Marilyn and Martin

Just an old article I linked to over a year ago and am passing along again, because it's such an interesting backstory:

http://tinyurl.com/y7vpy3ma

It's about the (working) relationship between Marilyn vos Savant and Martin Gardner, and about a slim oddball volume Marilyn penned back when Andrew Wiles 'proved' Fermat's Last Theorem.

Marilyn vos Savant Steps In It…

Marilyn vos Savant is widely-known for writing a column and giving answers to puzzles of all sorts... and also famous for sometimes having her answers challenged, only to have the critics often embarrassed — famously so in the instance of the Monty Hall problem, but occasionally with other problems as well (she’s also had to correct or refine given answers on various occasions).

I didn’t recall however her controversy over Andrew Wiles’ proof of Fermat’s Last Theorem ’til I read the below brief passage in David Wells' “The Penguin Book of Curious and Interesting Mathematics”:

“Less than five months after Wiles’s lecture, she published a book, The World’s Most Famous Math Problem (The Proof of Fermat’s Last Theorem and other Mathematical Mysteries), in which she claimed that non-Euclidean geometry is unsound, and so therefore is Wiles’s proof, because he uses non-Euclidean geometry. She also claimed that his proof depends on developments in mathematics that are relatively recent and poorly understood, and she encouraged her readers to try to ‘demolish Einstein’s theories of relativity’ by proving the parallel postulate.”

Wow, pretty harsh… I’ve never read her short (80-page) book, but as best I can tell, the consensus of professional mathematicians is more uniformly critical of it than some of her other writings; one mathematician calling the book “pure drivel” (and this is despite Martin Gardner writing the Foreward, initially calling the volume "a delightful, informative, and accurate book”).

IF I understand correctly, Marilyn did retract much of her criticism at a later date?

I recommend a very interesting read, by the way, about the whole Gardner/vos Savant relationship here:

http://tinyurl.com/y7vpy3ma  (link corrected, I think?)

Anyway, if anyone out there is more directly familiar with this particular controversy (and book), and cares to add anything further about it, I’d be curious to hear.

Is Savant Itchin' For a Fight?

Switch or don't switch... does that sound familiar?

Marilyn vos Savant is famous for (among other things) posing the original "Monty Hall puzzle" to a national audience, and baffling many, including experienced mathematicians. By now, almost anyone having interest in the puzzle no doubt knows the correct answer and why.

So it seemed a bit curious that in yesterday's Sunday "Parade" magazine column Marilyn deals with a similar-sounding puzzle that arrives at a different answer (the answer, 50/50, many had sought for the original Monty Hall). It's almost as if she were itchin' fer a fight, because I imagined that some folks, thinking back to Monty Hall, would reflexively argue she is wrong here. She is, of course, right, because the conditions or set-up are different from the Monty Hall example, but because she doesn't offer any lengthy explanation, it's predictable that she would churn up some naysayers who think she's inconsistent, and try to take her to task (...it has already begun in the comments).
See the column here:

http://parade.condenast.com/333629/marilynvossavant/should-you-swap-or-not/

By the way, a great book covering the Monty Hall puzzle in all its variations is, "The Monty Hall Problem" by Jason Rosenhouse from 2009.

Meanwhile, please be sure to also check out the very different, completely NON-mathy post over at MathTango today.

Of Primes and Probability

Two bits for a Wednesday...:

1) In a fascinating long-read for Quanta Magazine, Erica Klarreich covers the astounding progress so far made in the "prime number gap" of the Twin Primes Conjecture, in just six months since Yitang Zhang postulated a limit to the gap of 70 million!:

http://tinyurl.com/pw6hyyz

James Maynard, a post-doc, has wrestled the gap down to no more than 600, well below the result that even Terry Tao's Polymath group had yet achieved.

an excerpt to whet your appetite:

"Zhang’s work and, to a lesser degree, Maynard’s fits the archetype of the solitary mathematical genius, working for years in the proverbial garret until he is ready to dazzle the world with a great discovery. The Polymath project couldn’t be more different — fast and furious, massively collaborative, fueled by the instant gratification of setting a new world record.
"For Zhang, working alone and nearly obsessively on a single hard problem brought a huge payoff. Would he recommend that approach to other mathematicians? 'It’s hard to say,' he said. 'I choose my own way, but it’s only my way.'
"Tao actively discourages young mathematicians from heading down such a path, which he has called  'a particularly dangerous occupational hazard' that has seldom worked well, except for established mathematicians with a secure career and a proven track record. However, he said in an interview, the solitary and collaborative approaches each have something to offer mathematics.
“ 'It’s important to have people who are willing to work in isolation and buck the conventional wisdom,' Tao said. Polymath, by contrast, is 'entirely groupthink.' Not every math problem would lend itself to such collaboration, but this one did."

2) I mentioned a couple of posts back that in the Preface to his new book ("Will You Be Alive 10 Years From Now?") Paul Nahin gives an example of a Marilyn vos Savant column where the famous Mensa-ite gives the WRONG answer to a math question and sometime later corrects herself. The question, and her initial ill-fated answer ran as follows:

Q.: "I manage a drug-testing program for an organization with 400 employees. Every three months, a random-number generator selects 100 names for testing. Afterward, these names go back into the selection pool. Obviously, the probability of an employee being chosen in one quarter is 25 percent. But what’s the likelihood of being chosen over the course of a year?"

A.: "The probability remains 25 percent, despite the repeated testing. One might think that as the number of tests grows, the likelihood of being chosen increases, but as long as the size of the pool remains the same, so does the probability. Goes against your intuition, doesn’t it?"

Nahin points out that the actual probability of being chosen at some point during the four quarters of testing works out to 0.6836, considerably greater than Marilyn's 0.25.

In a later column Marilyn 'fessed up, "My neurons must have been napping" and corrected herself:

http://www.parade.com/45916/marilynvossavant/22-sunday-column-2/

You can also see the math involved at this Forum site where the problem was discussed:

http://www.aiqus.com/questions/34413/ask-marilyn-new-probability-question-controversy