Four From Friday

Friday brought several interesting, varied reads across my computer screen:

1) Scientific American got us started with a little math history lesson, centered around "infinitesimals" coming in and out of favor, and the re-casting of calculus:

http://tinyurl.com/k5ym5qd

2) On the light side, The Guardian offered an excerpt about our response to numbers, from Alex Bellos' newest book, "Alex Through the Looking Glass":

http://www.theguardian.com/books/2014/apr/04/why-all-love-numbers-mathematics

It starts off telling about a man named Jerry Newport, a retired taxi driver with Asperger's Syndrome who has "an extraordinary talent for mental arithmetic." Also, turns out that Jerry's living room includes "a cockatoo, a dove, three parakeets and two cockatiels"… THIS is a man I can relate to! ;-) -- I've had a similar living room in the past!… though I lack Jerry's number talents. Anyway, many of Jerry's unexplained skills interestingly center around prime numbers. (BTW, I touched on the subject of linkage between Asperger's and math ability a bit ago.)
The rest of Bellos' piece deals with various subjective (and seemingly inexplicable) oddities about integers, and our relationships to them.
An interesting, fun read, touching on language and psychology in addition to math.  If the rest of the book is this entertaining, jolly good!

3) A bit more advanced, Adam Kucharski writes a piece for Nautilus on the startling Weierstrass Function, which pre-saged "fractals" -- a fascinating function that is continuous, yet lacks a derivative at any given point (is "smooth" NOwhere). This was contrary to all prior math thought, and "With one bizarre equation, Weierstrass had demonstrated that physical intuition was not a reliable foundation on which to build mathematical theories":

http://nautil.us/issue/11/light/maths-beautiful-monsters

(this interesting extract comes from a longer article Nautilus subscribers can access)

4) Finally, in a fascinating bit of logical legerdemain, Arkady Bolotin has linked the P vs. NP Millennium Problem to quantum mechanics, and in so doing reached conclusions about both. A longstanding puzzle in quantum theory is how to apply equations that work so well at the quantum level to the world we actually live in and experience. Bolotin argues that while Schrodinger's equation has relatively simple solutions at the atomic-level, at the macro-level it becomes NP-hard (essentially unsolvable). Essentially he's killing two birds with one stone: claiming that P ≠ NP (which is what most assume, but have yet to prove) and that the quantum inscrutability of our world is the result of Schrodinger's equation being essentially unsolvable (within reasonable time) at the macro level:

https://medium.com/the-physics-arxiv-blog/7ef5eea6fd7a

And if you have any energy left after reading all these you can go catch the latest lengthy blather (re: math education) I've put up on MathTango this morning.

Thursday Potpourri

1) I'm delighted to learn that Noson Yanofsky's "The Outer Limits of Reason" has won a PROSE Award in the "Popular Science and Popular Mathematics" category for 2013.

"The PROSE Awards annually recognize the very best in professional and scholarly publishing by bringing attention to distinguished books, journals, and electronic content in over 40 categories. Judged by peer publishers, librarians, and medical professionals since 1976, the PROSE Awards are extraordinary for their breadth and depth."

I LOVED this volume, calling it a "phenomenal book" in my review last November (indeed it is my FAVORITE book of the last couple decades, and I'm glad to see it get further acknowledgement!):

http://mathtango.blogspot.com/2013/11/phenomenal-book.html

Congratulations to Dr. Yanofsky!

2) And in the 'suddenly-it-came-to-me' category, another nice story on the continuing saga of Yitang Zhang and his work on the twin-prime saga conjecture:

http://tinyurl.com/mbukg36

excerpt:

" 'There's nothing wrong with working at a Subway, but normally these proofs, these breakthroughs, are achieved by those that are working at Princeton, Harvard, these kind of really elite places,' Tony Padilla, a physics professor at the UK's University of Nottingham, says... 'And now we've got somebody who's literally come out of nowhere, that no one expected to produce this kind of results, and has done something impressive that many great minds were unable to do'...
"Zhang himself, a self-described 'shy person,' said in a UNH statement that the proof came to him during a vacation in Colorado, when he was feeling particularly relaxed. 'I didn't bring any notes, any books, any paper,' he said. 'And suddenly it came to me.' "

3) Last week I was writing about the age-old topic of math and beauty over at MathTango and now a new study points to a neuroscience substrate linking the two:

http://www.bbc.co.uk/news/science-environment-26151062 

4) Finally, h/t to Derek Smith of AMS blogs for pointing out a nice listing of interesting math-related documentaries available from this MathOverflow page:

http://mathoverflow.net/questions/100033/interesting-mathematical-documentaries

A Weekend Potpourri… (including Tegmark, Riemann, JMM14)

