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Wednesday, August 16, 2017

If I Had A Hammer

Sorry, I’m in a mood (someone put me there), so just a bit more music for the moment (‘cuz as bad as the 60’s were, they seem glorious compared to today):

Sunday, August 13, 2017

American Tune...

“And I don't know a soul who's not been battered
I don't have a friend who feels at ease
I don't know a dream that's not been shattered or driven to its knees
But it's alright, it's alright, for we live so well, so long
Still, when I think of the road we're traveling on
I wonder what's gone wrong, I can't help it I wonder what's gone wrong”

Category Theory via Eugenia Cheng

For Sunday reflection, Eugenia Cheng describing 'category theory':
"This is how category theory arose, as a new piece of math to study math. In a way, category theory is an ultimate abstraction. To study the world abstractly you use science; to study math abstractly you use category theory. Each step is a further level of abstraction. But to study category theory abstractly you use category theory."

Thursday, August 10, 2017

"the psychology of unspeakable truths"

I hope you've already seen it, but in case not, Scott Aaronson's latest post is both a thoughtful tribute to A.N. Kolmogorov and a somewhat stoic commentary about the world we  find ourselves in:

...an important read, though not for any math.

Tuesday, August 8, 2017

In Case I’m Banished to a Gulag

People love… and... hate, lists… at least they’re a fun time-and-space-filler, so I've been thinking about which books I’d grab off the shelf if Donald Trump, in his wisdom (spelled “p-a-t-h-o-l-o-g-y”) decided to banish me to a remote Gulag, only letting me take along 10 of my math-related books; which ones might I grab quickly for sustenance and entertainment? In no particular order, here’s what I chose (some aren’t particularly mathy though):
a) The Colossal Book of Mathematics  — Martin Gardner (...so much fun and games and puzzlement!)
b) How Mathematicians Think — William Byers  (...a long time favorite of mine about ideas permeating and underlying mathematics)
c) The Outer Limits of Reason — Noson Yanovsky  (...my favorite volume from the last few years, weaving together so many important subjects)
d) How Not To Be Wrong — Jordan Ellenberg  (...popular best-selling treatment of mathematical thinking)
e) Things To Make and Do In the Fourth Dimension — Matt Parker  (...jaunty, wise, diverse, instructive topics)
f)  Love and Math — Ed Frenkel  (...fascinating bio and intro to the Langlands Program)
g) Math In 100 Key Breakthroughs — Richard Elwes  (...succinct overview of key math topics)
h) The Music of the Primes — Marcus du Sautoy  (...'cuz I gotta have one volume devoted to the Riemann Hypothesis)
i)  Metamagical Themas — Douglas Hofstadter  (...some of the best stuff from Hofstadter's fertile mind)
j)  Beyond the Hoax — Alan Sokal  (...not math, but rich overview of critical thinking and much more)
Oddly two of my favorite math expositors, Keith Devlin and Ian Stewart, didn’t quite make the cut, though I’ve happily read more of their books than any of the above authors. Nor does it include the single volume I still most frequently recommend to lay people: Strogatz’s “The Joy of X.”  And a lot of other wonderful picks, including some older classics, go unmentioned as well.
Admittedly, an eclectic list, framed to my interests, that wouldn’t satisfy many of the math-folks likely beside me at the Gulag. Oh well, at the very least I suspect I'd have the company of Devlin, Ed Frenkel, and John Allen Paulos along to help entertain me! ;) (...and probably many more of you as well; hey, maybe even Andy Borowitz would be there to keep us all in good humor).

Monday, August 7, 2017

Sunday, August 6, 2017

Math Methods Versus Math Tricks

This week's Sunday reflection comes from Jim Propp in a recent Web piece:
"Mathematicians are people who like solving problems, and have the persistence to work on problems that take time to solve, and have collected a mental tool-kit consisting of methods that have helped them solve problems in the past. Some mathematicians distinguish between methods and tricks. A method is a tool that solves more than one problem, while a trick is a tool that applies to only one. Under this definition, I’d say that there are no tricks in math, and part of the discipline of getting good at math is to study every trick you encounter until you see the method hiding inside it."

Thursday, August 3, 2017


James Grime is a bit deranged in this recent Numberphile episode (or maybe he's a bit deranged in any Numberphile episode… and I mean that in a good way!):

Monday, July 31, 2017

Claude Shannon… & Guest Posts Anyone?

