Tuesday, March 20, 2018

Taking In the Forest From Above...

(via Wikipedia)
As most have heard by now, Robert Langlands, at age 81 (and it’s always great to hear of an 81-year-old mathematician receiving an award! ;), is the winner of the 2018 Abel Prize in mathematics.  Robert’s work, the Langlands Program, is fascinating even if all you grasp is the broad outline of what it attempts to do, without much understanding of its complex details.  Here are 3 of the general audience pieces already out on this momentous occasion:

Alex Bellos in The Guardian:

Kevin Hartnett at Quanta:

Davide Castelvecchi for Nature:

I suspect over the next week there will be additional excellent articles appearing on this subject (I may or may not add other links here as they come along.)

For those with the background, a longer, more technical piece from AMS here:

For any who've never read it, or are unfamiliar with it, Ed Frenkel's "Love and Math: The Heart of Hidden Reality" introduces readers, to the Langlands Program, Ed's specialty.

And rightly or wrongly, this whole unification of mathematics notion, reminds me of a favorite quote from Keith Devlin I’ve used multiple times before (from an interview he once did for the NPR program “On Being” — and, not meant to imply anything about his own specific knowledge of Langlands):

"...that's when I became a mathematician; that's what I stumbled on at age 15 or 16 when here I was learning all this mathematics because I needed it. I had a utilitarian view of mathematics. I was learning it because I needed to solve the equations because I was going to be solving them in physics. And then, at the age of about 16 or 17, it all fit because it all came together in my mind. It was no longer this disjointed collection of techniques you could use to solve problems. It all fell into place, into this wonderful landscape. It was as if I'd been stumbling around in a forest, and suddenly I've climbed to the top of a tree and looked out and thought, this is the most beautiful place in the world. You can't tell it when you're down in the trees, which I had been, but the moment you reach an elevation where it all falls into place and you can see the whole topographic display in front of you, then the beauty is incredible. And the moment I discovered it, I said, um, I want to study mathematics. And I've been studying it ever since."

(...not sure of the specific credit for creation of this fun map, that has been passed around a lot, or I'd give credit?)

Sunday, March 18, 2018

Bernie's Self-control...

Sunday reflection:
"[Walter] Mischel has priceless videos from some of the early experiments that demonstrate the difficulty kids had in exerting self-control. There is one kid I am particularly curious about. He was in the toughest setup, in which the bigger prize, three delicious Oreo cookies, was sitting right in front of him. After a brief wait, he could not stand it anymore. But rather than ring the bell, he carefully opened each cookie, licked out the yummy white filling, and then put the cookie back together, arranging the three cookies as best he could to avoid detection. In my imagination, this kid grows up to be Bernie Madoff."
                                                             -- Richard Thaler in "Misbehaving"

Friday, March 16, 2018

Wednesday, March 14, 2018

A Sad Pi Day

In honor of Stephen Hawking today I’ll just link to perhaps my favorite Hawking story (granted it’s probably more of a Sean Carroll story). Most science buffs likely already know it, but in case you’ve missed it over the years:

Additionally, here’s an older lecture Dr. Hawking published in Plus Magazine about his work:

Tuesday, March 13, 2018

Math Story-Collider

H/T to Jim Propp for pointing out this current 'Story Collider' edition offering up two quite different narratives (with important messages) from Ken Ono and Piper Harron:

Transcripts of the talks are also presented, but give the under-15-min. talks a listen if you have the time.

Sunday, March 11, 2018

"the distilled essence of who we are"

Paul Lockhart expounds:

“And I'll go even further and say that mathematics, this art of abstract pattern-making — even more than storytelling, painting, or music -- is our most quintessentially human art form. This is what our brains do, whether we like it or not. We are biochemical pattern-recognition machines and mathematics is nothing less than the distilled essence of who we are.” 

Thursday, March 8, 2018

In Honor Of...

In honor of International Women's Day a few links I’ve posted here before, but seem especially appropriate for today:

…and Evelyn Lamb maintains this list of female math tweeters:

Lastly, a little nostalgia:

Sunday, March 4, 2018

Video Games Versus Boredom

Sunday reflection:

“Every maker of video games knows something that the makers of curriculum don't seem to understand. You'll never see a video game being advertised as being easy. Kids who do not like school will tell you it's not because it's too hard. It's because it's boring.”
— Seymour Papert

Wednesday, February 28, 2018


Every now and then the maze that the above slice comes from makes the rounds of the internet. Cliff Pickover put it out there again recently on Twitter. It was created decades ago by a Japanese janitor over a 7-year period (but only discovered ~5 years ago), and it can actually be purchased these days, probably more as a work of art than an actual puzzle maze (anyway, I’ve never heard of anyone solving it):

If you prefer your mazes a bit tamer, here’s another one from Cliff’s site:

And finally, a h/t to @MathematicsProf on Twitter who recently linked to this kinda cool/fun free maze generator, for creating your own:

Sunday, February 25, 2018

Music, Math, Dancing

Sunday reflection:
“Music was not so very different from mathematics. It was all just patterns and sequences. The only difference was that they hung in the air instead of on a piece of paper. Dancing was a grand equation. One side was sound, the other movement. The dancer's job was to make them equal.” 
                                                          ― Julia Quinn ("The Sum of All Kisses")

Thursday, February 22, 2018

An Old Joke, a New Book, and a 42-year-old Film Clip

On Twitter the other day, Eugenia Cheng mentions this as one of her favorite “math jokes” (I’ve never thought of it as a joke per se, but do agree it is a favorite quickie logic puzzle):

3 logicians walk into a bar, and the bartender asks, “Would everyone like a beer?
The 1st logician says "I don't know.”
The 2nd logician says, “I don’t know.
The 3rd logician says, “Yes.

Richard Feynman once somewhat famously said, “Philosophy of science is about as useful to scientists as ornithology is to birds.” It’s not an uncommon sentiment among scientists. Nonetheless I do find some aspects of analytical philosophy and philosophy of science interesting, and a recent volume snagged my attention...
After all, how could anyone resist a book with the title “Exact Thinking In Demented Times”… yeah, it sounds like a volume about our current spiralling-to-fascism era, but is actually a historical account by Karl Sigmund (a math professor) of philosophy’s 20th century “Vienna Circle”. The Preface is written by Douglas Hofstadter, usually a significant endorsement in itself, though it turns out Hofstadter played a major role translating this volume from Sigmund’s original German, so has a stake in the book.  
But I am enjoying the volume thus far (less than 100 pages in), and haven’t even yet reached any discussion of the ideas and interactions of members of the famed Vienna Circle, which is what I am most looking forward to.
Anyway, to pique your interest I’ll pass along this bit that entertained me, where Sigmund recounts Ludwig Boltzmann presenting an address to the Philosophical Society with the “bland title On a Thesis of Schopenhauer,” and then opening his talk... 
“with the offhand comment that he had originally intended to use a somewhat more provocative title, to wit: Demonstration That Schopenhauer Is an Insipid and Ignorant Philosophaster Who, by Ceaselessly Propagating Hollow Twaddle, Spreads Nonsense Far and Wide and Forever Perverts Brains from Top to Bottom.  Amusingly enough, Boltzmann was actually giving Schopenhauer some of his own medicine, for none other than Schopenhauer had used exactly these same phrases to rail against the arcane writings of George Wilhelm Friedrich Hegel. Not that Boltzmann cared one bit for Hegel either.”
(I’ll assume this is just as humorous in the original German…;)

I may say more about the 400-page volume in the future.
(An MAA review of the volume is HERE.)
[ADDENDUM:  I've now overviewed the book HERE.]


Lastly, speaking of demented times, and in honor of today’s young people (acting when grown-ups won’t!), some timely old cinema from the “I’m-a-human-being-goddamn-it-and-my-life-has-value” Dept.:

Tuesday, February 20, 2018

“Duck and Cover”

I grew up in the 1950s when our biggest fear in America was of a nuclear bomb blast -- though in reality, as a child, I felt few fears, and virtually none on a daily basis.

(ahhh yes, “worse than a terrible suntan”…)

I can’t even imagine sitting at a schoolroom desk, worried about being shot in the head (nor being the parent who must drop their child off at the school front door) — the daily reality of today’s students/parents — far scarier than my generation ever felt about the nuisance of a measly atomic bomb.

Sunday, February 18, 2018

Man vs. Computer

From Davis and Hersh (in "The Mathematical Experience"):
"To the philosopher, there is all the difference in the world between a proof that depends on the reliability of a machine and a proof that depends only on human reason. To the mathematician, the fallibility of reason is such a familiar fact of life that he welcomes the computer as a more reliable calculator than he himself can hope to be."

Thursday, February 15, 2018

“Tears In Heaven”

“Time can bring you down
Time can bend your knees
Time can break your heart
Have you begging please, begging please”

How can a nation, that so utterly fails safeguarding its children and youth, succeed into the future.…

(...to the Parkland, FL. victims, and the many, many, many, many more who will assuredly follow)

Wednesday, February 14, 2018

How Do I Love Thee…

Let me count the ways, employing the real numbers of aleph-one.…
(this might take awhile)

OK, actually for Valentines Day just a few (finite) links:

Starting with Ben Orlin covering it last year:

Jennifer Ouellette’s classic piece I used to link to every year, but haven’t for awhile (and ought not be missed):

…and lastly this from someone who’s gone completely ridiculously bonkers overboard:

Sunday, February 11, 2018

Mathematical Knowledge

From Ed Frenkel's "Love and Math":
“Mathematical knowledge is unlike any other knowledge. While our perception of the physical world can always be distorted, our perception of mathematical truths can’t be. They are objective, persistent, necessary truths. A mathematical formula or theorem means the same thing to anyone anywhere – no matter what gender, religion, or skin color; it will mean the same thing to anyone a thousand years from now. And what’s also amazing is that we own all of them. No one can patent a mathematical formula, it’s ours to share. There is nothing in this world that is so deep and exquisite and yet so readily available to all. That such a reservoir of knowledge really exists is nearly unbelievable. It’s too precious to be given away to the 'initiated few.' It belongs to all of us.” 

Tuesday, February 6, 2018

Miscellaneous RFI...

Some real miscellany for today!:

1)  start with some actual mathy-ness: 
The continuum hypothesis involves a well-known conundrum (considered undecidable without new set theory) among mathematicians over whether any infinite sets exist between aleph-zero and aleph-one. But I don't recall hearing any arguments over whether there could be infinite sets between any other alephs (say, aleph-three and aleph-four) — of course these higher sets are all power sets, but I can’t recall ever reading any “proof” that there can be no set in-between… I assume this is a long-settled simple question, but am not sure what the simple answer is! or is it somehow axiomatic with no real proof... or does it not even much matter since there's already an infinity of infinite sets???

ADDENDUM:  I've now posed this question to a local retired math professor/number-theorist and he didn't know the answer, so at least I feel better at this point that it may not be a simple or dumb question to ask! (but have not heard from anyone else)

2)  Next, no math, just a question that I asked on Twitter but got little response to, so will try here:
Google search has given me sporadically crappy results for several weeks (sometimes NO results, and sometimes results having no or little bearing on what I’m searching for), so I’ve switched over to Bing for now, but just wondering what search engines other math-types are happy with (it’s not a privacy issue or any other concern, strictly quality/relevance of results)? And are others experiencing issues with Google search — seems like some real glitch involved?

3)  Finally, just a note… Two of the the greatest television shows ever when I was younger were Carl Sagan’s “Cosmos” and Jacob Bronowski’s “The Ascent of Man.” I’ve sometimes used Bronowski quotes and videos here on the blog, and just as “Cosmos” was re-done a few years back I feel like “Ascent of Man” should be re-run or re-done for each new generation.
Anyway, I stumbled across Bronowski on the Web a few days back and suddenly realized that he was trained as a mathematician (somehow I had him pegged in my mind as a physical scientist). Also didn’t realize he had died at the age of 66 (much younger than I thought) just one year after “Ascent…” was completed in 1973. Additionally discovered that “Ascent…” was originally commissioned by Sir David Attenborough. Just all interesting tidbits to me… and here is Dr. Bronowski voicing some of his thoughts about mathematics:

Sunday, February 4, 2018

"Mathematics is the music of reason"

Paul Lockhart provides this Sunday reflection:
“Mathematics is the music of reason. To do mathematics is to engage in an act of discovery and conjecture, intuition and inspiration; to be in a state of confusion—not because it makes no sense to you, but because you gave it sense and you still don't understand what your creation is up to; to have a breakthrough idea; to be frustrated as an artist; to be awed and overwhelmed by an almost painful beauty; to be alive, damn it.”