1) Not being an educator, I often ignore tweets appearing in my math feeds which seem geared strictly for teachers, but a recent one was getting RE-tweeted so often I finally caved and had to look at the link being passed along to see what it was. Indeed it was a delightful, simple idea most any primary school could employ… check it out if you've not seen it:

https://twitter.com/wterral/status/423755360512790528/photo/1

2) Below, a quick note on the packed talk covering recent twin-prime gap work at the Joint Math Meetings in Baltimore, MD.:

http://blogs.ams.org/jmm2014/2014/01/17/mind-the-gap/

3) I'm currently about half-way through Max Tegmark's new book, "Our Mathematical Universe."  Probably won't do a full review of it here since a) it's far more physics than mathematics (despite the title) and b) there are already many reviews of it around, so no need to add to the cacophony of publicity (good and bad) it's receiving.  Having said that, I will say I'm immensely enjoying it as a popular science volume -- in fact, it's one of the BEST cosmology reads I've yet come across (and I've read many)… which is not an endorsement of its views but simply of its readability… as cosmology books go, I'd call it a lively romp! For a more critical look though, see multiverse-phobic ;-) Peter Woit's review here, and be sure to peruse the comments:

http://www.math.columbia.edu/~woit/wordpress/?p=6551

A New Scientist review below (and Dr. Tegmark has been all over the Web promoting the volume as well, just google the book's title):

http://tinyurl.com/jwdfjbv

and more quick takes here:
http://space.mit.edu/home/tegmark/mathematical.html

4) Finally, a fantastic overview (in under 20 mins.) of the Riemann Hypothesis from that gregarious explainer James Grime (if anyone can make the Riemann Hypothesis fun, James can!):



That should fill your weekend for awhile.

A Big Serving of Monday Potpourri

Catching up on a few things:

1) First, Keith Devlin continues his fascinating series on his MOOC experience (now 6 recent posts to catch up on in his latest series, if you haven't been following along):

http://mooctalk.org/

2) And if you missed Keith delightfully talking on NPR this weekend about the excitement generated by Yitang Zhang's attack on the Twin-prime conjecture earlier this year, give that a listen here:

http://www.npr.org/2013/12/21/256003488/and-the-number-of-the-year-is-the-lowly-2?ft=1&f=1007

3) Meanwhile, Peter Woit writes about the incredible difficulty involved in verifying last year's proof from Shinichi Mochizuki of the ABC conjecture (perhaps unparalleled in the history of math):

http://www.math.columbia.edu/~woit/wordpress/?p=6514

4) And if anyone has missed it, my own latest interview with popular mathematician James Tanton is currently up at MathTango:

http://mathtango.blogspot.com/2013/12/james-tanton-making-math-accessible.html

5) Perhaps mathematicians are too shy or uncomfortable talking about their (or their colleagues') politics, but I'm still interested to hear from you, if you aren't:

http://math-frolic.blogspot.com/2013/12/are-mathematicians-liberals.html

6) And three for your mathematical entertainment:

a) Hat tip to The Aperiodical for pointing out this fun 30-min. BBC podcast on math and magic:

http://www.bbc.co.uk/programmes/b03ls7y2

b) Just this morning, Presh Talwalkar posted a nice triangle geometry problem with both a traditional algebraic solution and a 'quickie' simpler solution available:

http://tinyurl.com/mtovhpx

c) And finally, a link that got some play on Twitter last week is this old "urban legends" of math discussion from mathoverflow.com:

http://tinyurl.com/l6gapx6
(some interesting, fun, and quite technical 'urban legends' included...)

Thursday Potpourri

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:

http://blog.futilitycloset.com/2013/10/07/beef-cuts/#comments

2) The Aperiodical has posted a podcast interview with mathematician/blogger Evelyn Lamb:

http://aperiodical.com/2013/10/all-squared-number-10-maths-journalism/

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!

b. "Undiluted Hocus-Pocus" -- Martin Gardner's autobiography …enough said!!

