1) I always forget that Greg Ross's "Futility Closet" site now has an accompanying background blog that runs with it, and which is worth checking out from time to time. When I looked today, it had an interesting little algebraic puzzle, solved by readers:

3) There have been so many wonderful general audience math books out lately I want to again cite four to consider for your math-spending dollars (links given to posts I've mentioned or reviewed them in):

a. "The Simpsons and Their Mathematical Secrets" -- Simon Singh …been getting lots-and-lots of press attention lately… I haven't read it, but given the subject matter and Singh's writing talents, no doubt it's a good read!

c. "Love and Math" -- Edward Frenkel ...a bit more meat ("Langlands Program") than the above offerings, and not for the math-phobe, but definitely a rich, challenging read for those willing to take a plunge.

d. "The Outer Limits of Reason" -- Noson Yanofsky …I will have much more to say about this book in near future (am reading it now) -- it is quite simply THE BEST math-related book I've ever read, pulling together, as it does, all the sorts of issues I'm most interested in: self-reference, paradox, infinity, logic, uncertainty, epistemology, physics… I hope this volume reaches a much wider audience.

And again, a reminder to be sending in those submissions for the November "Carnival of Mathematics" (deadline, Nov. 10):

so I have to pass along this news from The Aperiodical that back issues of a mathematical magazine, "iSquared" are now downloadable (pdfs) for free here:

"Each magazine contains regular news items, a mathematical histories
feature, puzzles, book reviews and the life of a great mathematician as
well as special articles..."

An interesting piece below from Brian Hayes on vulnerability of the RSA encryption system, based upon occasional shared prime number factors (nothing that wasn't already known, but nicely-explained and interesting storyline):

"...The output was a list of 64,081 compromised keys for TLS hosts, about
0.5 percent of all such keys collected... "The good news is that none of the weak keys are guarding access to
major web servers hosting bank accounts or medical records or stock
markets or military installations. Most of them are found in embedded
networked devices, such as routers and firewalls. That’s also the bad
news. A programmer with malicious intent who can gain control of a
well-placed router can make a lot of mischief."

I know, I know… some of you feel overdosed on Martin Gardner by now… it's been a busy month of Martin Gardner memorials, between the release of his autobiography and this month's annual 'Celebration of Mind' gatherings. But I can't resist offering these two lengthy videotaped events that took place over the weekend remembering the man who inspired me to start this blog; one is a gathering at Princeton University and the other the next evening at the Museum of Mathematics in NY city, involving same speakers, including his son James:

And just a forewarning…: next year is the CENTENARY of Gardner's birth, so if you thought you heard a LOT about him this year, you ain't seen nuthin' yet!! Furthermore, a biographer is working on what will probably be the definitive biography of Gardner, and which I'm guessing may have a target date of next October.

This is waaaay (as in leaps-and-bounds) beyond my brainpower, but still I find the latest post from the always-worth-reading Tim Gowers, fascinating… he proposes to utilize a polymathematical (collaborative) approach to test an idea that he thinks (but also doubts) may have some merit, to the P vs. NP Millennium problem. Before even getting to the idea he wants to consider, he spends considerable time on the pros and cons of such a collaborative undertaking. It's a verrry long, and before the end, a very deeeep read, but if you're particularly interested in P vs. NP, or just in the polymath approach to problems, highly recommended:

I'm guessing that RJ Lipton's blog may have some response to Gower's proposal (or maybe he'll just send along a comment to Tim's blog), so if the subject does interest you, might be worth monitoring that as well:

Haven't featured a video from Numberphile for quite awhile, so I'll remedy that right now… James Grime on the interesting "Sloane's Gap" and the OEIS here:

Meanwhile, the unpredictable Clifford Pickover is out with his latest offering, "The Book of Black" -- who'd-a-thunk-it! an entire book on, well, see for yourself:

And next month, the 104th Carnival will be hosted right here at Math-Frolic (around mid-November), so be thinking about your submissions for that. Official submission page here:

Just a 'filler-post' today... it's been a bit of a sad week in the science blogosphere, so perhaps some levity is in order:

And just to get you in the mood:

Lists of favorite math jokes appear regularly on the Web… so I'll throw my hat in the ring with a dozen that I find most chuckle-worthy -- no real knee-slappers here, nor anything particularly fresh, but in case you've missed any of these along the way:

1)Q: What does the "B" in Benoit B. Mandelbrot's name stand for?

A: "Benoit B. Mandelbrot"

2) A mathematician and his wife are driving along the Scottish countryside when the wife turns to her husband and says, "Oh, look dear, those sheep have been shorn." The husband looks across to the field and replies, "Well, at least on this side."

