...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, March 23, 2018

Friday Potpourri

From Donny’s standpoint tomorrow may be the perfect Saturday for a long-awaited massacre; but I think it better for catching up on some mathy reading from the week:

1)  A nice visual introduction to statistics for the right age group or knowledge level (h/t Max Roser):

2)  Tying together math illiteracy and politics:

…and another piece on teacher Eddie Woo (h/t Egan Chernoff):

3)  Wonderful interview via Erica Klarreich elucidating “Proofs From THE BOOK”:

4)  H/T to Jim Propp for pointing out this recent great David Kung video from the Museum of Mathematics on “mind-bending paradoxes” (it’s long but wonderful and well-worth it, and may give teachers some ideas for the classroom):

(the entire series of “Math Encounters” talks at MoMath look great)

5)  The mathematics of Gabriel’s Horn:

6)  When Andrew Gelman writes that “the emperor has no clothes” he is one of the few NOT referring to Donald Trump:

7)  An old ETS ratio problem via David Marain:

8)  NOT at all math, but folks know I'm a Scott Aaronson fan, and yesterday Scott posted a long review of Steven Pinker's latest offering (I don't personally read any of Pinker's non-language/linguistic stuff, but still really appreciate Scott's take on this):

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

1)  Linguistic illusions… I found this recent YouTube video interesting:

2)  And keeping with a language theme, also enjoyed this recent Vsauce video using a Venn diagram to talk about words:

I stumbled upon the above video, by the way, after seeing this Vsauce tweet from the week:

Friday, March 16, 2018

Another Mishmash of Picks from the Week

This week, while the Donald was hearing the ever louder-growing theme from "Jaws" playing in what passes for his brain, I was busy composing another math potpourri:

1)  Fascinating bit on math whiz Erik Dermaine and origami (h/t  Earl Samuelson)

2)  The math of reel-to-reel tapes from the always interesting, unpredictable “DataGenetics” (h/t Patrick Honner):

3)  5 books focussed on women in mathematics:

4)  The logic of “common knowledge” from “Point of Infinity”:

5)  Of course a lot of mathy pieces about the NCAA basketball tournament (“March Madness”) in the last week; this was one of them:

6)  Also, of course, a LOT of posts on Wednesday in honor of Pi Day. This was the take from FiveThirtyEight):

…and for those with some spare time for computing pi out, Ben Orlin offers a few alternative ways to do so:

…OR, if Pi Day leaves you feeling a bit curmudgeonly, then this Evelyn Lamb view may be for you:

7)  That mysterious connection between math, pi, and physics:

8)  Rob Eastaway takes the old, popular 9-dot problem and gives it a fresh look:

9)  Checkers, Chess, Go… now AI is taking on ‘March Madness’:

10)  If it’s assistance in economics research that you’ve been looking for, consider your need filled ;):

11)  ICYMI, last weekend I interviewed blogger Dr. James Dilts:

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

1)  Just one of those weird/fun/quirky stories that we all need just to get through a typical day anymore:

2)  I’ve linked to this TED parody talk before; perhaps worth doing so again:

Sunday, March 11, 2018

James Dilts.... mild-mannered mathematician and blogger

Math-Frolic Interview #43

"[James Dilts] works as a mild-mannered mathematician by day and as… well… a mild-mannered mathematician by night. The Missus disputes the mild-mannered part. Despite the best efforts of his middle and high school teachers, he discovered that math is awesome, and has decided that everyone else needs to know this too. His academic research is some combination of general relativity, differential equations and differential geometry, which he promises is super cool. He has an Erdös number of three."

                                           -- from James Dilts' blog

Dr. James Dilts is the proprietor (with his wife) of the "Infinity Plus 1" blog which I  stumbled across a bit over a year ago, and have enjoyed since. His posts aren't particularly frequent, but always cover some interesting, and sometimes difficult or unpredictable topic, in a lively, entertaining, well-planned-out fashion (with "the Missus" adding the illustrations). He definitely has a knack for writing. While currently a west-coast post-doc, he has plans to leave the "panic mode" of academia for possible opportunities in computer programming. And here's more:


1)  Tell us a little about your background that led to a major in mathematics.

Honestly, I have no idea how I ended up as a math major. My family growing up was more science-y than most. (My 3 older brothers are all programmers, for instance.) But, I didn't have any particular role models at all. I didn't know a single professor. I'm not even sure how I learned that "mathematician" was a valid job! But, sometime in high school, I decided I wanted to do research, and figured that I'd try math first, and if that didn't work, switch to physics or chemistry. I went to Brigham Young University for my undergraduate, and my first year there I took the intro to proofs class. I loved it! When we covered Cantor's diagonalization proof (available on our post "A bigger infinity"), I knew that I wasn't going to switch to physics.

2) Is there any particular backstory to the name of your blog, “Infinity Plus 1”?

When I decided to start writing the blog, we of course wanted a name that was light-hearted and memorable. And every kid has, at some point, tried to pull out "infinity plus one" to win an argument, so it seemed like a good fit. It also was a great segue into our first posts, where I wanted to talk about Cantor's diagonalization proof, for obvious reasons.

3)  Your posts always have a light-hearted feel to them, even when you’re dealing with difficult, abstract ideas.  I get the feeling you have a lot of fun writing them. Do you have a couple of favorite posts that were especially fun or satisfying to write? And do you have any idea which posts have been most popular with readers?

The most popular question is easy. Every time we've written a biography post (for Cantor, Schwarzschild, and Godel), they've always been more popular than the rest. The Godel post, in particular, got picked up by some service, and ended up with about as many views as the rest of the posts combined!

Oh, I'm bad at "favorite" questions. I've only written posts about topics I feel passionate about, and that I think are super interesting, so it's kind of hard to pick. Well, if I have to pick, let's pick the black hole posts, of which there are a few, starting with Black holes suck. Black holes are something that lots of people know about, but very few people actually understand. It doesn't help that the mathematics uses graduate level geometry... So, in those posts, I got to talk about the actual mathematics behind these super cool objects, and talk about all the interesting things we still don't know. (Really, there are a ton of questions left about black holes, which I never got to cover. Ah well.)

4)  Who are some of your own favorite math/science writers (or, feel free to mention writers of any sort who have been important to you)?

Honestly, I've gotten most of my information from class and textbooks and talking to professors, even the fun stories. But probably the most important science writer for me was Isaac Asimov. Most people who've heard of him know him for his science fiction, which I love. But he also had a PhD, and wrote a lot of science essays about all sorts of topics, from mathematics to physics to nuclear chemistry to why it's a tragedy we have a moon. Sure, none of the science is up to date anymore, but I'd still recommend his essays to anyone. His style was always light-hearted, and though I didn't think about it till now, I'm confident he heavily influenced my own writing.

[...interesting, I grew up when Asimov was the most prolific science-writer around, but I rarely hear his name brought up anymore, except maybe in science fiction circles; as some folks know, he was also quite a limerick-writer, but I won't go there ;)]

5)  You write that “My research is focused on the Einstein constraint equations, a coupled system of non-linear elliptic equations, and related geometric problems, such as the (conformally) prescribed scalar curvature problem. The main goal is a complete parametrization of the set of solutions of the constraint equations.”

Is it possible to put that in more layman terms? ;)
And is this an area that involves more strictly abstract or pure mathematics, or applied math as well?

In normal, Newtonian gravity, initial data is arbitrary, which means that you can plop down planets wherever you want, and feel free to evolve them. Newtonian gravity won't break. But relativity is different. In general relativity, your initial state of the universe has to satisfy certain conditions, and those conditions are the Einstein constraint equations. Now, unlike some equations, there are a lot of solutions to the constraint equations. 

One goal is to try to understand all the possible solutions to the constraint equations. One way to approach that is to try to parameterize all of the solutions, which means that if you give me some inputs x, y, and z, then I can turn around and give you a unique solution. That turns out to be a difficult problem. My research has focused on trying to find ways to show that the equations do or do not have solutions for certain inputs. 

It's a pure mathematical question, but numerical techniques have been helpful. Relatively recently, we realized that no one really knew what the right thing to try to prove was, which makes it really hard to prove anything. It was a huge road block. So, we used some numerical techniques to figure out what was going on, which turns out to be much more complicated than anyone had thought.

6)  I believe you’re currently job-hunting (coming off of a post-doc) and looking more into computer programming… say a little about what you’re most looking for in a new position or in the future?

I want to continue to work on interesting problems. A lot of programming jobs are just making another app, or working on the company's website and backend. Those are important jobs, but not what I want to do. Programming can be a powerful tool for investigating difficult questions, as I saw in my research, and my ideal job would let me contribute to that.

7)  Besides your blog, are there any social media or other websites where readers can particularly look for you?

I'm actually anti-social media! I have a Facebook page and a Twitter for the blog, since many people want to receive them in that way, but I'm otherwise completely off of Facebook and Twitter and all the usual culprits. I'd much rather spend my time on more important things.

8)  When you’re not doing mathy sorts of things, what are some of your favorite activities/hobbies/interests?

I'm an avid rock climber and unicyclist. I also love reading, especially classic science fiction, and playing games of all sorts. Of course, a lot of my time is spent making sure the Epsilons [my kids] don't destroy the Missus!


Thanks for participating here James, and take care to keep your rock-climbing and unicycling separate, OK! ;)
Hope too you find what you desire in a computer career, and hope your clear talents for writing and explaining continue as well in some form!
If you've never read James' blog before, definitely check it out; you're in for a treat!
(His list of posts/topics is HERE.)

Friday, March 9, 2018

This Week's Potpourri

While The Obstructor-and-Chief was experiencing a rather Stormy week, I was compiling more math bits:

1)  Approaches to teaching mathematics:

3)  “The Best Question to Always Ask When Learning Mathematics”…:

4) The power of compound interest via DataGenetics:

5)  Somewhat bizarre application of prime numbers in a paper (a couple years back) that was cited by some folks in the Twittersphere this week:

7)  Plus Magazine celebrated International Women’s Day with a lot of interesting links:

8)  Laura Taalman has a Favorite Theorem:

9)  New post from Keith Devlin today:
10)  On Tuesday, here at MathTango, I reviewed a recent volume:

…and on Sunday, right back here, I’ll have a new interview posted, so please do return for that.

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

1)  Seems like good advice worth passing along:

2)  If you're not already familiar with it, NASA has a cool 'live feed' YouTube channel for the International Space Station:

Tuesday, March 6, 2018

"Demented Times," Indeed -- a book review

A book blurb today.... (I mentioned this volume briefly a couple weeks back):

Exact Thinking In Demented Times” is a wonderful title that sounds very apt for current times… but in fact it’s the title of a volume from mathematics professor Karl Sigmund recounting philosophy a century earlier in Europe. The subtitle is: “The Vienna Circle and the Epic Quest for the Foundations of Science.” For any who don’t know, the Vienna Circle was a group of philosophers and scientists who regularly discussed logical positivism and analytical philosophy underlying science (and stood largely in opposition to metaphysics). They included some of the dominant academics and intellectuals of their time.
Like several books I’ve reviewed here over the years, this is more a volume at the fringes of mathematics, than about math itself or doing mathematics. I loved this volume, but one’s enjoyment will hinge on having some inherent interest in the philosophical thought and luminaries that dominated 20th century European philosophy.

This is my first strong book recommendation of 2018, but worth noting it actually came out in the English version toward the end of 2017, and the original German version was even out in 2016. Renowned Douglas Hofstadter wrote the Preface for this edition, and he apparently had much to do with the German-to-English translation as well.

Among the many names that frequent these pages are:

Ludwig Wittgenstein
Bertrand Russell
Kurt Gödel
Karl Popper
Moritz Schlick
Ludwig Boltzmann
Rudolf Carnap
Hans Hahn
Albert Einstein
Friedrich Waismann
Otto Neurath
David Hilbert
Karl Menger

…and many more

I was mainly interested in this volume to read more specifically about the 1) ideas and 2) interactions/personalities of the members of the so-called “Vienna Circle.” The book fulfilled the second of those wishes, but less-so the first. Like other things I’ve read about the Vienna Circle, this volume skirts above the surface of the nitty-gritty philosophical arguments/ideas that resounded back in the day. It may simply be the case that getting down into the weeds of deep philosophical arguments would make for dry, boring reading and is thus voided. The narratives, personalities, and history are what make this a fascinating volume.

The first four chapters (or ~100 pages) are essentially background to the Vienna Circle before the next two chapters really begin discussion about the Circle itself. The next couple chapters veer off again to some elements tangential to the Circle. The second half of the book (my favorite half) returns in large part to a focus on the interactions/clashes/personalities of the Circle members and associates. In total I suspect one third to one half of the volume is concerned with people or history outside the Circle (for example, there is a lot of material on Karl Popper, though he was never an actual member of the Vienna Circle itself).

I more-or-less fathom the fame of Russell, Popper, Gödel, and Carnap, but not as clearly that of some of their contemporaries, and this work doesn’t make some of the other prominent names any more scrutable to me. In particular, I’ve never quite grasped what, beyond a blustery, assertive style, made Ludwig Wittgenstein such a towering figure in 20th century philosophy (interesting, yes, but why so dominating?) — and this volume doesn’t flesh that out any further for me (despite the many pages devoted to him).
Still, overall, this is a highly enjoyable, rich read. 

Finally, I must offer an additional reason to read this historical account — it very much reminds one of the broader events of the world, principally Europe, in the 1930s (and how easily/quickly democratic institutions can be undone in troubled times), which eventually led the world to exclaim in unison, “NEVER again!” A reminder… which today… is very timely.