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):

http://tinyurl.com/krobqjp

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

Tweetfest

Haven't had time of late to write anything up, but will pass along a number of miscellaneous links (in no particular order) I've been tweeting in the last week that may be of interest if you've missed them:

1) A little math history synopsis from LiveScience:

http://www.livescience.com/38936-mathematics.html

2) "Matroid Theory" and Rota's Conjecture:

http://tinyurl.com/n45h5xz

3) Ingrid Wickelgren at Scientific American promotes John Mighton's "JUMP math" program:

http://tinyurl.com/pn5kjeu

4) A quick look at 'category theory' from AMS blogs with links for more info (also links back to this post at "Mathematics Rising" on the interweaving of math and physics: http://mathrising.com/?p=1055 ):

http://tinyurl.com/lyxt8sh

5) A letter from the reclusive genius Alexander Grothendieck:

http://sbseminar.wordpress.com/2010/02/09/grothendiecks-letter/

(by the way, I recently read Amir Aczel's "The Artist and the Mathematician," which is focused on "Nicolas Bourbaki," and while I only thought the volume was so-so overall, I did especially enjoy the sections at beginning and toward end on Grothendieck.)

6) Another nice little post on infinity here:

http://ieet.org/index.php/IEET/more/dvorsky20130813

7) A post from the always-good Richard Elwes on the "Perko Pair" and knot theory:

http://richardelwes.co.uk/2013/08/14/the-revenge-of-the-perko-pair/

8) And last but not least... rigorous, a discussion from Patrick Honner and Grant Wiggins on "rigor" in mathematics:

http://mrhonner.com/2013/08/14/a-conversation-about-rigor-with-grant-wiggins-part-1/


Hope everyone will find at least one thing of interest from the above for their weekend time and perusal....

Potpourri

Just another potpourri of bits catching my attention lately:

1) An odd, quirky, but I thought interesting, little blog post here:

http://unimodular.net/blog/?p=453

2) Kiki Prottsman (founder of Thinkersmith ), with a special interest in steering more girls toward computer science, is a great listen in the latest podcast from "Inspired By Math":

http://wildaboutmath.com/2013/07/14/kiki-prottsman-inspired-by-math-31/

3) Will note that Hilda Bastian is moving to the Scientific American blog corral with a blog entitled "Absolutely Maybe" on statistics, epidemiology, and various clinical issues. I like that title… it reflects how I feel about pretty much most "science" these days!:

http://blogs.scientificamerican.com/absolutely-maybe/

4) Off on a tangent, I suspect most math fans either are, or were at some time, interested in chess, in which case you'll find this blog post drawing attention to three of the greatest chess games ever played (from 1851, 1956, and 1999) of interest:

http://mathwithbaddrawings.com/2013/07/17/historys-greatest-chess-matches/

5) And finally, for entertainment (and since I've been seeing a lot of posts pertaining to 'game theory' lately), I'll repeat this clip that Steven Strogatz called "a stunning display of game theory," which I played here just a few months ago (...and which leads inevitably to the deep, pressing cultural question: is the game title of "Golden Balls" as snicker-inducing to a British crowd as it would be to an American audience???):

A Little Catch-up

Just a small catch-up potpourri of things from this week's world of math. Besides the Yitang Zhang news related to prime number gaps, the other big news was Harald Helfgott's proof of the "ternary" or "weak" Goldbach conjecture (every odd number above 5 is the sum of three prime numbers). Evelyn Lamb covers it well at her Scientific American "Roots of Unity" blog here:

http://blogs.scientificamerican.com/roots-of-unity/2013/05/15/goldbach-variations/

Speaking of Scientific American, I was happy to see Joselle Kehoe, who blogs at Mathematics Rising, get to do a guest blogpost for them today (math, language, biology/evolution, and reality in a single post!):

http://tinyurl.com/atg7mbx

Mark Chu-Carroll over at "Good Math, Bad Math" blog has initiated a series of posts on "discrete probability theory." Ought to be good given Mark's methodical approach to most subjects. His first introductory post is here:

http://scientopia.org/blogs/goodmath/2013/05/12/probability-and-interpretations/

And, in the event that "probability" is your thing, here's another page of links to some sources on probability theory (based largely on the work of E.T. Jaynes):

http://bayes.wustl.edu/

Finally, if you're in the mood for a puzzle, Futility Closet has put up a little algebra brain-twister (from the 2003 Moscow Mathematical Olympiad) here:

http://www.futilitycloset.com/2013/05/16/going-up/

Monday Morning Buffet

Catching up on a few math links today:

1) Interesting view on how the trendy interest in "data science" or "big data" is different from academic statistics… and is that for good or ill:

http://simplystatistics.org/2013/04/15/data-science-only-poses-a-threat-to-biostatistics-if-we-dont-adapt/

2) Story on elite school, Amherst, rejecting affiliation with MOOC promoter EdX:

http://tinyurl.com/cqtbbh5

I'm curious how many, if any other, elite institutions have rejected outright invitations to participate in MOOC programs???

3) A nice introduction to limits from the "Better Explained" site here:

http://betterexplained.com/articles/an-intuitive-introduction-to-limits/

4) Have to admit I'd never heard of prodigy and lightning calculator Shakuntala Devi, an Indian math genius and astrologer(!), but apparently she was well-known to many. She passed away yesterday at 83. Learn about her interesting life and prowess at Wikipedia (which has additional links):

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

5) …and lastly, I've put up an overview of Jim Holt's 2012 "Why Does the World Exist" volume over at my MathTango blog:

http://mathtango.blogspot.com/2013/04/from-whence.html

ADDENDUM: haven't had a chance to listen yet, but just realized Sol Lederman has a new podcast up with Ken Fan of "Girls' Angle," an organization specifically devoted to improving girls' experience with high school math:

http://wildaboutmath.com/2013/04/21/ken-fan-inspired-by-math-29/

Saturday Potpourri...

A few sundry items for your artful attention and possible perusal ;-):

1) Lance Fortnow, computer scientist and author of "The Golden Ticket," (which I reviewed a bit ago), all about P vs. NP, is Sol Lederman's latest podcast guest at Wild About Math:

http://wildaboutmath.com/2013/04/12/lance-fortnow-inspired-by-math-28/

2) A nice little primer on the nature of real numbers and pi from physicist Matt Springer here:

http://scienceblogs.com/builtonfacts/2013/04/12/everything-in-pi-maybe/

3) An interesting-looking list here of 24 video lectures in number theory:

http://www.infocobuild.com/education/learn-through-videos/mathematics/introduction-to-number-theory.html

4) Just a heads-up that E.O. Wilson is scheduled to be on NPR's Sunday "Weekend Edition" (tomorrow). I assume there will be some discussion of his recent much-debated commentary asserting that scientists need not know advanced mathematics to be successful.

5) Finally, a site I only recently learned of called "Ideas Roadshow" which looks interesting and includes this recent 5-minute clip by philosopher James R. Brown on Platonism in mathematics:

http://www.ideasroadshow.com/issues/james-robert-brown-2013-04-12

Four For Tuesday

A few of the things that crossed my screen yesterday…:

1) Another interesting article from the Simons Foundation, this time on the nature and fragility of networks, or as they say, "extreme fragility of interdependency" in the modern world. Be it urban infrastructure, the stock market, even the human body, or other networked systems the risks of small failures leading to chaotic cascading effects seems ever-present, as scientists try to figure out ways to evade catastrophes. From the article:

"While scientists remain cautious about using the results of simplified mathematical models to reengineer real-world systems, some recommendations are beginning to emerge. Based on data-driven refinements, new models suggest interconnected networks should have backups, mechanisms for severing their connections in times of crisis, and stricter regulations to forestall widespread failure."

Read further here: http://tinyurl.com/bom9eym

2) Hat tip to The Aperiodical for bringing this to my attention… a 40-page Shinichi Mochizuki paper intended to assist those trying to understand his "proof" of the ABC conjecture. I certainly don't grasp the paper (although there are a few words I can understand: "the," "of," "with," "for"… ;-) and 99% of folks won't comprehend it, but what's absolutely amazing is that there exists human brain wiring that IS capable of such production/comprehension!:

http://tinyurl.com/d6pje5l

3) And a hat tip to Patrick Honner for pointing me to this NY Times piece about "online proctoring" for MOOC course testing, a topic that is sure to draw more discussion as time goes on:

http://tinyurl.com/cstz6xa

4) Finally, even if you're tired of the question, "Is mathematics discovered or invented?" you may find the below New Scientist article interesting… it moves that question into the realm of business, software, and the debate over patentability, before concluding: "The rallying cry of a good many critics remains 'software is mathematics', meaning that software shouldn't be patentable. The odds are stacked against them, though – there's too much money at stake":

http://www.newscientist.com/article/mg21729086.300-should-business-be-allowed-to-patent-mathematics.html

Monday Math Buffet...

Another potpourri of offerings, if you've missed any of these…:

1) I love this relatively brief recent post from a secondary educator:

http://practicaltheory.org/blog/2013/02/28/we-dont-know-how-to-teach-math/

Also have to smile a bit at this particular line from the piece: "Seymour Papert said that math represents the failure of progressive education because the way we teach math always reintroduces coercion back into education."

But every line is good, and it largely reminds me of a fantastic, (looong) older post by Fields Medalist Timothy Gowers (which drew over 160 comments) that deserves frequent re-visiting:

http://gowers.wordpress.com/2012/06/08/how-should-mathematics-be-taught-to-non-mathematicians/

2) Latest (#96) Carnival of Mathematics is now up at "Math Mama Writes" blog:

http://mathmamawrites.blogspot.com/2013/03/carnival-of-mathematics-96.html

...Plenty of variety!

3) "Futility Closet" recently highlighted the delightful (to me) Yablo's Paradox:

http://www.futilitycloset.com/2013/02/22/yablos-paradox/

4) On the same day that I interviewed Evelyn Lamb over at MathTango, she put up a new post at her blog on the four-color theorem:

http://blogs.scientificamerican.com/roots-of-unity/2013/03/01/4-color-map-theorem/

5) Once again Keith Devlin covers some aspects/difficulties of running a MOOC at his "Devlin's Angle" blog (Keith is running at least 3 separate blogs, plus a Huff. Post column!):

http://devlinsangle.blogspot.com/2013/03/can-we-make-constructive-use-of-machine.html

...and over at Huffington Post Keith writes about the dropout rates for MOOCs, and why an 80+% dropout rate isn't necessarily a problem:

http://www.huffingtonpost.com/dr-keith-devlin/moocs-and-the-myths-of-dr_b_2785808.html

6) Math educator Maria Droujkova, with a focus on toddlers and youngsters, is Sol Lederman's 24th podcast interviewee here:

http://wildaboutmath.com/2013/03/01/maria-droujkova-inspired-by-math-24/

7) And finally, if you have any mental energy/time left, a long, thought-provoking read from the Simons Foundation on the future of computers in mathematical proofs (can we trust computers, as we turn to them more and more in the future for proofs of highly-complex theorems?):

https://simonsfoundation.org/features/science-news/in-computers-we-trust/

Weekend Potpourri

So many mathy reads to choose from this weekend, if you've missed them (really enough for a couple of weekends!)....

1) Brand new from Sol Lederman, a wonderful podcast with mathematician/writer Erica Klarreich:

http://www.buzzsprout.com/5316/78729-erica-klarreich-inspired-by-math-22

I've previously mentioned my belief that interviewing lesser-known math figures is almost more enticing than interviewing the titans in the field because readers/listeners already know so much about the 'big names' out there that much of what they say may seem repetitious (even if important) of things they've voiced before. Lesser-known folks have a fresher appeal as there is so much new to learn about them, and I think this podcast demonstrates my point. I was fascinated hearing Erica's views and experiences on a wide range of topics. See if you don't agree.
And below, some of Erica's prior writings for the Simons Foundation:

https://simonsfoundation.org/?s=erica+klarreich&submit

2) MIT physicist Max Tegmark is famous for his belief that the Universe is "built" of mathematics. He expresses his viewpoint in this straightforward interview from the ScienceNow site… and attracts a lot of comments in the process (including cynical ones):

http://news.sciencemag.org/sciencenow/2013/02/do-we-live-inside-a-mathematical.html

3) Julie Rehmeyer, who I just posted about a few days ago, has a new piece on Fermat's Last Theorem and its axiomatic basis, in ScienceNews here:

http://tinyurl.com/a4ujnx5

4) Patrick Honner again laments a question from a NY State Regents Math exam that entails unstated assumptions and in so doing short-circuits deep mathematical thinking:

http://mrhonner.com/2013/02/21/regents-recap-january-2013-unstated-assumptions/

5) Some bloke named Keith Devlin has a fantastic longread on math games in American Scientist, leading up to release of his own company's new animated game for math learning. He sets forth the criteria or qualities a video needs to possess to be successful as a math instruction tool (and explains why MOST games FAIL):

http://www.americanscientist.org/issues/pub/the-music-of-math-games

From the description, it sounds to me as if the prospective player (young person) of these new games will learn math in a manner reminiscent of the original Karate Kid (the movie) learning karate without ever knowing it from his master Mr. Miyagi. Keith's discussion of the "symbol barrier" and symbol manipulation in math is especially enlightening, but the entire piece is GREAT. He employs a music (piano) metaphor to explain what a successful math game should be like.

