing the new Stewart volume I stumbled upon his much older “The Problems of Mathematics” (at a garage sale) which is a wonderful read and overview of mathematics (a bit dated in parts), and highly recommendable.   
And 3 more current books in my queue at the moment:

Ten Great Ideas About Chance” — have barely started it, but coming from Persi Diaconis and Brian Skyrms looks quite good, though I’m tiring a bit of the many popular treatments of chance/probability/statistics in the last 3 years. Still, an important topic, and leafing through it, the volume does appear to have a somewhat fresh take and organization.

The Best Writing In Mathematics 2017 — Micea Pitici’s latest entry in his ongoing series (the 2016 edition also came out earlier this year, so two in one year!). The volume is, as usual, a very wide-ranging collection of writings/topics from 2016, as Pitici shows again how “panoramic” and “versatile” mathematics really is. Some of your favorite popular math writers from the internet are included, and it is handsomely produced by Princeton University Press.  I couldn’t detect a theme or prevalence of topics in this year’s edition, just the usual disjointed variety that Pitici brings together.
He mentions at the end that he has switched his own career focus over to library science now, from mathematics, and I’m not clear if that will affect his production of this volume in the future (though I suspect not).

A Most Elegant Equation by David Stipp — How could you go wrong writing about everybody’s favorite equation in mathematics, Leonhard Euler’s  e^(iπ)+1=0.  Even when the writing is a bit dry or stodgy the topic is so inherently interesting as to pull you along. 

These are all books that will make my recommended list for end-of-year Holiday shopping, but several other books of a more specialized nature have crossed my desk the last few months, and I’ll probably leave them un-noted.

Friday, November 3, 2017


Three indictments down, and what... maybe at least another 8 to go? 
Anyway, some math from the week:

1)  Gelman re-focuses on quality control in statistics:

2)  Nice piece on Karl Weierstrass’ monster from Nautilus:

3)  Fascinating Quanta piece on “The Atomic Theory of Origami”:

4) Mathematics Rising” looks at meaning and mathematics:

5)  Bill Briggs on replacing p-values:

6)  A wee bit of stock market/finance math for you:

7)  Evelyn Lamb’s “TinyLetter,” covering her doings for the month of October, is now out (hopefully by now most of you are receiving it in your email box each month):

8)  In case you’re not already aware of it, Vi Hart has begun a Patreon crowdfunding effort for her work:

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

1)  Intriguing piece on the linguistic evolution of words from the always-interesting Ed Yong:

2)  OK, along with the hysterical comments, surely my favorite tweet of the week:

Friday, October 27, 2017

Some Math From the Week

A week with liddle Republicans coming apart at the seams, and Melania Trump, drenched-to-the-bone in irony, speaking of a campaign (LOL) against bullying, and our own Gov’t., in a demonstration of why so many revile it and see neo-fascism as an appealing alternative, deciding that 25 years just wasn’t enough time to figure out how to release a trove of JFK documents as ordered to by law. (What else can’t possibly be accomplished in 25 years? I mean other than healthcare, tax reform, fair re-districting, gun control, banking reform, truth-in-advertising, climate change regulation...). Is it any longer a surprise that so many voters perceive government workers as lazy, incompetent, pencil-pushers, and Steve Bannon thinks his future looks bright...
'This too shall pass'... or, maybe not.
Oh well, some bits of math from the week:

1)  The Cantor Set and more explained:

2)  Caltech’s Barry Simon wins Heineman Prize for mathematical physics:

3)  This week’s Futility Closet podcast highlighted Swedish mathematician Arne Beurling:

4)  H/T to Cathy O’Neil for pointing out this piece on possible problems in a complex DNA testing algorithm:

5)  There are so many fantastic free math instructional videos around these days… and yet Grant Sanderson still seems to have advanced to a league of his own. I hope you all are keeping up with his incredible offerings at 3blue1brown:

It will be interesting to see if we witness a significant increase in math majors and basic math literacy in the future just because of all the great content now freely available online at people’s fingertips.

6)  The 150th Carnival of Mathematics is now up at:

7)  Physicist Sabine Hossenfelder has a new book on the way next year, “Lost In Math”:

8)  Prices at Whole Foods:

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

1) The 11-min. ‘Prologue’ (with a female airline pilot) to last week’s “This American Life” was pretty dang entertaining:

2)  Perhaps my favorite tweet from this week:

Friday, October 20, 2017

A Very Few Math Bits From the Week

Some of the math bits that interrupted this week's stream of demagoguery:

1)  Alex Bellos’ latest book, “Puzzle Ninja”:
(I don’t believe it’s in American bookstores yet, and when it is, may show up under a different title as British math books often do)

2)  Just in time for your next cocktail chatter… ;) David Butler tweeted this week: “For every prime after 66600049, you can cross out some of its digits and find a smaller prime.

