...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, April 20, 2018

Some Math From the Week

My calls to the White House are still going un-returned, so I’ll divvy up some math instead:

1)  Ben Hambrecht on his decision to go work for Grant Sanderson and 3Blue1Brown:

2)  An online “first course” in Galois theory (h/t Gary Davis):

3)  As usual, Jim Propp’s monthly offering intertwines several interesting ideas at once while asking ‘What is a number?’:

4)  A report on the recent 13th “Gathering For (Martin) Gardner” (h/t Egan Chernoff):

5)  ICY somehow missed it, Evelyn Lamb’s first piece for Quanta, on an old graph theory problem and an amateur mathematician:

6)  Another take on the classic “two-envelopes” problem:

7)  Pension math:
8)  At Math-Frolic it was a week of posts (every day) primarily prompted by an old David Wells volume, “The Penguin Book of Curious and Interesting Mathematics” — a gem of a book!  If you missed any of the posts go catch up now.

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

1)  If language perception interests you, a fascinating little piece:

2)  And a couple of Twitter entries to end with:

a)  This long, uplifting Twitter thread (h/t to Keith Devlin for me, though no doubt many passed it around):

b)  And this one, because, well… koalas!:

Friday, April 13, 2018

Friday-the-13th Math Potpourri

Your guess is as good as mine as to who Cult-leader Donald might fire first this weekend, but I plan to stay busy catching up on some math morsels:

1)  5 book recommendations for philosophy of mathematics:

2)   A little math history (of the “when-will-I-ever-use-this” form) about Huygens and Leibniz (h/t Evelyn Lamb):

3)  Math, physics, geometry, symmetry… via Kevin Hartnett:

4)  Wonderful interview with Cathy O’Neil on the need for “a hippocratic oath with teeth” in data science; very timely with current Facebook woes (unfortunately, at end, I don’t feel, and she does’t sound, all that optimistic :-/ ):

5)  A follow-up to John Cook’s earlier post that every positive integer is the sum of 3 palindromic numbers (I don’t know, is it a stretch to say this almost has a Fourier transform ‘feel’ to it?):

6)  Natalie Wolchover interviews statistician Donald Richards:

7)  Scott Aaronson on some recent progress regarding a couple of open problems:

8)  Andrew Gelman takes a social psychology study to task over ‘truth versus inference’:

9)  For more math-reads, a wonderful new “Carnival of Mathematics” from Theorem of the Day:

side-note... am currently reading "The Calculus Story" by David Acheson -- new, slim little volume, bought on a whim, but halfway in am enjoying it more than expected as a succinct, clear introduction to basic calculus concepts for the right student or layperson.

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

1)  Last weekend Krista Tippett replayed her delightful “On Being” episode (from a few years back) with Helen Fisher on love, sex, relationships, the human brain:

2)  Occasionally, believe-it-or-not, Twitter can help restore one's hope in humanity:

Sunday, April 8, 2018

Weird Math

A book blurb today. Usually I’ve heard/read some buzz about books I receive review copies of in the mail, and then have built-in expectations. Occasionally though a volume shows up I’ve heard nothing about, nor even seen the authors names before. “Weird Math” arrived recently as such a book. The authors, David Darling and Agnijo Banerjee are a science writer and math prodigy pair bringing forth another compendium of some of math’s most interesting/intriguing topics for a general readership. 
The subtitle for the book reads, “A teenage genius and his teacher reveal the strange connections between math and everyday life.” Many of the topics involve pure or abstract math, so I question whether readers will see the connection to “everyday life” in many instances, though that doesn’t detract from the appeal of the topics.  

The chapters generally get more complex or deeper as they go along, the final chapter being on Gödel’s work, and the subjects are ones often covered in this potpourri type of math book: dimensions, probability, chaos, infinity, prime numbers, AI, topology, paradoxes, number theory, proofs… Each chapter is more-or-less self-contained, though you may want to read them in order just to follow the progression from easier to tougher material, and I personally enjoyed the second half of the book more than the first half.

The volume’s style/format very much reminds me of Matt Parker’s wonderful/successful Things To Make and Do In the Fourth Dimension,” a favorite offering from 2014 (I don’t really like the title of either book, but that’s a minor side-note). Parker’s fun volume is a longer, more engaging, better-illustrated, and more mathematical read, with the added benefit of Parker’s British wit/humor! — I especially recommend it for young people already enticed by, and comfortable with, mathematics (also splendid for teachers). “Weird Math” is a perfectly satisfactory volume, especially to introduce the uninitiated to this set of curious math topics without the intrusion of very much required math. Also, it has one distinct advantage being new enough that it includes information missing in older volumes: for example, coverage of recent artificial intelligence news around chess, poker, and GO playing robots. Or in a chapter on large numbers it includes several much larger than ‘Graham’s number’ (which, perhaps in my ignorance, I still thought of as the "largest" number).

More and better illustrations and a livelier writing style would have made this volume a more enticing read (though it’s hard to compete against Matt Parker), but as is, it’s still a fine volume to add to your math library shelf or to introduce a young person (or layperson) to this set of always-intriguing math topics if they're not already familiar with them.