6) The brilliant Barry Mazur, recent recipient of the National Medal of Science, gives us a rich (and philosophical) piece called "Shadows of Evidence" on what constitutes "evidence" in the realm of mathematics. The essay ends with a quote from Chris Anderson essentially arguing that "modeling," as traditionally used in science, is becoming obsolete (because ALL models are, technically, flawed), and that with the advent of computer number-crunching ability, only "correlation" derived from huge data sets will be needed. To which Mazur responds that, "correlation alone will never replace the explanatory power of mathematics.":

http://tinyurl.com/bhzrjgf

This essay in turn leads to an even longer Mazur read entitled "What Is Plausible" here (pdf):

http://www.math.harvard.edu/~mazur/papers/Plausibility.Notes.3.pdf

7) Finally, perhaps appropriately after all of the above, I'll end with 50 varied quotations just put up by Guillermo Bautista on what mathematics is:

http://mathandmultimedia.com/2013/02/23/50-mathematics-quotes/

a few of my favorites:

"Mathematics is no more computation than typing is literature." – John Allen Paulos

"Mathematics, in the common lay view, is a static discipline based on formulas…But outside the public view, mathematics continues to grow at a rapid rate…the guide to this growth is not calculation and formulas, but an open ended search for pattern."  -- Lynn A. Steen

"Mathematics compares the most diverse phenomena and discovers the secret analogies that unite them." — Joseph Fourier 

.... ADDENDUM:  Experimenting with shorter time segments, Sol Lederman has already put up another podcast interview (22 mins.), this time with Jason Ermer, creator of the "Collaborative Mathematics" project (who I referenced a bit ago):

http://www.buzzsprout.com/5316/78788-jason-ermer-inspired-by-math-23

Mathematicians have been at the forefront of bringing productive Web collaboration to academic subjects, and now Jason is attempting it at lower levels. Check it out!

Devlin, Dunbar, Dominoes...

1) Registration for the second run of Keith Devlin's Stanford MOOC course, "Introduction to Mathematical Thinking" is underway (course beginning Mar. 4 for 10 weeks). More details here (where it states, "The goal of the course is to help you develop a valuable mental ability – a powerful way of thinking that our ancestors have developed over three thousand years").:

https://www.coursera.org/course/maththink

I've previously (highly) recommended the 92-page book Keith authored for this course (same title as course), but it would be incomparably better if read in conjunction with the course itself, than on its own.  I've not taken the course myself, but sincerely hope that some readers here do imbibe in Dr. Devlin's offering (and maybe even report back to us!?). There is very little computational math involved, but the ideas/work required for completion still may not be easy (depending on your background).

2) I wrote about the so-called "Dunbar number" here last year (the notion that neurological constraints limit one's close friendships or interpersonal relationships to very roughly 150 people). Now a much longer general article on Dr. Dunbar and his illustrious number:

http://www.businessweek.com/articles/2013-01-10/the-dunbar-number-from-the-guru-of-social-networks#p1

3) A recent nice little tutorial on the number e and ln here:

http://tinyurl.com/bnpfle6

 4) And lastly... how to knock over the Empire State Building with dominoes… and a little physics (a short, fun, but also educational, video):

Monday Potpourri

Time to catch up on a few things from the past couple days.

Readers seem to always enjoy 'quickies' as I call 'em, so here's a delectable one from a recent Twitter feed for all the foodies out there:

https://twitter.com/nerdfaced/status/289867477305937920/photo/1

'Wild About Math's' latest podcast is with Mircea Pitici, the editor of the annual "The Best Writing On Mathematics" series. The ~hour-long podcast is here:

http://wildaboutmath.com/2013/01/13/mircea-pitici-inspired-by-math-15/

I reviewed Pitici's latest 2012 edition on the blog HERE, and also included it in my book shopping list recommendations for Christmas a couple months ago.
[ADDENDUM: Yikes! Sol is churning out the podcasts lately and already has a lengthy, newer one up with Steven Strogatz -- haven't had a chance to listen yet, but undoubtedly HAS TO BE good stuff!]

Finally, what's worrying mathematicians these days…? We get a hint from John Brockman.
Brockman's cutting-edge/contemplative 'Edge' site has posted responses to its 2013 question "What should we be worried about?":

http://edge.org/contributors/q2013

Lots (150+) of good contributions of course, but I'll just link to three of the mathematicians who replied, and pique your interest with the first couple of lines from their entries:

Keith Devlin: http://edge.org/response-detail/23783

"Are we about to see advances in mathematics come to an end? Until last year, I would have said no. Now I am not so sure."

Clifford Pickover: http://edge.org/response-detail/23670

"I used to worry that our mathematical and physical descriptions of the universe grow forever, but our brains and language skills remain entrenched. Some of our computer chips and software are becoming mind-numbingly complex."

Steven Strogatz: http://edge.org/response-detail/23820

"In every realm where we exist as a collective — in society, in the global economy, on the Internet — we are blithely increasing the coupling between us, with no idea what that might entail."