[Alan Lightman reviewed the volume for the Washington Post here:

Friday, March 2, 2018

Friday Potpourri

While attempting to compute just how fast the revolving door at the White House was spinning this week, I compiled another set of math bits:

1)  A listing of some free online math courses:

2)  3Blue1Brown takes on the Uncertainty Principle:

3)  Lots of ideas for teachers from “Math = Love”:

4)  Of math and recent movies…:

5)  Applied group theory via Peter Woit/Greg Moore:

6)  Another young math prodigy:

7)  h/t to Frank Harrell pointing to this recent piece on Bayesian inference:

8)  “Hybrids” in mathematics, from “Mathematics Rising”:

9)  NovaPBS ran “Prediction by the Numbers” this week, their introduction to probability and forecasting:

10) The latest from unpredictable mathemusician Vi Hart:

11)  Another podcast with Eugenia Cheng:

13)  If you need still more to read, another whole set of links from David Eppstein:

...also David lists 64 female mathematicians on Wikipedia here:

...and at another site, 32 women in statistics and data science:

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

maybe just a couple of tweets to end with:

1)  It's looking like Anthony Weiner may be loose in the UK, but those Brits can handle it:

2)  less certain if we can handle things:

Friday, February 23, 2018

For Those Wanting Math Instead of MaraLago on the Weekend

Short Potpourri this week, as I’ve been too busy watching NRA officers and our knuckledragging Groper-and-Chief pretend, against all evidence to the contrary, that they have human feelings…

1)  Brief NY Times book blurbs on statistical inference:

2)  I was a bit surprised by how many and varied comments this Cliff Pickover algebraic tweet generated:

3)  If you have dual interests in music and math you’ll want to read Evelyn Lamb’s review of a recent book on such:

4) Seven Questions With Francis Edward Su”… a short interview with Dr. Su, with wonderful questions!:

5)  Patrick Honner is the latest guest on My Favorite Theorem:

6)  Brian Hayes wrote briefly of some older books HERE, and I blurbed about a recent volume yesterday.

side-note: I don't visit Terry Tao's blog often (not having the math chops for it), so not sure how long ago this happened, but when I stopped by this week his blog banner had changed to a quote from the Statue of Liberty:

“Keep, ancient lands, your storied pomp!” cries she
With silent lips. “Give me your tired, your poor,
Your huddled masses yearning to breathe free,
The wretched refuse of your teeming shore.
Send these, the homeless, tempest-tossed to me,
I lift my lamp beside the golden door!”

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

1)  Interesting Slate Money Podcast last weekend on cryptocurrencies:

2)  Last week TED Radio Hour ran (or re-ran) the story of Daniel Kish, who, blind from early on, developed his own click/echolocation technique for navigating the world (and now teaches the method to other blind people). I’ve linked to his story before, and still consider it one of the most phenomenal, almost incomprehensible, stories of human behavior/ability I’ve ever heard:

Friday, February 16, 2018

Another Weekly Mathy-mix

In the event li'l Donald wanted to read some math this weekend, I compiled a few things:

1)  Banach-Tarski patiently explained (…by someone needing a job):

2)  "Linguistics Using Category Theory" via John Baez (a bit heavy reading requiring some understanding of category theory, but potentially interesting):

3)  Patterns?… “Mystery and Music of the Kaprekar Constant”:

4)  “Orthogons” via Brent Yorgey (h/t Patrick Honner):

5)  Probabilistic judgements via Quanta Magazine:

6)  Dave Richeson learning some math from his son’s Algebra 2 class:

7)  Tanya Khovanova offers a puzzle for our times:

8)  The latest issue of online journal Inference has some math-related content:

9)  Tangential to math, Scott Aaronson took a Wash. Post writer to task (on quantum computing) leading to a slew of comments:

10)  For those of you with mathematician spouses, Ben Orlin offered Valentine poems this week that could melt their hearts (… or… maybe NOT):

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

1)  The disappearance of airline flight MH370 is surely one of the greatest mysteries of my lifetime… and, we’re told, it could happen again (h/t Mike Lawler):

2)  Sabine Hossenfelder tweeted out this helpful, graphic link to rhetorical and logical fallacies this week:

Friday, February 9, 2018


While the Colluder-In-Chief tries to consolidate his fiefdom and schedule parades, I consolidated some math offerings:

1)  Yet another profile of mathematician/hedge fund manager Jim Simons:

2)  Do Google searches predict Bitcoin prices?:

3)  Patrick Honner back in Quanta Magazine (on vaccines):

4)  Did you miss e Day?… Ben Orlin celebrated!:
(if you missed it, it will come around again in Europe later this year)

…and of course Evelyn Lamb will never miss any mathy-excuse to celebrate either:

5)  Statistics crash course:

6)  Tanya Khovanova asks… and answers “Why?”:

7)  More of Keith Devlin on math education and math application:

8)  Videos from the San Diego Joint Math Meetings in January have now been posted:

9)  hmmm... flipped classrooms... how about flipped conferences (goes beyond just math conferences):

10)  And a little bit of math weirdness from Futility Closet:

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

1)  The latest, and last, ‘annual question’ from John Brockman’s “Edge”:

2)  will end with yet another guitar rendition of Pachelbel Canon (…before an Executive Order gets issued commanding that we all listen to Wagner):