Newly out, “A Mind At Play,” a biography of Claude Shannon:
(the title seems to be a play on Siobhan Roberts very successful/excellent bio of John Conway entitled “Genius At Play”)
Also, John Horgan has posted a piece on the bio and on Shannon’s life (including an old interview):
Meanwhile... I’m having limited time to devote to blog posts at moment with too many summer things intervening, but if anyone is interested in writing a math-themed “guest” post for either here or MathTango, let me know [sheckyr[AT]gmail…] and I’d consider that to pick up some of the slack! Just let me know what you have in mind (...please, no proofs of the Riemann Hypothesis, P vs. NP, etc. ;)

Sunday, July 30, 2017


From a recent Michael Harris essay:
“The ideology of mathematical certainty and objectivity is our most potent weapon; we should not allow it to be used to undermine democracy. With regard to mathematical modeling, we should constantly remind anyone who is willing to listen that a model is not objective or scientific just because it is mathematical.”

Thursday, July 27, 2017

Michael Harris Asks "Do Mathematicians Have Responsibilities?"

H/T to Peter Woit for pointing out this provocative piece from Michael Harris (author of "Mathematics Without Apologies") on Reuben Hersh, politics, Embodied AI, and mathematics: 

Tuesday, July 25, 2017

Replicate THIS

If you missed it, last week’s NPR’s “On The Media” show included a nice segment (number 2 out of 4) on the ongoing replication problems in psychology:

Sunday, July 23, 2017

Real Numbers... not simple at all

a reflection on the reals...:

"The metaphor of the real numbers as a line... is very simple and self-evident. In fact, the identification of the real numbers with the picture of a line is almost too simple because it gives people the impression that the real number system itself is simple and easily understood. Yet real numbers are not simple at all -- in fact, real numbers are one of the most complex creations of the human mind. Even today, all kinds of questions about real numbers are not understood, and remain unresolved."

-- William Byers in "The Blind Spot"

Thursday, July 20, 2017

Prime Stuff...

Always elusive prime numbers...

1) Super piece from Kevin Hartnett in Quanta today about the work of Kaisa Matomäki on prime factors and related ideas:

2) ...and timely, as it follows up on a new Numberphile video yesterday with James Maynard on prime gaps:

3)  And earlier in week Evelyn Lamb pointed out this fun li'l excursion into prime numbers I'd missed from a few weeks back:

Wednesday, July 19, 2017

Robert Langlands

Wonderful piece on Robert Langlands... not sure what the date on it is (I assume recent?), but h/t to Graham Farmelo for pointing it out on Twitter:

Sunday, July 16, 2017

In Memoriam

For Sunday reflection, this from Maryam Mirzakhani in a prior Guardian interview (re-published from the Clay Mathematics Institute):
“…the most rewarding part is the ‘Aha’ moment, the excitement of discovery and enjoyment of understanding something new – the feeling of being on top of a hill and having a clear view. But most of the time, doing mathematics for me is like being on a long hike with no trail and no end in sight…. 
“I don't think that everyone should become a mathematician, but I do believe that many students don't give mathematics a real chance. I did poorly in math for a couple of years in middle school; I was just not interested in thinking about it. I can see that without being excited mathematics can look pointless and cold. The beauty of mathematics only shows itself to more patient followers."
[also see yesterday's posting ]

Saturday, July 15, 2017

"A Light Was Turned Off Today..."

VERY sad news today in the math world with the announcement of mathematician/Fields Medalist's Maryam Mirzakhani death from cancer at the all-too-young age of 40. When I see some more lengthy tributes to her posted I’ll add some links below. For now I'll pass along Erica Klarreich's profile from a few years back... and, a Neil Diamond oldie:


Terry Tao posted this:

This from Stanford University where she was a professor:

The New York Times obituary now here:

This from The Guardian:

And Evelyn Lamb weighs in here for Scientific American:

And John Baez on Google+:

The wonderful Siobhan Roberts in the New Yorker:

Sunday, July 9, 2017

Fearing the Wrong Things

Sunday reflection from David G. Myers in John Brockman’s volume “Know This”:
“News-feed images can make us excessively fearful of infinitesimal risks. And so we spend an estimated $500 million on anti-terrorism security per U.S. terrorist death but only $10,000 on cancer research per cancer death. As one risk expert explained, ‘If it’s in the news, don’t worry about it. The very definition of news is ‘something that hardly ever happens’…. 
“Media researcher George Gerbner’s cautionary words to a 1981 congressional subcommittee ring true today: ‘Fearful people are more dependent, more easily manipuated and controlled, more susceptible to deceptively simple, strong, tough measures and hard-line postures.’ 
“Ergo, we too often fear the wrong things. And it matters.”