Odds 'n Ends of Note... Enjoy!

An odd variety of sundry things catching my attention lately...:

1) Impressed?... plenty of folks might be. Math often bedazzles the easily impressionable! That's the basic conclusion of a study cited recently by both Mother Jones and the Wall Street Journal, demonstrating that just adding mathematics (even nonsense math!) to a journal article can increase its perceived quality among some reviewers:

http://www.motherjones.com/kevin-drum/2012/12/how-technical-sounding-nonsense-can-boost-your-career-prospects

http://online.wsj.com/article/SB10001424127887323374504578219873933502726.html

2) Mr. Honner recently highlighted a simple example (Google search), most of us can relate to, of how "conditional probability" operates in our everyday world:

http://mrhonner.com/2012/05/17/google-and-conditional-probability/

3) Is Henry Pogorzelski following in the steps of Shinichi Mochizuki…? A 90-year-old emeritus mathematics professor named Henry Pogorzelski believes he has proven the Goldbach Conjecture, but his effort may be too long and involved for anyone else to follow (similar to the problem mathematicians are having checking the complex work of Mochizuki on the ABC Conjecture); interesting Boston Globe piece:

http://www.boston.com/bostonglobe/ideas/brainiac/2012/12/math_even_mathe.html 

4) Futility Closet highlights a sort of self-referential geometric construction set from, as they say, "the ever-inventive" Lee Sallows:

http://www.futilitycloset.com/2013/01/03/construction-set/

Lee Sallows homepage is here: http://www.leesallows.com/

He is especially famous for his linguistic "self-enumerating pangrams" like the following:

"Only the fool would take trouble to verify that his sentence was composed of ten a's, three b's, four c's, four d's, forty-six e's, sixteen f's, four g's, thirteen h's, fifteen i's, two k's, nine l's, four m's, twenty-five n's, twenty-four o's, five p's, sixteen r's, forty-one s's, thirty-seven t's, ten u's, eight v's, eight w's, four x's, eleven y's, twenty-seven commas, twenty-three apostrophes, seven hyphens and, last but not least, a single !"

You can see more examples here:

http://www.fatrazie.com/EWpangram.html

5) Just learned of this online journal, "The Mathematics Enthusiast," that's been around for awhile and should be of interest to educators:

http://www.math.umt.edu/tmme/ 

6) A recent Twitter feed asked for suggestions of inspiring books to recommend to HS math students. What surprised me was how often Douglas Hofstadter's "Godel, Escher, Bach" (or GEB as it is often called) came up. Dr. Watkins also mentioned it very positively in the interview I did with him a few days back. GEB, is one of my favorite books as well (and it has certainly won many awards); still, I've never thought of it particularly as a math book… a book for those interested in psychology or philosophy perhaps, or even computer science, but not necessarily math buffs. In fact, Wikipedia states:

"Hofstadter has emphasized that GEB is not about mathematics, art, and music but rather about how cognition and thinking emerge from well-hidden neurological mechanisms."

...and here's an older Slashdot review of it:

http://books.slashdot.org/story/99/04/23/147248/godel-escher-bach----20th-anniversary-edition

Great book; I'm just not sure I'd be recommending it to HS math students, unless they're also very interested in cognitive science. (On-the-other-hand, possibly one could argue that what GEB does touch upon is not math itself, but the kind of "mathematical thinking" that Keith Devlin so emphasizes... I'm not sure???)

7) Finally, for a bit of entertainment, a clever, fun bit of magic (...and cognitive science of a sort) from Richard Wiseman. Not really math, but one thing I've learned since doing this blog is that for a lot of folks "magic" is actually a gateway into an interest in math.
If you're familiar with Wiseman's "tricks" you may see through this one fairly quickly... or... you may not (if YOU'RE not fooled by it, try it on a friend):

Catching Up On a Few Thangs

HAPPY NEW YEAR!!

An eclectic potpourri of links to get 2013 underway….

1) Last week, American Radioworks had a wonderful (hr.-long) show on the varieties of online higher education (not restricted to math education, but in general), entitled "Keyboard College." A highly worthwhile listen, if you missed it:

http://americanradioworks.publicradio.org/features/tomorrows-college/keyboard-college/

2) The Indian prodigy mathematician Ramanujan continues to amaze long after his death. Fascinating piece on mystical deathbed conjectures the young Indian made (inspired by a Hindu goddess) that have been proven true 90 years later:

http://www.dailymail.co.uk/sciencetech/article-2254352/Deathbed-dream-puzzles-renowned-Indian-mathematician-Srinivasa-finally-solved--100-years-died.html

...also, apparently a film of Ramanujan's life, "The Genius of Ramanujan" is due for release next March.

3) For William Thurston fans (of which there are many), a quite long read here on Thurston and the Haken conjecture:

http://www.scientificamerican.com/article.cfm?id=getting-into-shapes

4) The below site, I only recently learned of, may appeal to young math problem solvers and contestants out there:

http://blog.brilliant.org/

It offers up (level-appropriate) 'challenging' problems to participants on a weekly basis. Be sure to read the "FAQ," "How It Works," and "Blog" sections.

5) I remember Tom Lehrer as a satirical singer-songwriter in the 1960s when I was growing up. A recent post from another blog though reminds/informs? me that Lehrer was actually a professional Harvard-trained mathematician before he found entertaining on a stage more lucrative.
Anyway, as a victim of the 60's 'New Math,' this is how I remember him:



6) I haven't posted a puzzle on the blog for awhile, but here's a beautiful geometry one recently posted at "Futility Closet":

http://www.futilitycloset.com/2012/12/23/belt-loop/

7) And, in case that was too easy for you (though I doubt it) you can always download this PDF to learn about "the hardest logic puzzle ever" (originally stemming from Raymond Smullyan, and involving asking questions of gods):

http://www.snsanalytics.com/ask7y0


...and next up will be the first brand-spanking Math-Frolic interview of 2013... introducing someone most of you likely don't know.

Weekend Potpourri

To go along with your leftover turkey sandwiches another potpourri of mathy schtuff(ing) to choose from:

1) First, if you missed it, this nice little demonstration of the Pythagorean Theorem using water as a tool (it's not a technical or real "proof" but a very good 'visual' effect):




2) If you missed NPR's "This American Life" last week (…and you ought NEVER miss TAL), the prologue to the week's stories dealt with Frank Nelson Cole, who back in 1903 proved that a 21-digit number which Marin Mersenne had identified as prime centuries earlier, was in fact a composite number… worth a listen (to at least the opening prologue):  

http://www.thisamericanlife.org/radio-archives/episode/450/so-crazy-it-just-might-work

3) Not exactly math, but an interesting British piece on wartime (WWII) cryptography and pigeons flying secret codes; a recently found dead pigeon from the period has a small sheet of code attached to a leg that has stumped modern-day code-breakers:

http://www.bbc.co.uk/news/uk-20456782

"...without fresh information this pigeon may well have taken its secret to the grave." The BBC is actively asking for suggestions to decipher the message.

[ADDENDUM: great followup on this story from James Grime here:
http://singingbanana.tumblr.com/post/36586139513/the-curious-case-of-the-wwii-carrier-pigeon-and ]

4) Finally, a good discussion of Bayesian versus frequentist "inference" here, with plenty of comments:

http://normaldeviate.wordpress.com/2012/11/17/what-is-bayesianfrequentist-inference/

Some Longreads et.al.

While I'm working on interviews other things have a way of building up... so another list of links to pick-and-choose from today:

1) Long but GREAT presentation of 'simple groups' by Richard Elwes (from a few years back) that I've been meaning to pass along:

http://plus.maths.org/content/enormous-theorem-classification-finite-simple-groups

2) Nice small collection of classic "counterintuitive conundrums" here:

http://datagenetics.com/blog/may12012/index.html

3) Interesting, recent long read on "insanely long proofs" from John Baez:

http://johncarlosbaez.wordpress.com/2012/10/19/insanely-long-proofs/

4) And if you're not too phobic of philosophical (and perhaps computational) discussion you may enjoy this longish post on the "many worlds" interpretation of mathematics:

http://math.andrej.com/2012/10/03/am-i-a-constructive-mathematician/

5) On the more practical side, a list of resources for math teachers, of possible interest (but I haven't checked them out thoroughly myself):

http://new-to-teaching.blogspot.com/p/web-20-tools.html

6) And lastly, some quickie visual entertainment... I don't often link to optical illusions, because there are just TOO MANY good ones on the Web, but I hadn't seen this simple, effective one before, so passing it along:

https://twitter.com/Todd_Roy/status/231144475290923008/photo/1

....late Mon. or early Tues. I'll have interview #5 up-and-running, and it's from someone I was especially delighted to have take part!... but I'll hold you in suspense 'til then! ;-)
[The tab below the blog header above, btw, will take you to an ongoing list of all the interviews conducted.]