3)  For “World Maths Day,” The Royal Society highlights 66 mathematicians:

4)  Our computer overlords are on the way… a couple of write-ups on the stunning progress of AlphaGoZero:

5)  The Pythagorean Theorem as you may not have seen it discussed before (from “Better Explained”):

6)  Brand new issue of Chalkdust magazine now online:

7)  Arguing in favor of research p-values < 0.005:

8)  In a week when I didn't expect to have much to post at Math-Frolic, I ended up with 3 posts, including today involving Scott Aaronson.

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

1)  Steven Wright quotes (just because):

2)  And as we all know nothing is written in stone… er, uh, ohh, wait….

Friday, October 13, 2017


It's Friday the 13th; what could be more fitting than having Donny Trump as president...
Oh well, here's some math:

1)  The “power pose” and more (or less):

2)  And relatedly, also from Gelman, I suspect anyone involved in psychology or social science research, ought read this post (and comments):

3)  Meanwhile Kaiser Fung warns about the ubiquity of fake data:

4)  Lot of talk about neural networks these days, which has John Cook worried about the problem of ‘overfitting’ the data:

5)  Transcribed interview with Dr. Holly Krieger here:

6)  Devilishly-tricky little problem from Futility Closet:

7)  And this lovely little problem from Ed Southall:
(some nice explanations in comments)

8)  You just never know what Ben Orlin will teach you about next:

9)  I wouldn’t normally bother citing yet another piece on the Monty Hall Problem… except that this one is from Keith Devlin and connects it to the more general backsliding of scientific thinking evident in today’s citizenry:

10) I reported on Brian Hayes’ new book, “Foolproof,” last weekend:

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

1)  Krista Tippett with Daniel Kahneman on “On Being” last weekend:

2)  Lastly, in important news of the week, kneeling at the national anthem may be problematic, but maybe flipping the bird at it is constitutionally-protected:

Sunday, October 8, 2017

Overview... "Foolproof, and Other Mathematical Meditations"

"Mathematics is too important and too much fun to be left to the mathematicians." 
                             -- first sentence of Brian Hayes' Preface to his new volume

One of my favorite Murphy Law corollaries states, “Nothing can be made foolproof because fools are so damn ingenious”... while the quote doesn't pertain to Brian Hayes' new book, it was the first thing I thought of upon seeing his offering. ;) The quote, I think, does pertain to the world we live in, and Hayes is nothing, if not an astute observer of that world.  “Foolproof and Other Mathematical Meditations” is a compendium of 13 updated versions of previously-published Hayes' essays with the “Foolproof” essay actually being the last, and one of the most enjoyable, of the slim volume. But before I say more, let me digress further…

A common joke when I was growing up reading Scientific American, was that the magazine was just a wrapper for getting Martin Gardner’s monthly column into your mailbox. No doubt there literally were some readers who subscribed to the magazine just for Gardner's column. His writing was succinct, descriptive, intriguing, on topics that were unpredictable from month-to-month. Another reason I think many loved Gardner was that he was NOT a mathematician (if memory serves me right he never even took an academic math class after high school) — it gave some hope that non-professional math enthusiasts could still contribute to the field or at least communicate some math to others (in the sciences usually astronomy is often cited as one of the only areas where ‘amateurs’ have a fair chance of making a significant contribution).

Anyway, I mention all this now because Brian Hayes’ writing, to my sense, has the ring of Gardner’s popular writing. In fact, when I interviewed Hayes awhile back, I specifically asked if he consciously copied Gardner’s style (he overlapped with Gardner, working at Scientific American). He admitted, like so many, being a huge fan of Gardner, but said he never deliberately tried to mimic Gardner’s craft — but took my question as the compliment it was meant to be. Still, as I read these ‘Foolproof’ essays I could almost hear Gardner’s voice in the background. Martin’s writing was more “recreational,” perhaps even casual, while Hayes has a more technical or academic bent to it, but still the style and step-by-step presentation are similar. And the resemblance goes beyond their meticulous exposition, as Hayes too is not a professional mathematician, just a sort of dabbler in it, who like Gardner, is unpredictable in what topic may capture his interest next.

Enough about all that. Hayes' new book is a delight… with one shortcoming: at 200 pages and 13 essays it is too SHORT. I don’t know what the criteria was for essays that made it into this volume, but plenty of good Hayes material is left out.

Every offering here contains interesting little gems or tidbits that I suspect a math teacher could incorporate into a classroom discussion at the middle or high school level, while also containing many bits for the professional mathematician to mull over. Computer science is Hayes’ specialty, so several of the pieces are focused there. My own favorites, in addition to “Foolproof" though are the more mathematically-inclined pieces, including: “The Spectrum of Riemannium,” “Playing Ball in the nth Dimension,” and “Quasirandom Ramblings.” But your own favorites will depend on your own proclivities as Hayes jumps around from one wild, quirky musing to another, on biography, method, pure and applied math: Gauss, arithmetic, Sudoku, space-filling curves, statistics, Markov chains, pi, computer software, randomness, math history, the abc conjecture, and more are here… almost always dipping in deep enough at some point to make you slow down in order to grasp what he's positing.

This rich, mind-stretching book has come along at a time when I was feeling a bit frustrated by the lack of “generalist” popular math books showing up this year (plenty of books appealing to narrower niches), and will certainly be among my favorites from the last 12 months. Reading it reminds me a bit of what they say about Chinese meals… each essay here felt deep and satisfying while reading it, yet an hour later I was hungry for more! ;)

Finally, Hayes’ dedication for the book reads: “To the mathematics community that has taught me and charmed me.” He constantly returns that charm in spades.

Friday, October 6, 2017

1st Potpourri of October

Incredible as it seems, we’re now into October and Donald Trump remains President of the U.S.  Oyyy...
Anyway, some math from the week:

1)  Another brilliant math mind lost to us too soon last week, Vladimir Voevodsky at age 51:
h/t to Nalini Joshi for tweeting this fascinating 2013 Julie Rehmeyer piece on Voevodsky’s work:

2)  RJ Lipton and KW Regan pay tribute to Voevodsky and the even younger demise of Michael Cohen here:

3)  If you missed it, this math meme was making the rounds last week:
Solve carefully!
     230 - 220 x 0.5 =    ?     

You probably won't believe it, but the answer is 5!
[If the explanation doesn’t hit you in a few moments, look it up; shouldn’t be too hard find on Web.]

4)  A post sharing resources on the topic of ‘mathematics and music’:

5)  Evelyn Lamb’s latest “Tinyletter”:

6)  A new quite surprising paradox, “the bingo paradox”:

7)  Of Gelman’s 58 posts this week (…ok, so I exaggerate a bit) this one was probably my favorite (but only if you’re not sick of hearing about p-values, a topic he admits he’s “blogging to death”):

8)  Numberphile connects Fibonacci to Mandelbrot:

9)  Bit of an update on traveling salesman problem:

10)  H/T to Mike Lawler and Drew Lewis for calling attention to this interesting discussion (of a meme I had ignored because, as Alon Amit says, so many of these memes are trivial… but not this one):

11)  3Blue1Brown on neural networks (new video):

12)  and speaking of videos, The Unreasonable Effectiveness of Physics In Maths” is a new hour-long video several folks pointed out this week:

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

1)  If you didn’t hear it, this RadioLab treatment of the ’Trolley car problem,’ may be worth a listen:

2)  The always-interesting “Best-illusion-of-the-year” contest is back for 2017:

Friday, September 29, 2017

A Short-ish Potpourri

Between pickleball and what passes for politics in this country I’ve been pretty distracted this week, so a short potpourri:

1)  Futility Closet posed this classic logic problem:

2)  Math and music from Marcus du Sautoy:

3)  A(nother) guide to null hypothesis testing:

4)  “Likeable primes”…:

5)  My only post of the week touched on “fuzzy logic” with Bart Kosko HERE, and if you enjoyed that there's a much longer (2 hr.) audio piece with Kosko and Art Bell (yes, THAT Art Bell) from 2009 below (it's very good, covering a lot of interesting, interlocking topics):

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

1)  Fake news… we’ve only just begun (…aka, we’re screwed):

2) …and ICYMI, for any who still don’t believe in karma ;) :

Friday, September 22, 2017

A Math Mishmash To End the Week

Math to enjoy after 33 weeks of Amateur Hour in the Oval Office and on the golf course:

1)  Very brief article touching on math learning and ‘linguistic relativity’:

2)  “Persiflage” gets a few things off their chest:

3)  The September “Carnival of Mathematics” blog entry awaits you:

4)  “Computational Complexity” takes on a “FiveThirtyEight” Riddler problem:

5)  A nice listing of some math YouTube channels:

6)  Blackboards instead of desks…:

7)  Tim Gowers on the recent account of two infinities found to be equal:

…he may have been inspired in part by John Baez’s critical take here:

8)  Someone named Evelyn Lamb wrote some math this week (as she’s been known to do), including this piece on the work of Michael Pershan:

…speaking of which, a new interview (covering some diverse ground) from AMS with Dr. Lamb here:

9)  Keith Devlin pays tribute to Jonathan Borwein:

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

1)  Seems like every week now I have a favorite tweet (and followup comments), and this week it may be this one:

2)  ICYMI, the end of Project Cassini to Saturn, as reported here: