Encryption and Uncertainty...

Two tidbits I encountered in the last 24 hours that I found interesting, and so am passing along (perhaps, in some odd way, there's even a tiny thread of linkage between the two!??):

1)  RSA encryption researchers make "an astonishing find" (essentially that encryption keys aren't nearly as random as one might expect):
http://www.pcworld.com/article/2897772/researchers-find-same-rsa-encryption-key-used-28000-times.html

and,

2)  Ed Frenkel advocating the importance of human uncertainty in science (I couldn't agree more) -- even scientists who acknowledge uncertainty, nonetheless often fall into the trap of assuming certainty about specific matters. The epistemological nature of uncertainty is difficult to internalize (I think) because we must operate in our daily lives as if we are certain of a great many things... but this ought not detract from the importance of recognizing uncertainty in a scientific perspective... anyway, read Ed and the Facebook discussion that follows (be sure to click on "See More" to expand Ed's full initial response):

http://tinyurl.com/ljam3lm

p.s.  -- the Lawrence Krauss New Yorker piece that is referenced (and inspired Ed's response) is here:
http://www.newyorker.com/news/news-desk/teaching-doubt?intcid=mod-latest 

Make It An Ed Frenkel Weekend

Ed Frenkel

NOT Ed Frenkel

'Some truths are out there...'  -- Edward Frenkel

The hottest ticket in mathematics these days surely must be Ed Frenkel!

Yesterday I offered plenty of mathy links for the weekend over at MathTango (including a podcast with Ed)… but when you're done with those, carve aside another hour+ for the below video of Dr. Frenkel giving a public presentation (for about 20 minutes) at the LA Public Library before Chris Carter of X-Files fame joins him on stage (and later they take questions from the audience) -- I absolutely LOVE this whole talk which covers a lot of ground, but nothing too technical! (my favorite video yet involving Dr. Frenkel). If you don't find it inspiring, well, you may need to go have your pulse checked ;-)

Edward Frenkel and Chris Carter: Love, Mathematics and The X-Files from ALOUDla on Vimeo.


[p.s. -- as I watched this I suddenly couldn't help but think how much Dr. Frenkel resembles David Duchovny! ;-) -- above pics, Frenkel from his Google+ page and Duchovny from Wikipedia]

Secondly, in a 15 minute NPR "Snap Judgment" segment Frenkel describes his incredible, inspiring math upbringing in the then Soviet Union (even if you've read or heard of his Russian background before, again, I recommend listening to this wonderful narrative):

http://tinyurl.com/oxdpym7

LA Times, The Atlantic… The Message of Math Going Mainstream

Ed Frenkel's latest piece for the LA Times, with his message of bringing math appreciation (and ability) to a wider circle of students, has already been cited quite a bit around the Web, but in case you missed it:

http://tinyurl.com/l5l3czc

In it he notes that, "...abstraction is all around us — and math is the language of abstraction...
"For the next generation to operate effectively, they must gain proficiency with abstraction, and that means mathematical knowledge plus conceptual thinking times logical reasoning — all things that a wider view of math would bring to the math classes at our schools."

Others frequently talk about this same focus on abstraction in terms of 'pattern recognition,' and in turn, many now use that focus on patterns to stress engaging children in math via their natural, playful interest in patterns.

The Atlantic had a great piece with Maria Droujkova that nicely dovetails, and fleshes out, Frenkel's article (somewhat interestingly, both Frenkel and Droujkova are immigrants from the old USSR):

http://tinyurl.com/mr9tlsk

Droujkova notes that the complexity of ideas and the difficulty of doing them "are separate, independent dimensions,” and children are capable of much more (math) learning than people think. She notes a progression from more informal ideas to more abstract ones and maintains that a "playful aspect" can be "retained along the entire journey": “This is what mathematicians do—they play with abstract ideas, but they still play.”  
Both Droujkova and Frenkel are combating the contagion of so many young people being turned off to math at an early age.


I would urge all parents and educators of youngsters, not already familiar with Droujkova's work, to read the article, and followup with visits to her "natural math" website and related online materials:

http://www.naturalmath.com/site-pages/about-us.html

I've said it before, and will say it again, we are so lucky to be living in a time when not only does the Web present a vast array of resources at one's fingertips for learning math, but a time when so many passionate people actively take the message of math farther and wider than ever before.


ADDENDUM: on a tangential subject, this morning's Diane Rehm Show (NPR) spent the last hour in a wide-ranging discussion of the controversial Common Core standards (as wide-ranging as could be squeezed into 1 hour):

http://tinyurl.com/kkuwlej

Clones Amongst Us? ;-)

Two people who have pretty obviously been cloned, since they keep showing up everywhere(!) evangelizing for mathematics literacy, are Ed Frenkel and Keith Devlin... (no doubt, in some sort of brilliant disinformation strategy, they've been cloned by the very governmental agencies they keep warning us about ;-)

As for Frenkel... science sites, sure; math sites, well of course; NY Times, why not; and needless-to-mention Twitter... now this week Ed  (or one of those clones) appears in Mother Jones online edition exhorting the importance of mathematics and his frequent message that it is not just for the gifted few, but IF taught right, for the masses.
Includes a podcast interview with Frenkel, whose Russian accent is almost as enticing as Keith Devlin's British one!

http://www.motherjones.com/environment/2014/02/inquiring-minds-edward-frenkel-math-doesnt-suck

Lots of good points made by the man who dared to title a book, "Love and Math."
excerpt (from Mother Jones):

"...Frenkel views math as an 'archipelago of knowledge' that's universally available to all of us, and he's been everywhere of late spreading the word. In particular, Frenkel is intent on warning us about how people are constantly using (or misusing) math to get our personal data, to hack our emails, to game our stock markets. 'The powers that be sort of exploit our ignorance, and manipulate us more when we are less aware of mathematics,' said Frenkel."...
"To him, math—not religion—is the one shared body of firm, unchanging knowledge that we all possess and that nobody can ever take away from us… 'It's a great equalizer,' Frenkel says"....

"Forget the idea that [math is] alienating and hard. According to Frenkel, life is hard without it."

And Keith Devlin continues his math promotion, equating solving math problems with mountain biking (another of his passions), while hailing the lowly amygdala!:

http://devlinsangle.blogspot.com/2014/03/how-mountain-biking-can-provide-key-to.html

His discussion of math's "Eureka" moments is especially interesting:

"How does the human mind make a breakthrough? How are we able to do something that we have not only never done before, but failed many times in attempts to do so? And why does the breakthrough always seem to occur when we are not consciously trying to solve the problem?
"The first thing to note is that we never experience the process of making that breakthrough. Rather, what we experience, i.e., what we are conscious of, is having just made the breakthrough!
"The sensation we have is a combined one of both elation and surprise. Followed almost immediately by a feeling that it wasn’t so difficult after all!
"What are we to make of this strange process?"

All of which leads to some interesting cognitive/neuroscience speculation and praise for the amygdala's role in problem-solving.
Enjoy the whole piece... and then, go take a bike ride!

Learning, Books, Puzzles, P-values

Trying to get my blogging energy back after the 104th Carnival of Math sapped more of it than I expected 8-/
Will just point to a few pieces I enjoyed over the last few days:

1) The always-interesting Jo Boaler writes in The Atlantic about how the controversial Common Core approach to math education could help break down "math stereotypes." She believes the Common Core curriculum can produce students with more math confidence "who can develop mathematical models and predictions, and who can justify, reason, communicate, and problem solve… who are powerful mathematical thinkers and who have not been held back by stereotypical thinking and teaching":

http://tinyurl.com/lnmyv7r
(...of course not everyone in the 250+ comments agrees with her ;-)

2) Yet another wonderful podcast interview with Edward Frenkel (author of "Love and Math") this time from The Guardian:
http://tinyurl.com/kqrp5tw

3) "I just don't get no respect anymore"… THAT's what statistical p-values must be saying to themselves these days... a couple more articles critical of their standard use:

http://tinyurl.com/pcmfo2w (from Ars Technica)
http://tinyurl.com/mm9aceb (from Scientific American)

4) And an interesting little probability puzzle from Presh Talwalkar here:

http://tinyurl.com/lnpveb7

5) Speaking of probability, Paul Nahin fans will be delighted to see that Dr. Nahin has a new book out, "Will You Be Alive 10 Years From Now?" -- frankly, I think it's a crummy title, but nonetheless looks like a fantastic/entertaining read if you enjoy probability puzzles (which is the entire focus of the volume -- I'll likely employ some of the content for blogpost material here eventually).
Don't know when I'll find time to review it though, since my current priority is Noson Yanofsky's "The Outer Limits of Reason" which I regard as the most important popular math-related volume in quite some time.

Monday Meanderings

4-ingredient potpourri today...:

1) As a follow-up to Friday's post here's an interesting and more general recent article on the "Fields Medal" for mathematics (includes a couple of audio-casts):

http://tinyurl.com/m7m25uc

2) This week's NY Times "Wordplay" column again focuses on Martin Gardner, and again includes a quotation that's too wonderful not to pass along. This is from Gardner's editor, Robert Weil:

"Martin just didn’t care about money. I think you find with some overly creative people they can be overly generous. They undervalue their own work. Sometimes creative people have agents to counterbalance this tendency but Martin didn’t believe in agents.
"Martin was an Oklahoma boy who happened to be a genius. He was the opposite of pretentious. He was something out of the Wizard of Oz. To know Martin — he was something out of a time warp. He lived in his stories. He lived in Lewis Carroll. He was frozen in the land of Oz. Part of him is Dorothy just skipping." 

I love that imagery, Martin Gardner as "Dorothy just skipping." The whole puzzle column is here:
http://wordplay.blogs.nytimes.com/2013/10/14/gardner-4/?_r=0

3) Yet another very interesting interview with Edward Frenkel, the current mathematician du jour! ;-) (and author of "Love and Math"):

http://www.timesofisrael.com/?p=691188

4) Finally, on the education front, West Coast Khan Academy and East Coast Phillips Academy (a premier New England prep school) are planning to collaborate on a first-year calculus course, hopefully to be ready before end of 2014. "The goal for the offering is to provide a personalized and adaptive instructional program for students":

http://blogs.edweek.org/edweek/curriculum/2013/10/the_khan_academy_is_expanding.html

CCSSM... "the real work must begin"

I'm slowly (very slowly) making my way through Edward Frenkel's "Love and Math" -- I love the story he tells and what he is attempting to accomplish with this volume, even though much of the mathematics eludes me. He gets an A+ though for his sheer effort at making the Langlands Program (and other cutting-edge abstract math) comprehensible to us novices.  At some point I'll say more about the book, but for now what I find interesting is that Frenkel keeps popping up in various other popular media commenting on several different math subjects (not merely publicizing his book).
A recent piece is this one at Huffington Post which is a follow-up to one at the Wall St. Journal (both co-written with Hung-Hsi Wu).

These articles concern the controversial "Common Core State Standards For Mathematics" or CCSSM. Different folks have put forth arguments pro and con this initiative that has now been established by the great majority of states. I found Frenkel's clear support for CCSSM interesting, since one of the storylines of his new book is how uninspiring he found the standard math schooling in his own native Soviet Union... only the luck of encountering an especially creative, interesting, one-on-one mentor drew him over to the subject.
(Parenthetically, when I told a friend I was reading a book entitled "Love and Math," she immediately responded, "Now THAT'S an oxymoron! those are two words that ought never be used in the same sentence." :-( Of course she speaks for a LOT of people in feeling that way, and that is exactly the anti-math bias Frenkel wants to ultimately overcome.)

He lays out his support for CCSSM in the WSJ article, but then in the HuffPost piece admits that CCSSM will fail dismally ("setting back math education in this country by decades"), UNLESS it is accompanied by the proper textbooks and teacher training to make it successful. He contends that the texts currently used for the "national curriculum" have "staggering" "deficiencies," but newer options are on the way, and there is MUCH work to do to insure CCSSM's much-needed success.

The article ends this way:

"Math education is a multi-dimensional problem. Its solution will require time, money, effort, and deep commitment from everyone involved. But this is a problem we must confront because the future of a generation of students is at stake. By introducing rigorous national standards, the CCSSM have made a major breakthrough, laying the groundwork for progress. Now the real work must begin."

If you're an educator, or otherwise interested in CCSSM, do read his HuffPost piece and its links.

Of course there's plenty more info/discussion about CCSSM available on the Web, as well:

http://tinyurl.com/ktsalzq

Books, Links, Calculus...

I'm busily putting final touches on a long review of Martin Gardner's autobiography [now up HERE], while simultaneously reading Edward Frenkel's new "Love and Math" and Raymond Smullyan's "The Gödelian Puzzle Book" -- don't know if I'll write reviews of either, but have no hesitation recommending both. The latter is typical 'Ray Smullyan,' and perhaps his best, most focused attempt yet to elucidate Gödel's theorems via paradoxical puzzles. The Frenkel book thus far looks wonderful (deep, yet accessible) and I hope will confer (to my naive brain) some sense of what the cutting edge Langlands Program is all about.
For now, I just have time to pass along to readers a few miscellaneous links I've enjoyed the last few days:

1) Just today, the same Edward Frenkel had an interesting piece in Slate on NSA and their 'backdoor' cryptography practices:

http://tinyurl.com/jvq87n6

2) Another fun read from Simon Singh (on The Simpsons' comedy writers), promoting his new book:

http://tinyurl.com/md2x5sz

3) And finally, recently Steven Strogatz enthusiastically tweeted a link to this intro for Robert Ghrist's 1st-year calculus course (from Coursera):

https://www.youtube.com/watch?v=vyYgt_qHYrM

The reason I provide this link at all is because quite awhile back an emailer asked me to recommend a video site on the Web for learning first-year calculus, and even though I'm aware of many, I wasn't confident endorsing any particular one. When I asked readers if they had definite recommendations I got no response. But if Steven Strogatz is willing to give a thumbs-up to this one, I trust his judgment!
One thing that makes it look interesting, beyond the quality of graphics put into it, is Ghrist's unconventional use of Taylor series (which usually come at the end of 1st year calculus), near the beginning of the course.

Weekend Reads

Just a couple of good reads for the weekend….

For any who missed it, this somewhat low-key, yet fascinating (and non-technical) interview with Yitang Zhang ('rags-to-riches/fame' worker on the twin-prime conjecture) last week in Nautilus:

http://nautil.us/issue/5/fame/the-twin-prime-hero

Secondly, a Scientific American excerpt from Edward Frenkel's new book, "Love and Math: The Heart of Hidden Reality" (now showing up in bookstores):

http://tinyurl.com/mrpsxuk

"The Heart of Hidden Reality"

Two great math memoirs in one month!... Martin Gardner's autobiography should be showing up in bookstores shortly, and already University of Calif./Berkeley mathematician Edward Frenkel's book "Love and Math" is popping up as well. The title of this post, is the subtitle of the book. Peter Woit has a positive review here:

http://www.math.columbia.edu/~woit/wordpress/?p=6266

Frenkel is a leader among those studying the "Langlands program" and mathematical physics.

From Peter's review:

"What’s really wonderful though is his dedication to the cause of the opposite of obscurantism, that of doing the hard work of trying to explain mathematical insights to as wide an audience as possible. His book is packed with mathematics and physics, full of enlightening explanations of difficult topics at all different levels of mathematical sophistication.
"Perhaps the most remarkable part of the book though is the way it makes a serious attempt to tackle the problem of explaining one of the deepest sets of ideas in mathematics, those which go under the name of the “Langlands program”….
"I heartily recommend this book to all with an interest in mathematics or its relation to physics. If the 'Love' of the title has you hoping for a tale of romance between two people, you’re going to be disappointed, but you will find something much more unusual, a memoir of the romance of mathematics and its relation to the physical world."

...and if that's not enough to get you interested, read the scintillating reviewer blurbs at the Amazon page linked to above (which affords you about 20 pages of free reading, plus ~40 pages of endnotes!).