3) A statistician going through airport security is found to have a bomb in his bag. He explains to the security officer, "Statistics show that the probability of a bomb being on an airplane is 1/1000. However, the chance that there are two bombs on one plane is 1/1000000. So thusly, I am much safer.…"

4) Some engineers are trying to measure the height of a flag pole with a tape measure and are quite frustrated as it keeps slipping before the measurement is complete. A mathematician comes along and asks what they are doing, and they explain.
“Well, that’s easy…” says the mathematician.

He pulls the pole out of the ground, lays it down, and measures across it easily.

After he walks away, one of the engineers smirks: “Sheeesh, that’s so typical of those mathematician-types! We need the height, and he gives us the length!”

5)Q: What is the difference between a Ph.D. in mathematics and a large
pizza?

A: A large pizza can feed a family of four

6) A mathematician and an engineer agree to take part in an experiment. The experimenter has them stand at one end of a room in which a beautiful naked woman stands at the opposite end. The experimenter says that after every minute the two participants will be permitted to travel half the total distance between themselves and the woman. The engineer says "okay, I understand, let's get started." But the mathematician grunts knowingly and storms out of the room, imploring the engineer as he departs, “don’t you see, silly, you’ll never actually reach her!” To that the engineer replies, equally knowingly, “au contraire, I dare say I'll soon be close enough for all practical purposes!”

7) Q: How many mathematicians does it take to screw in a light bulb?

A: 0.999999999999999999999.....

8)Q: How do you tell an extroverted mathematician from an introverted
one?

A: An extroverted mathematician stares at YOUR shoes when talking to
you.

9) Infinitely many mathematicians walk into a bar. The first says, "I'll have a beer." The second says, "I'll have half a beer." The third says, "I'll have a quarter of a beer." The bartender shrugs and serves up two beers exhorting, "Here guys, know your limits."

10) And I'll use any excuse I can to throw in a little Steven Wright along the way:

"What happens if you get scared half-to-death… twice?"

11)Three logicians walk
into a bar. The bartender asks, “Would you all like something to drink?”
The first logician says, “I do not know.” The second logician says, “I
do not know.” The third logician says, “Yes.” (...more an actual logic puzzle than a joke)

12) Lastly, I have to throw in the classic definition attributed to Paul Erdos: "A mathematician is a device for turning coffee into theorems."

And here's a long exposition on math humor from a 2005 AMS piece (pdf):

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):

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."

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":

Fields Medalists turned slackers??? No not really, but interestingly, a Harvard/Notre Dame study claims that for "...recipients of the Fields Medal, the most prestigious prize in mathematics, winning big actually kills productivity. Mathematicians who win it publish far less in the years afterwards than similarly brilliant 'contenders.' " In fact, according to the below article, "the drop off [in productivity] is pretty massive":

"Though they publish less, winners also take more risks in the future. They've already reached the pinnacle of their fields, so they feel free to pursue moonshots, new areas of mathematics that they think are fascinating or vital."

In short, the winners increase their "cognitive mobility" or tendency to move out of their core specialization.

And the piece ends with this two-edged sword:

"It's important to reward achievement, but it may also have the unintended side effect of creating complacency. "At the same time, there's something
to be said for giving top performers the opportunity and safety net
required to do really innovative work, even if it's less certain and
takes longer."

Check out the full summary article from Business Insider, or see the original study it is based upon here:

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:

Apologies for being so Martin-Gardner-centric lately, but one more Gardner post:

Gardner's autobiography makes brief mention of many of those Gardner encountered in his storied career, especially those who gained attention through his Scientific American columns, but one name I was surprised not to see mentioned was Scott Kim, who Gardner shined a light on for his creative and fascinating "ambigrams" (upside-down or backwards script writing). I don't know if there's any particular reason Kim got left out of the volume (unless I missed him somewhere), but at any rate, Scott is in some YouTube videos that briefly recount his connection to Gardner and to the "Gathering For Gardner" events he has participated in (these aren't new videos, so you may well have seen them before):

Also, Scott's own website of what-all he's into, is here:

This will likely be a month of a lot of Martin Gardner reminiscences on blogs, with the combination of his birthday approaching (10/21) and his new autobiography making the rounds (I've reviewed the autobio. twice over at MathTango: short review & long review ).

The most recent NY Times "Wordplay" puzzle column is dedicated to an old Gardner classic problem (Monkey and the Coconuts), but what I enjoy most about the column is hearing from Martin's son James who relays some brief memories of his famous dad:

James remarks at one point, in words that I've heard echoed by others:

“The thing I find fascinating — in some realms Dad was a rock star. He had groupies. People were excited to meet him. In other realms … if you were not enmeshed in his writing, you had no idea who he was."

I too always found this true. Over the years when I mentioned to friends that I was a Martin Gardner fan, the response was either along the lines of, 'Oh yeah, isn't that guy great!' or alternatively, 'Whooooooooo???' …or, on still other occasions, 'isn't he the guy that wrote those pages at the back of Scientific American for awhile?' …to which I always wanted to reply, 'Uhhh, yeah, sorta like that Einstein guy, who fiddled around with light for awhile, I guess'….

Also worth noting that The Aperiodical recently ran a podcast talking to Colm Mulcahy specifically about Gardner here:

In other notes, but still speaking of math popularizers, one of my favorite current ones, Richard Elwes, was recently interviewed here, promoting his most recent books:

And finally, as a heads-up, looks like I'll be hosting the November"Carnival of Math" so be thinking of posts (yours or others) you'd like to send along for inclusion (I'll probably be putting out a reminder each week through end-of-month). The submission page is here:

I suppose writing a book about the most popular animated series (and one of the most long-running TV shows) of all time is a good way to insure a best-seller, and if the publicity surrounding physicist/writer Simon Singh's latest book is any indication, he has accomplished that. Another wonderful piece on Singh and his latest volume, "The Simpsons and Their Mathematical Secrets":

The book is readily available in the UK, but I haven't personally seen it in a US bookstore yet, though I'm sure it won't be long, and of course is available for order online.

According to the article, Singh's "trick is to find a hook, tell an interesting story, and then ensure that science is slipped into it – a little bit like hiding the sprouts at the bottom of a child's favourite dinner." Singh notes that The Simpsons is "the world's most popular TV series and nobody knows that there's this band of mathematicians at the heart of its writing team. People don't know that they smuggle maths into the series."

and one more bit:

"But should a science writer really be watching episodes of The Simpsons on repeat or could he be doing something more productive? He laughs. He says his wife, Anita Anand, a journalist and radio presenter who is writing a book on Sophia Duleep Singh, the Indian princess and suffragette, spends all day at the British Library, transcribing personal diaries. 'She comes back and I'm just lying on the sofa watching The Simpsons. I think she has a huge amount of fun doing that, but rather her than me. I'm happy watching The Simpsons at home.' "

The whole piece is great; check it out, and if you're either a Simpsons geek or a math geek (I think that covers about everyone), get the book.

1)MathBabe posted this blurb about comments of Andrew Wiles in regards to the "abuse" or misuse of mathematics within the world of high finance (and how it 'tarnishes' "his chosen subject’s reputation"):

…made more interesting because her post comes on the heels of a weekend Twitter back-and-forth involving Ed Frenkel and Keith Devlin versus an individual purporting to be a former NSA employee, about the dangers of 'secret' uses of math by the NSA as alluded to in this Frenkel Slate piece I've linked to previously:

2) An enthusiastic review from Marcus du Sautoy for Edward Frenkel's new book (that "seeks to lay bare the beauty of mathematics for everyone"), "Love and Math":

3) And a hat tip to MathMunch for this interesting video on "God's Number" (the minimum required number of moves to solve any Rubik's Cube -- which turns out, surprisingly, to be 20):

In his latest "Devlin's Angle" Dr. Devlin speaks articulately on math education, both in terms of his MOOC course (now in its third iteration) and math digital games (specifically his company's Wuzzit game). As always, great thoughts (this time with a focus on the "team" approach necessary in today's digital education world)….

(title for this post, by the way, derives from an analogy Keith makes in the article).

His bottom-line take-home message is, that as great as new technology is, it still requires people, working collaboratively, to 'make it all happen' when it comes to successful education.

...And for ardent Martin Gardner fans, my longish tribute to Gardner and his new autobiography is up over at MathTango:

I'm a number-luvin' primate; hope you are too! ... "Shecky Riemann" is the fanciful pseudonym of a former psychology major and lab-tech (clinical genetics), now cheerleading for mathematics! A product of the 60's he remains proud of his first Presidential vote for George McGovern ;-) ...Cats, cockatoos, & shetland sheepdogs revere him (and he, them). ...now addicted to pickleball.

............................... --In partial remembrance of Martin Gardner (1914-2010) who it's been said, “...turned 1000s of children into mathematicians, and 1000s of mathematicians into children.” :-) ............................... Rob Gluck