Thursday, February 27, 2014

Conrad Wolfram, Friday Potpourri, and...

1) "The central change in real-world maths of the last 50 or so years is that we automated the hell out of calculating." That's Conrad Wolfram in the course of espousing his view of digital reform for British math education (and singing the praises of Estonia for adopting a more computer-based math education system):
(...not surprisingly, he gets some push-back in the comments)

2) Several science bloggers do regular end-of-week linkfests to articles they found interesting over the prior week. I've been doing little "potpourri" posts haphazardly here at Math-Frolic from time to time to direct readers to pieces that I don't care to write a whole post on. I'll now try (as an experiment) to do a once-per-week "potpourri" offering over at MathTango (probably on Fri. or Sat.) of all the extra stories I want to take note of... a sort of weekly mini-math carnival solely of my own picks-of-interest.
Check MathTango tomorrow for the first one! (And then on Sun. or Mon. the next Math-Frolic interview will be up over at MathTango as well.)

3) Speaking of interviews... Frederick at White Group Mathematics recently interviewed yours truly for his blog (...wherein you learn that I'm waiting for a call from Taylor Swift ;-):

Tuesday, February 25, 2014

Mathematical Thinking and Black Swans

Inspired by Nassim Taleb, Veritasium's Derek Muller demonstrates our propensity for finding patterns (...that aren't there):

Monday, February 24, 2014

Don't Answer Too Fast

Haven't had time to post lately so for now just a re-run from a couple of years back to keep a grin on your face:

Monday, February 17, 2014

Empathy and Asperger's From the Lewis Thomas of Mathematics…

(Now with Addenda, at bottom....)

Not for the first time ;-), a tweet by Steven Strogatz caught my eye today.

But before I get to that tweet let me say that Strogatz was actually responding to another tweet from Jordan Ellenberg linking to a recent piece Strogatz did about the need for "empathy" in effective math communication:

A wonderful read, especially delightful for its interesting discussion of three of Strogatz's science communication "heroes": Richard Feynman, Stephen Jay Gould, and Lewis Thomas.

So DO read that piece. The tweet, however, from Dr. Strogatz that caught my eye ran as follows:

"A lot of us in math are on the Asperger's-autism spectrum, which can make the empathy issue even more challenging."

I thought that was a rather interesting remark, that 140 characters couldn't do justice to, so I googled around to see what I might find about Aspergers relation to math. Essentially, from what I saw, it seems safe to say that Aspergers individuals exhibit no significantly better mathematical (or other analytical) skill than the general population; indeed, many struggle greatly with math, the Asperger's spectrum being quite wide. But this isn't really what Strogatz is hinting at anyway… he's coming from the other side of the equation and implying that the population of (professional) mathematicians may have a higher number of Asperger's individuals within it than the population as a whole (i.e. the population of mathematicians might tend toward high Aspergers scores, even if Aspergers individuals, as a whole, don't tend toward mathematical aptitude) -- I really didn't find much in my brief search empirically addressing that question.

So am curious if anyone knows of any studies that have looked at say PhD.-level mathematicians or just working mathematicians, to see what percentage of them may score high for Aspergers, and is it greater than the general population?  It would be an easy study to conduct, since there are simple verbal tests to indicate (not diagnose, but nonetheless, indicate) one's potential position on an Aspergers scale, and by administering such a test to a large enough random sample of working mathematicians, one might get an initial indication of mathematicians' standing relative to the overall population.

ADDENDUM:  Thanks to all who sent along references/links to studies of this question. Possibly the best, easily-referenced source is this 2001 study from Simon Baron-Cohen and colleagues:

Baron-Cohen is one of the main proponents of the notion that mathematicians/scientists do indeed have increased predilection for the high end of Asperger's spectrum. Not everyone agrees with that, and the issues/variables are very complex, but here's part of the conclusion from the above study which utilized the AQ test as a measure of tendency to high-functioning autism:

"Finally, scientists score higher than non-scientists, and within the sciences, mathematics, physical scientists, computer scientists, and engineers score higher than the more human or life-centred sciences of medicine (including veterinary science) and biology. This latter finding replicates our earlier studies finding a link between autism spectrum conditions and occupations/skills in maths, physics, and engineering."
Of course all this plays into the stereotypical view people often hold of nerdy, geeky mathematicians... I don't really have too great a problem with that, except to caution that all generalizations are mushy, and "mathematician," like any other category includes a wide range of individuals and personalities.

ADDENDUM II:  Now someone sends along this link to an abstract further indicating a relationship of high-functioning autism with mathematicians:

A point I'd want to emphasize (given my cautionary statement above) is that while the mathematicians here exhibit significantly higher diagnoses than a control group, even among the mathematicians the rate of autism remains low at 1.85%. (For what it's worth, might also note that the subjects in this study, were all undergraduates at a single university, not randomly-selected professional or working mathematicians).

Monday Miscellany

...Science fiction, savantism, mushy Common Core, MOOCs, take your pick:

1) Both math and science fiction geeks should find Sol Lederman's latest wide-ranging podcast with Chuck Adler, physicist and recent author of "Wizards, Aliens, and Starships," interesting; lots of ideas tossed around:

2) I sometimes take note of prodigies and savants here, and the Jason Padgett story is one of the most interesting (Jason attained his mathematical artistic talents only after having been mugged and receiving a severe head injury). A new book out, "Struck By Genius," chronicles his story:

3) and then there's this:
“If you were to graph the creative flexibility afforded our highly educated and maximally qualified teachers over time with common core, you would find that both the first derivative of the function and, most alarmingly, the second derivative of the function, are negative. There is no point of inflection as the function approaches infinity (i.e., increasingly decreasing teacher autonomy, with no turnaround in sight.)”
If you haven't a clue what that's all about, read the rest of an engineer's commentary on Common Core here:

4) Finally, MOOCs are full of good, bad, and uncertainty, and continue receiving lots of criticism from outside observers -- sure, there are various numbers/statistics that give rise to such negative views, BUT I for one continue to think we're still very early in the game of a revolutionary development.  Perhaps no one has thought about (and worked on) MOOCs any more than Keith Devlin, and so another quick take from him defending their future:

Thursday, February 13, 2014

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!):

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:

" '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: 

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:

Wednesday, February 12, 2014

Heeeeere's Mathbabe… and Steven too

I'm delighted today to direct readers over to MathTango for an interview with Cathy O'Neil, "Mathbabe" of the blogosphere:

If you don't already follow her blog regularly you should! -- I consider it must-reading. Cathy is a former Wall Street 'math quant' who deals with a variety of topics and issues, including some not generally found on math blogs (and also some pure humor), and it is one of the best-written math blogs out there. At the end of the interview I link to another excellent video interview she did with PBS's Frontline series 2 years ago, and you ought try to find 40 mins. free to watch that as well (gooood stuff!).

...Also, in interview mode, Patrick Honner conversed extensively with Steven Strogatz in the current (Feb.) issue of Math Horizons and a nice excerpt is available on the Web here:

I love that this particular section goes into some detail about the writing of Strogatz's 2009 book "The Calculus of Friendship" -- a volume he calls "emotional" and "raw, yet understated."  Just a few days ago I tweeted that every math-lover should read this book (and it has more math in it than you might expect, even though it is primarily an intimate, moving life story), and so the timing of this excerpt is excellent.
What better way to spend a snowed-in wintry day than with Cathy and Steve!

Sunday, February 9, 2014

Relaxing on Sunday with Frank, Mike, Fawn

My last two posts (Feb. 4 & 9) at MathTango touch on the frequent topic of "beauty" in mathematics (including Frank Wilczek's take); if you missed them, easy reading for a lay-back Sunday morning:

…and if you missed this engaging Mike Lawler rendition of a Fawn Nguyen problem for her middle-schoolers, also worth a Sunday gander:

Friday, February 7, 2014

Language and Math… and a PhD. (and Navier-Stokes)

Je l'aime quand vous parlez fran├žais....*

Perhaps I've just been too long outside the loop of higher academia, but here's something I was completely unaware of:
"...a little-known fact: to get a PhD in maths from Harvard, you need to be a language buff. The university points out that 'almost all important work' is published in French, German, English or Russian, and so 'every student is advised to acquire an ability to read mathematics in French, German and Russian'. This makes it sound optional, but if you want the PhD you have to pass a two-hour written exam in two of these three languages."
That's the beginning of a new piece in the New Statesman which is actually about the recent claim of a Kazakh mathematician to have proven the generality of Navier-Stokes equations, one of the Millennium Prize problems. Because of the complexity of the proof, and the fact that it is written in Russian, it will take significant time to confirm, and so we face what the author calls "a mathematical pile-up at the language barrier."

The article is interesting for its brief discussion of Navier-Stokes, but I was more struck by the "little known fact." Assuming the author is correct, and a knowledge of two languages outside English is indeed a requirement (not merely highly-advised) for the Harvard math PhD., I'm curious if this is now the norm at most top-flight mathematics graduate schools, or does it vary considerably from PhD. program to PhD. program? Also, does the "ability to read mathematics in French, German and Russian" perhaps entail significantly less proficiency than would be required for fluency or conversational ability in the languages?

(*  "I love it when you speak French" ;-)

Thursday, February 6, 2014

Prime… Yes or No

Returning from their excursion into the addition of infinite series, to just plain ol' normal levels of incredibleness ;-) Numberphile is back with the AKS primality test (initials from the names of its three originators), which amazingly, is an algorithm discovered only in 2002, for testing whether or not any integer is a prime. There are some other similar algorithms, but as Wikipedia states, "AKS is the first primality-proving algorithm to be simultaneously general, polynomial, deterministic, and unconditional." And from Wolfram MathWorld this Paul Leyland quotation regarding the finding: "One reason for the excitement within the mathematical community is not only does this algorithm settle a long-standing problem, it also does so in a brilliantly simple manner. Everyone is now wondering what else has been similarly overlooked."
Anyway, watch and enjoy as James Grime explains further:

ADDENDUM:  just discovered that Grey Matters blog has also done a nice explanatory post on the Numberphile video here:

Monday, February 3, 2014

Re-visiting Sleeping Beauty

(via Rachel CALMUSA/WikimediaCommons)

In chapter 11 ("Is Time an Illusion") of Max Tegmark's new book "The Mathematical Universe" the author, while discussing the nature of time and human consciousness, touches upon the "Sleeping Beauty" puzzle/paradox, which I mentioned here almost two years ago:

This is one of the most interesting and delicious (perhaps even complicated, in some ways) puzzles around, as people argue vociferously for either of two different answers (1/2 or 1/3), because of the conditional probabilities involved.
[Here is one statement of the puzzle: Sleeping Beauty undergoes the following experiment, being told all these details ahead of time. On Sunday she will be put to sleep. A fair coin will then be tossed to determine which experimental procedure is undertaken. If the coin comes up heads, Beauty is awakened and interviewed on Monday, and the experiment ends. If the coin comes up tails, she is awakened and interviewed on Monday AND Tuesday. But when she is put to sleep again on Monday, she is given an amnesia-causing drug which ensures she cannot remember the prior awakening. In this case, the experiment ends after she is interviewed on Tuesday.  Whenever Sleeping Beauty is awakened and interviewed, she is asked, "What do you believe is the probability that the tossed coin landed on  heads?" -- What is her answer?]
In re-visiting the links I provided in my original blog post I discovered that the "Tanya Khovanova" link has since added further lo-o-ong discussion of the issues by two commenters back-and-forth, which is probably worth checking out if you are especially interested in probability in general, or this problem in particular (if these areas don't interest you, don't visit it, lest you fall into a deep, deep coma, or alternatively, your head explode ;-)