A Mathematician's Sequel

 So many books… and so little time! Paul Lockhart is out with "Measurement," possibly the most deceptively boring title I've seen for a likely wonderful treatment of mathematics (for both the student and professor alike).

What many of us especially look for in a 'popular' math book is not just a good or even great presentation of mathematical concepts/ideas, but an evocation of the very joy and wonder that math can render. All indications are that Lockhart has accomplished that in this new volume (I have only begun reading it, but from thumbing through the pages and perusing reviews, that is my expectation).

Here, a blurb from Publishers Weekly:

http://www.publishersweekly.com/978-0-674-05755-5

and an audio review here:

http://www.dailymotion.com/video/xstoas_science-book-review-measurement-by-paul-lockhart_creation

This volume is in some sense a sequel to the author's well-known 2002 essay/rant? (later made into book form) "A Mathematician's Lament," which brought Lockhart some notoriety with his critique of American K-12 math education; available from Google documents here:

http://tinyurl.com/8oeevn7

Addendum: if you haven't read them before, here are 2 columns Keith Devlin wrote on Lockhart some years ago:

http://www.maa.org/devlin/devlin_03_08.html

http://www.maa.org/devlin/devlin_05_08.html

Consumer Math

"This is your brain on shopping, and it's not very smart," according to this
interesting piece from "the Atlantic" a bit ago, covering '11 ways consumers are hopeless at math':

http://www.theatlantic.com/business/archive/2012/07/the-11-ways-that-consumers-are-hopeless-at-math/259479/

I think I find #4 the most interesting one... or perhaps just the one I'm most susceptible to!

Algebra... the Discussion Continues

If you missed it today, the Diane Rehm Show (NPR) did an hour with Andrew Hacker and other guests on the issue of "Is Algebra Necessary" which Hacker raised to the forefront in a recent NY Times op-ed. The podcast is available here:

http://thedianerehmshow.org/shows/2012-08-29/algebra-necessary

You can hear the frustration/aggravation in Dr. Hacker's voice as he defends his position against the backlash he created. If anything, he may be stating his case more staunchly now than in the original article. Clearly the arguments can go back-and-forth for a long time; several of the listeners' call-in comments/experiences are interesting as well. I still find fault with Hacker's overall take, but I respect his ability to stand his ground.

In the end, he says he is simply asking that we "re-think" our insistence on algebra as a "requirement" for all high school graduates. I wouldn't completely oppose that... so long as we also "re-think" the insistence on various English, literature, history, art and music requirements as well.

If You Win You Lose...?

I've mentioned this basic paradox previously, but recently ran across it again, and find it worth a re-telling:

 *****************************

Wiley was a young law student who apprenticed under a keen-minded legal genius named Mencius. Mencius made the same contract with all his students: They need pay him no instructional fee until after they won their first case, at which point his stipend would immediately come due. But after completing his education Wiley decided to forego law practice after all, and become a car mechanic instead, thus not paying Mencius anything. Frustrated, Mencius claimed that failing to practice law was not one of the permissible options, and sued Wiley to attain his just compensation, at which point Wiley acted in his own defense.

Mencius believed he had an open-and-shut case for getting his money: if he WON the court case then the judge would be ordering Wiley to pay the fee that was owed. AND, if Mencius LOST the case, then that would mean it was Wiley's first court victory, and by contract, he would now have to pay Mencius the same fee due. To Mencius it was a no-lose situation!

However, Wiley saw matters in a completely opposite way: IF he WON the case then it would mean that the judge was ruling that he was NOT required to pay his former mentor Mencius. AND, if he LOST the case then, by contract, he would not owe Mencius anything yet, since he was to be paid only upon a court victory.

 *****************************

 ....I s'pose in the end, all one can say is that it is true that this sentence is false. ;-)

'Tipping' Mathematics

I'm not a huge Malcolm Gladwell fan myself, but if you are, you may enjoy this "Math4Love" post asking if we can make mathematics "tip"? i.e. make it more widely popular to a majority of Americans:

http://mathforlove.com/2012/08/how-to-make-math-tip/

From the posting:

"The real goal is to change the culture around mathematics. Here’s the good news: I think it’s been happening for while anyway. The first mainstream breakthrough I remember was Good Will Hunting, and since then we’ve had A Beautiful Mind, Proof, Numbers, The Big Bang Theory, and more. When Steve Strogatz wrote pieces for the New York Times, they received hundreds of comments. Scientists are cooler than they’ve been in my lifetime. Is it happening? Is math tipping?"

and ending thusly:

"What needs to happen? Do the cool kids need to start trying to find a simple proof of the 4 color theorem? Do we need a bad boy/girl mathematician (or scientist… a rising tide raises all ships) to cool it up in the media like Feynmann did for a while?...
"I’d love to end with a solution to this problem, but all I’ve got for a moment in the question: what needs to happen for people in our culture to think that knowing math is standard and being good at it is cool?"

I'm doubtful math can "tip" in this sense anytime in the near future, but it is interesting and encouraging how widely programming/coding and computer science more generally, are taking hold for young people (not exactly math, but math-related). Stephen Wolfram, and many others, have urged the centrality that such areas should (and almost certainly will) play in future education. It would be interesting as well to know how successfully the current ongoing "Code For America" and "CodeAcademy" projects are going???

Mind-wrenching….

Call me a masochist, but I do love these self-referential or recursive logic puzzles (that shred my brain to itty-bitty, miniscule, pulsating pieces!). The one below I've encountered multiple times over the last year-or-so, and seen several different answers offered as solutions. Most of them don't check out when applied carefully, but one does seem to work well, and because there is at least some wiggle room in interpretation of the statements there may be one or more other successful answers.

So I'm curious if anyone knows the precise origin of this logic puzzle, and definitively what the proper answer(s) are supposed to be?

And, if you've never seen it before, well, knock yourself out…:

***********************************
Given the following 12 statements which of the statements below are true?

1.  This is a numbered list of twelve statements.
2.  Exactly 3 of the last 6 statements are true.
3.  Exactly 2 of the even-numbered statements are true.
4.  If statement 5 is true, then statements 6 and 7 are both true.
5.  The 3 preceding statements are all false.
6.  Exactly 4 of the odd-numbered statements are true.
7.  Either statement 2 or 3 is true, but not both.
8.  If statement 7 is true, then 5 and 6 are both true.
9.  Exactly 3 of the first 6 statements are true.
10.  The next two statements are both true.
11.  Exactly 1 of statements 7, 8 and 9 are true.
12.  Exactly 4 of the preceding statements are true.

***********************************

...I've already used several of these type puzzles on the site before, but if you have a favorite you think I may like send it along to me via email and I'll consider posting it and acknowledging the sender.

[...In a few days I'll state one of the answers that works on the above in the comments section, for those interested.]

Testing the Tests

Patrick Honner has done a series of posts critically evaluating the most recent New York State Math Regents Exam... interesting reading (and one suspects similar issues arise in other standardized tests across the US):

http://mrhonner.com/2012/08/08/regents-exam-recap-june-2012/

A few will say that nitpicking is going on, but as Patrick notes,

"...precision is important in mathematics; it should be modeled for students on official assessments.  And those writing these important exams should be familiar enough with the content to write precise and accurate questions."

also:

"Tests should stand as models of mathematical content and practice for students; they should not reinforce bad mathematical habits..."

 ...and finally:

"The consistent appearance of erroneous mathematics on these exams calls into question their validity as a measurement of 'student achievement'."

One wonders if imprecise or ambiguously-worded composition has simply always been a problem in standardized testing, or has it grown worse in recent times (perhaps with the growth/prevalence of less-precise English exposition brought on by the Internet)?

More Math Bloggers On the Way

(via Cortega9 at Wikimedia)

Since I'm not directly in the K-12 education 'loop' I don't closely follow many of the jazillion math-teaching-oriented blogs that are out there, but there are many good ones... AND more in the pipeline all the time.

I just learned of a math "blogger initiative" that was begun this month to heartily encourage still more participants in instructional math blogging. Even with so many already-established math blogs, I'm all for this 'more- the-merrier' approach.
If you haven't heard of the initiative you can go here to read about it:

http://samjshah.com/2012/08/06/new-blogger-initiation-pledge-by-tuesday-august-14th/

And then look at this kickstart of the initiative, linking to many of the new math posters as they get their feet wet in blogging:

http://samjshah.com/2012/08/24/round-up-of-week-one-of-the-math-blogging-initiation/

If you're teaching or doing math, but not yet blogging... hey, what are ya waitin' fer? ;-)

Math and Mysticism

In another provocative post, RJ Lipton proposes that maybe, perhaps, just possibly, we need to open the door more to "mysticism" in formal mathematics and computational theory.

http://rjlipton.wordpress.com/2012/08/23/do-we-need-mysticism-in-theory/

He starts off with some talk of chess and a Boris Spassky response (about auras) to a question, before moving on to "pattern matching" and then mathematics:

 "We think of math as one of the most rational fields of thought. Results are not based on appeal to authority, nor to your own visions, they are not based on instincts, nor on wild guesses. A theorem is the rock on mathematics, and no measure of belief in theorems matters in the final analysis except proof. A proof, while subject to human errors, is an argument that should be reproducible by others. It is a gold standard of correctness that makes math special.

"Yet there is a place in math, believe it or not, for auras, for beliefs with no proof, and for a kind of Mysticism."

Lipton then proceeds to use as an illustration, the "quest for a field with one element." The discussion that follows is, I'm afraid, beyond my pay grade ;-) but I still enjoy the very idea and bravado of associating math and mysticism in a conjoined way.

And he finishes thusly:

"The point of all this discussion is to show that mainstream math is willing to be more flexible, more creative, and more mystical, than we seem to be in complexity theory. Perhaps this mysticism is the key to unlock new secrets of computing? What do you think?"

Food for thought with the weekend approaching...

(photo via Michael Maggs/Wikimedia)

William Thurston R.I.P.

Math circles this week have been noting the death of outstanding and influential mathematician/topologist (and Fields Medalist) William Thurston on Tuesday at age 65.
Terry Tao's obituary to him here:

http://terrytao.wordpress.com/2012/08/22/bill-thurston/

A famous essay Thurston wrote entitled "On Proof and Progress In Mathematics" is available online here:

http://tinyurl.com/8symrpq

(or you can google it if you prefer it in pdf form)

ADDENDUM: just adding a couple more links (to Scientific American and the NY Times) from the many memorials to Thurston : 

http://tinyurl.com/dyyf8nc

http://tinyurl.com/c3lbkmg

New Tammet Book

Autistic savant Daniel Tammet has a new book out, "Thinking In Numbers" (Hooray!!):

http://www.bbc.co.uk/programmes/b01m0kj6

http://tinyurl.com/8llkr35

http://www.amazon.com/Thinking-Numbers-Daniel-Tammet/dp/1444737414

On-line Courses, Cheating, Honor Codes, Mastery...

Another thought-provoking post from RJ Lipton/Ken Regan, this time on the efficacy of on-line learning (it addresses on-line learning, in general, and is not specific to math courses):

http://rjlipton.wordpress.com/2012/08/21/cheating-or-mastering/

They bring up a practice I was totally unaware of, and can't help but wonder how widespread it truly is: students signing up multiple times for a free online course offering, as "Bob1, Bob2, Bob3, Bob4," for example, so as to be able to take an exam multiple times hopefully improving their score with each taking. There are honor codes to discourage such activity, but enforcement is difficult (and not even necessarily in the interest of online schools that may wish to publicize the numbers of people that sign up for their courses).

What is fascinating is to see the authors go from what the reader anticipates will be criticism of the system to contrarily point out that "Bob" is actually taking extra steps (and doing extra work), to try and insure a good grade… and in so doing likely 'mastering' the material better (through repetition). Is this not a good thing!? Indeed, the authors ask whether multiple-opportunity test-taking ought not be brought out of the shadows and made an explicit/official part of course-teaching wherever possible:

"What Ken and I find interesting is that many students are apparently motivated to do so well. Is this a better way to learn, or is it cheating? Should we allow students in “normal” classes to take the exam multiple times or not? We never thought about this previously because we could not afford to have students take more exams, since we had one grade to give by a human grader. But if all exams are auto-graded, then there is no cost.

"Is this a better way to learn? Should we encourage it? I suggested that we make Bob’s strategy explicit: students do not have to have multiple “phony” sign ups; they can have official multiple tries at the exams."

...hmmm, 'cheating' (of a sort) as the road to 'mastery'... who'd a thunk it!

Math Problems Galore

Only recently discovered this page over at "Wild About Math" blog of "math contest problem links." A collection of sites with problems (usually pdfs) from various past mathematical competitions, ranging mostly from high school level through college (but some younger):

http://wildaboutmath.com/math-contest-problem-web-links/

If you've got some time to wile away, not a bad place to hang out for awhile.

It's Not Necessary…

to beat a dead horse, but I will link to yet one more response to the NY Times "Is Algebra Necessary?" piece which drew a lot of fire (ire?) earlier in the month. This one from Jennifer Ouellette that I missed a week-or-so ago:

http://blogs.scientificamerican.com/cocktail-party-physics/2012/08/14/make-us-do-the-math/

A bit therefrom:

"I spent ten years training in jujitsu, yet I have yet to use my skills to defend myself from a real-world attack. So I guess those ten years were a waste, right? Wrong! The most important lessons I gleaned from martial arts had to do with learning to fail: getting my ass kicked and getting back up, again and again and again, until I mastered a given skill. Why wasn’t I willing to do the same for math?
All we’d end up teaching kids with Hacker’s strategy is avoidance. I was a master of avoidance. But learning to buckle down and do unpleasant things that don’t come easily to us prepares us for life…

"There’s a lot to be said for confronting fear and anxiety head-on, and fighting through a wall rather than throwing up one’s hands in defeat."

…I dare say we haven't heard the last on this topic.

Sudoku... Math In Disguise?

(via Wikimedia Commons)

Tanya Khovanova just now got around to reviewing Jason Rosenhouse and Laura Taalman's "Taking Sudoku Seriously" (I'll let you guess what it's about ;-)) She, as others, gives it a very favorable review:

http://blog.tanyakhovanova.com/?p=418

I've not read the volume, as I've never much cared for Sudoku, but based on Rosenhouse's previous fantastic book "The Monty Hall Problem" (I'll let you guess what it's about also), have no doubt it's a good read. One line in Khovanova's review caught my eye a little bit:

"The book is written for people who like Sudoku, but hate math. This is so strange. Sudoku is math. People who are good at Sudoku are good at math, or at least they are supposed to be."

Actually, the majority of Sudoku 'addicts' I've known have little advanced math skills. And I've always had difficulty with this concept of Sudoku as "math." Sudoku of course involves "logic," and could be done with any set of 9 symbols/objects: letters of the alphabet, hieroglyphics, colors, whatever, (numbers are handy but unnecessary)... but doesn't involve doing math or computation, nor high-level abstraction. Still, Keith Devlin reviewing the same volume months ago made the very same point as Khovanova (of Sudoku as math) noting that the book could help the reader "come to understand the nature of mathematics" though also admitting it Sudoku was "mathematics in significantly diminished form." And I wouldn't want to ever be on the opposite side of Keith in a debate! His review is a great read itself, by the way:

http://online.wsj.com/article/SB10001424052970204301404577173022950738492.html

Moreover, I've just discovered that Wikipedia has a wonderful page dedicated to the "Mathematics of Sudoku" here:

http://en.wikipedia.org/wiki/Mathematics_of_Sudoku

So perhaps I need to read the book to better comprehend this connection!


Finally, worth noting that 'Wild About Math' blog interviewed Rosenhouse and Taalman about their book, in a podcast, last February:

http://wildaboutmath.com/2012/02/24/jason-rosenhouse-and-laura-taalman-inspired-by-math-3/

ebook Math

I'm not yet into ebooks myself, but I do like the "Better Explained" website, and I trust Presh Talwalkar's reviews, so if you're an ebook fan check out Presh's positive review of a new math offering from the former here:

http://mindyourdecisions.com/blog/2012/08/10/math-betterexplained-ebook-review/

Nomography… Ever Heard of It?

…me neither… until I ran across it at this site run by a fellow named Ron Doerfler who is interested in "the lost art of nomography.":

http://myreckonings.com/wordpress/

According to Wikipedia, a nomogram or nomograph "is a graphical calculating device, a two-dimensional diagram designed to allow the approximate graphical computation of a function… Like a slide rule, a nomogram is a graphical analog computation device, and like the slide rule, its accuracy is limited by the precision with which physical markings can be drawn, reproduced, viewed, and aligned. Most nomograms are used in applications where an approximate answer is appropriate and useful."

According to Doerfler, his blog "... attempts to capture my occasional encounters with the technically elegant but nearly forgotten in the mathematical sciences—artistically creative works that strike me as particularly brilliant. These can be small, clever things (say, an algorithm for calculating roots), or they can be ingenious technical inventions of  more general application, basically anything that makes me think ‘Wow, that’s neat!’ Think of pendulum clock escapements; of beautiful precision sundials, astrolabes and other antique scientific instruments; of music theory and instrument design; of early, desperate attempts to calculate logarithms and trig values; of stereo photography and linkage mechanisms; of difference engines, trinary arithmetic and slide rules; of old map projections and vacuum tube op-amps.

Posts here are brief records of unusual things of this nature that I read or hear about, supplemented with references and some amount of research I typically do on these topics. Any longer papers that emerge (particularly on mental calculation and antique scientific instruments) will be placed in my main website area http://www.myreckonings.com.

Comments on the posts are appreciated! A forum has also been added for discussing anything related to lost art in the mathematical sciences at http://www.myreckonings.com/forum. Also, feel free to use the Contact link to send me general comments or any ideas for new topics."

His posts aren't very frequent, but you might find some of them of interest.
(He also has a homepage here: http://www.myreckonings.com/ )

Speaking of things I'd never heard of, Joselle, at "Mathematics Rising" had a recent piece on "Anosognosia" which is interesting though only of tangential mathematical interest:

http://mathrising.com/?p=845

Toward the end she writes:

" I would suggest, however, that the conceptual grounding of modern mathematics shares something with Edelman’s ideas about the power of ambiguity in language, when the structure and range of mathematics’ applicability was enhanced with its very broad generalizations.  For Edelman, associativity and metaphors start things off and then computation is applied.  But mathematics occurs in both.  And I would agree with Dyson.  I also prefer 'to live in a universe full of inexhaustible mysteries, and to belong to a species destined for inexhaustible intellectual growth.'  I often see mathematics as the evidence for, as well as the access to, these inexhaustible mysteries."

AMS... Check It Out

Just came across a good AMS (American Mathematical Society) "public awareness" portal page that I hadn't encountered before:

http://www.ams.org/about-us/pao/pao

It links to several of their other wonderful pages...

One link goes to the interesting AMS "Who Wants To Be A Mathematician" high-school level competition site, which looks like a great idea:

http://www.ams.org/programs/students/wwtbam/wwtbam

Another page has some wonderful downloadable posters:

http://www.ams.org/samplings/posters/posters

It's always fun to check their "Math In The Media" page as well for monthly updates:

http://www.ams.org/news/math-in-the-media/math-in-the-media

And there are other links… just a good place to bop around a bit if you have some time to kill for some mathy browsing!

Inquiry-based Learning

(pic via Wikimedia Commons)

Even though I never intended to much address math education when I started this blog, it keeps coming up again and again. With the advent of Khan Academy, education issues that always existed, and were always important, have come to the forefront.
Anyway, an older post from Keith Devlin (very worth reading, especially for its analysis of DNA identification probabilities) referred me to something I was unfamiliar with called "Inquiry-based learning," a form of active or participatory learning that can be applied to most fields (and may be especially effective for science/math teaching), that has apparently been formally around for a good while. The impetus is to get away from the common straight lecture format:



The above is part 1 of 3 parts. The other 2 parts are here:

part 2: http://www.youtube.com/watch?v=UVDfDTmqAuc&feature=channel&list=UL

part 3: http://www.youtube.com/watch?v=OMpNXJyrfSo&feature=BFa&list=ULUVDfDTmqAuc

More (not altogether complementary) information on the referenced mathematician/topologist Robert L. Moore, who popularized this teaching approach (sometimes called the "Moore Method"), is available at Wikipedia here:

http://en.wikipedia.org/wiki/Robert_Lee_Moore

There is even an "Academy of Inquiry Based Learning" with a website here:

http://www.inquirybasedlearning.org/

They also have a Twitter feed: https://twitter.com/iblmath

and a blog: http://theiblblog.blogspot.com/

...Meanwhile, also worth following Keith Devlin's updates on his own venture into teaching a "massive open online course" here:

http://mooctalk.org/

Undergrad Math

Too late for this fall, but is anyone out there searching for a good undergraduate education in mathematics…?

Dave Richeson has posted links at his blog to the mathematics depts. of the top-ranked 60 small liberal arts colleges in America:

http://divisbyzero.com/2012/08/16/mathematics-departments-at-liberal-arts-colleges/

I'm happy to say my sage alma mater is in there, somewhere within the first 47 listed ;-)

Friday Puzzle

First, a note to my regular readers… all 3 of you ;-))

My usual format here has been to gather math-related material I find interesting from around the Web and then parse it out, 1 post per day, through the week over 5 or 6 days, usually setting aside Friday as a "puzzle" day. Starting now(!), things will be less standardized. I'll post things in a more free-form way… there could be 2 or even 3 posts in a single day, or several days with no posts; or, a single post might include multiple unrelated topics and links. And Friday will no longer be relegated to puzzles, though I'll still post puzzles from time-to-time, in a more random manner.

Trying this out just to make things less regimented and more easy/flexible at my end, without set timetables. If it doesn't work well, can always revert to the old style.
None of this will likely much affect those of you getting an RSS feed, but if you're in a habit of checking this blog each morning (when I usually post) or only stopping by on Fridays for the puzzle, it may alter your routine.

With all that said, one last easy Friday thought puzzle for now:

When my digital clock shows 2:35 a.m. it is the very first time past midnight that 3 and only 3 different prime numbers appear. What will be the last time before noon when all 3 numbers on the digital readout are different prime numbers?
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7:53

MAA spokesperson responds to the recent controversy over algebra education in this longish piece:

http://www.maa.org/pubs/FOCUSoct-nov12_Steen.html

A core part:

 "So we face three distinct challenges:

-    Addressing the many weaknesses evident in mathematical learning;

-    Reducing the gulf between the traditional pre-calculus curriculum and the quantitative needs of life, work, and citizenship;

- Teaching mathematics in a way that encourages transfer—for citizenship, for career, and for further study.

I suggest that these three challenges are manifestations of a single problem, and that all three can be addressed in the same way:  by organizing the curriculum to pay greater attention to the goal of transferable knowledge and skills.

There are many ways to accomplish this, for example:

- by embedding mathematics in courses focused on applications of mathematics;

- by team-taught cross-disciplinary courses that blend mathematics with other subjects in which mathematical thinking arises (e.g., genetics, personal finance, medical technology);

- by project-focused curricula in which all school subjects are submerged into a class group project (e.g., design a solar powered car).

- by career-focused curricula in which a cohort of students focuses all their school work on particular career areas (e.g., technology, communications, or business)."

Chess Fans…

(image via Wikipedia Commons)

A very interesting post from KW Regan on the rapid growth in networked communication (via computers/internet) here:

http://rjlipton.wordpress.com/2012/08/14/the-speed-of-communication/

The last third-or-so is a recounting of an event I don't even remember: a "Kasparov versus the world" chess match in 1999 between then-reigning world chess master Garry Kasparov and a collaborative world community. Kasparov, heavily-favored, eventually won the game after an amazingly hard-fought 62 moves and called it the "greatest game in the history of chess."

The earlier portion of the post deals with archival Kurt Gödel correspondence.
Great stuff!

Why Can't Brits Speaketh English ;-)

Yo, Americans, does it annoy you when those Brits (and others) talk about "maths" instead of "math"? And Brits, does it annoy you that your neighbors across the pond are annoyed at your annoying, peculiar, ill-begotten, outdated, foolish, vexing, persnickety language habits? Well, then here's the post (& comment section) for you (...incisive, patriotic Sean Carroll takes a stand; and he's married to a word-maven, don't forget):

http://blogs.discovermagazine.com/cosmicvariance/2012/08/14/maths/comment-page-1/

Girls, Math, Winnie Cooper

Actress/mathematician/author, Danica McKellar, recently got 8 minutes to tout mathematics learning (especially for girls) on MSNBC's "Morning Joe." But hey, before that, can't resist a trip down memory lane with Winnie Cooper ("The Wonder Years") back in the days before MSNBC:



...and now all-growed-up:

Visit NBCNews.com for breaking news, world news, and news about the economy

Set Theory Objections?

Ya never know what will show up on BoingBoing… this recent longish piece is on the objections of some Christian fundamentalists to set theory:

http://boingboing.net/2012/08/07/what-do-christian-fundamentali.html

From the piece:

"Set theory, particularly the stuff about infinity, has a bit of that wibbly-wobbly, timey-wimey flavor to it. It doesn't make sense on the level of 'common sense'. It's dealing with things that aren't standard, simple numbers. It makes links between nice, factual math and floppy, subjective philosophy. If you're raised in Christian fundamentalist culture, all of that—every last bit—absolutely reeks of modernism. It's easy to see how somebody at A Beka [a Christian publisher] would look at set theory and conclude that it's really just modernist propaganda. To them, set theory is just a step on the road to godless atheism."

…and young homeschooled minds are being filled with this stuff.

Glut of Ph.Ds and STEM Students

Statistician John McGowan offers a rarely-heard take on the mathematics of the Ph.D. "glut" and what it means concerning STEM education:

http://math-blog.com/2012/08/11/the-mathematics-of-the-ph-d-glut/

...bottom-line, according to McGowan: there IS a Ph.D. glut and in turn there is NO shortage of STEM students (despite frequent claims) in general, even though there are a lot of now-very-highly-specialized positions that are short of applicants.

a blurb from his contrarian conclusion:

 "Yes, there is a Ph.D. glut. In fact, there has been a Ph.D. glut for over forty years, since about 1970. This is inherent to the structure of the current government funded system of scientific research. It is a matter of public policy. Sometimes the Ph.D. gluts get especially bad as in physics in 1970 and 1992/1993 and now in biology and medicine, but there has always been and are sizable Ph.D. gluts in almost all scientific disciplines since 1970.

The remarkable persistence of Ph.D. and scientist shortage claims in the major “mainstream” media should raise questions about the reliability and independence of the major media. This evident lack of basic fact-checking is not what one should expect of a 'free press.'

"Finally and most importantly, there is considerable evidence that the Ph.D. glut has not worked. Far from accelerating the rate of scientific and technological progress, it has contributed to a slowing rate of progress."

There's Something About Triangles

What is it about triangles that make them and their geometry endlessly fascinating?
...I don't know, but I can't think of anyone better to elucidate the topic than Alfred Posamentier. He and co-author Ingmar Lehmann have yet another new book out, a delight for geometry fans, "The Secrets of Triangles," devoted entirely to these simple geometric figures. I think Euclid would be pleased! ;-)

From the Amazon-listed reviews: "an irresistable exploration," "enticing and addictive," "wonders of geometry emerge," "reveals a compelling and natural aesthetic beauty."

Friday Riddle

Simple wordsmithing today...
If an English dictionary included all of the integers, with their names arranged in alphabetical order, what number would appear first and what last?
(I think I probably first saw this at "Futility Closet" but not certain. At any rate, answer below...)
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 ANSWER:
Eight would appear first and Zero last

Not Exactly Avatar...

Reclusive Russian genius mathematician and Fields winner (and snubber-of-$1 million award) Grigori Perelman is to be the subject of a James Cameron movie according to various reports:

http://rt.com/art-and-culture/news/hollywood-mathematician-grigory-perelman-720/

http://www.math.columbia.edu/~woit/wordpress/?p=4990

Says a cautious Peter Woit:

"I’m finding it hard to figure out how Hollywood will dramatize the story of reclusively thinking about the Ricci-flow equations for seven years or so. I guess it will all be in the special effects, for which Cameron is famous."

Only From Them Brits!

Steven Strogatz recently pointed out this old, oddball, comedic "math" video from the BBC on the Net (originally from a show entitled "Look Around You"):




I suspect everyone will have their own different favorite bits from it… (I especially like "Problem one").

Devlin, Online Education, and Self-Publishing, Oh My

 Keith Devlin's latest posting, as his online course, "Introduction to Mathematical Thinking," approaches:

http://devlinsangle.blogspot.com/2012/08/the-future-of-textbook-publishing-is-us.html

He employs Amazon's "CreateSpace" for self-publishing a math textbook, noting that "...the whole process is so well designed, there is no reason why anyone who can use LaTeX should do anything other than self-publish from now on."

And toward the end this,

"So the key to making something like this work is, I think, to build up a Wikipedia-like community of instructors who, for five weeks each year, will make available their expertise to the thousands of students around the world who are taking advantage of a MOOC [massive open online course] to obtain an education they would otherwise not have access to.

"The benefit to the students in the transition classes given by MOOC-participating instructors is that their learning will assuredly be enhanced by acting as tutors for the students who are not so privileged. Both because teaching others is a powerful way to learn – as most of us discover when we become TAs at graduate school – and because those students will surely feel much more incentivized to understand by playing such a feel-good role."

 

Carnival of Mathematics

Get some popcorn and balloons and settle down for the 89th blog 'Carnival of Mathematics,' with its usual variety of mathy content:

http://aperiodical.com/2012/08/carnival-of-mathematics-89/

Puzzle Re-Play

For a Friday puzzle just re-running one of my very favorites that ran 7 months ago here (apologies to all who are quite familiar with it). In turn, I took it directly from Richard Wiseman's blog, where it was stated thusly:

"Imagine there is a country with a lot of people. These people do not die, the people consists of monogamous families only, and there is no limit to the maximum amount of children each family can have. With every birth there is a 50% chance its a boy and a 50% chance it is a girl.  Every family wants to have one son: they get children until they give birth to a son, then they stop having children. This means that every family eventually has one father, one mother, one son and a variable number of daughters.  What percent of the children in that country are male?"

For the answer you can go back to my original post, last January, here (which also links back to the original Wiseman page):

http://math-frolic.blogspot.in/2012/01/is-answer-obvious-or-obscure.html

--> Addendum: I just learned that there was a lengthy, interesting discussion of this puzzle over at MathOverflow a couple years back:

http://mathoverflow.net/questions/17960/google-question-in-a-country-in-which-people-only-want-boy

Be sure to read beyond where it says the question is "closed" to see all the commentary (in the end, under the usual assumptions, the answer remains 50/50).

Mathematics Underlying Brain Structure

Study from British neuroscientists looks at the mathematical nature of neuronal growth:

http://www.kurzweilai.net/simple-mathematical-pattern-describes-shape-of-neuron-jungle

Excerpt:

"Neurons look remarkably like trees, and connect to other cells with many branches that effectively act like wires in an electrical circuit, carrying impulses that represent sensation, emotion, thought and action...

"Over 100 years ago, Santiago Ramon y Cajal, the father of modern neuroscience… proposed that neurons spread out their branches so as to use as little wiring as possible to reach other cells in the network. Reducing the amount of wiring between cells provides additional space to pack more neurons into the brain, and therefore increases its processing power.
"New work by UCL neuroscientists has revisited this century-old hypothesis using modern computational methods. They show that a simple computer program that connects points with as little wiring as possible can produce tree-like shapes that are indistinguishable from real neurons — and also happen to be very beautiful."

Goldilocks and the 3 (in base 10) Bears

New Jersey mom gains publicity and a following for offering bedtime math problems to youngsters. NPR audio report here:

http://www.npr.org/templates/archives/archive.php?thingId=157644780

And her own website here:

http://bedtimemathproblem.org/

(... with any luck, by the time they reach high school, algebra will be a breeze ;-))