Friday, April 6, 2018

Soooo Much Winning...

While our Aryan President was busy (in-between rounds of golf) consulting with his ass-kissing, rubber-stamping sycophants, er I mean, staff, I toiled alone authoring another weekly math potpourri:

1)  Math as a bedrock to life… this is a few weeks old, but I only came across it last weekend:

2)  Mathematical proofs and the mind, via “Mathematics Rising”:

3) The Conversation” looks at prime numbers:

4)  Rock-paper-scissors and game theory via Patrick Honner and Quanta:

5)  Catch up with Evelyn Lamb via latest issue of her monthly newsletter:

…she also has a new post on books here:

6)  A simple tutorial on statistical correlation:

7)  Some in-the-classroom thoughts:

8)  Andrew Gelman’s post for April 1, was dead serious:

9)  In case you didn’t get enough math tomfoolery on April 1, Nalini Joshi pointed out this older page where you can get plenty more:

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

1)  ICYMI, there appear to be 1000s of black holes at the center of our Milky Way galaxy:

2)  And from Twitter, no idea what this is exactly, but felt the need to pass it on:

Friday, March 30, 2018

ICYM Any of These...

In lieu of any new porn-star interviews to enjoy this weekend, I'll offer up instead another math potpourri:

1)  Free, online course on applied category theory:

2)  Every positive integer the sum of 3 palindromes:

…another John Cook post, on probability and juries:

…and one more from John, this week, on the normal distribution:

3)  Perhaps one of my favorite “favorite spaces” from Evelyn Lamb (though it’s hard to choose):

4)  Latest edition of the IntMath Newsletter:

5)  KW Regan discusses American chessmaster Fabiana Caruana, upcoming challenger to world champion Magnus Carlsen, and asks if there’s such a thing as a ‘hot hand’ in chess:

6)  Latest from Grant Sanderson (3Blue1Brown):

...and a new one from Infinite Series as well (on tangles, knots, & biology):

7)  Erica Klarreich on some inductive proofs:

8)  And much more mathiness via the latest (40th anniversary) online issue of The Mathematical Intelligencer (h/t Brian Hayes):

9)  As if I don’t have enough to read right now, Steven Strogatz this week pointed out a forthcoming volume of the letters of Freeman Dyson

(which reminds me in turn of Richard Feynman’s older book of letters, Perfectly Reasonable Deviations, compiled by his daughter, that, despite much mundane content, I think lends a better overall sense of Feynman the person than his more embellished autobiographical work, which often gets criticized).

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

1)  Is psychology’s “replication crisis” bleeding over to biology…:

2)  And, from the Dept.-of-Sudden-Cardiac-Events, this gave me a chuckle:

Sunday, March 25, 2018

More Book Looks…

When it rains, it pours… books. Around the first of January I resolved to read fewer books than usual this year, and free up that time to work for the overthrow of the despotic/maniacal regime masquerading in Washington ;)…  didn't consider it a difficult resolution since the stream of popular math books in 2017 seemed below average, and I thought that trend might continue forward. BUUUT, it’s not even April and a number of books have already caught my eye:

Recently enjoyed and reviewed Exact Thinking in Demented Times by Karl Sigmund (from 2017):  

And books already in the queue include:

Skin In the Game, latest from Nassim Taleb   
As a counterweight to Taleb ;) I may read Richard Thaler’s older volume, Nudge too.
Closing the Gap (on prime numbers) from Vicky Neale has gotten good reviews and looks enticing.

Sabine Hossenfelder’s upcoming Lost In Math is more physics than math, but certainly of interest. 

Recently received a review copy of Weird Math by David Darling and Agnijo Banerjee, having heard nothing about it beforehand, but just leafing through it, looks possibly interesting also.    

Two other 2018 volumes of some interest:
Reverse Mathematics by John Stillwell    
Music By the Numbers (forthcoming) by Eli Maor   

(...and, as a sidebar, trying to squeeze in Robert Wright's Why Buddhism Is True somewhere along the way as well.)

In short, so many books, so little time….

Tangentially, a person on Twitter started a #WorldviewIn5Books hashtag for folks to list 5 books that somehow represent their personal “worldview” (whatever that means to you -- and not necessarily favorite books, but ones that capture your outlook on the world):

It naturally generated LOTS of widely-varied, interesting choices, perhaps worth a look.
[ADDENDUM: one of the works I was unfamiliar with and which the above lists led me to (and I’ll pass along), is Eliezer Yudkowsky’s Rationality: from AI to Zombies which looks very interesting to me; so thanks for that!:
I've previously posted here lists of favorite popular math books, and a list of books I'd take to a desert island, but picking just 5 choices that somehow represent a worldview is much harder. I eventually settled on an idiosyncratic set for my own list:

Beyond the Hoax — Alan Sokal
Natural Prayers — Chet Raymo
Animal Liberation — Peter Singer
Who Knows? — Raymond Smullyan
Language In Thought and Action — S.I. Hayakawa

With two others as close runners-up:

The Pleasure of Finding Things Out — Richard Feynman
Pilgrim At Tinker Creek — Annie Dillard

Anyway, a sort of fun exercise to think about.

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: