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Monday, August 21, 2017

Probably Not Just Coincidence...

I’ve adapted this little puzzle from one of the recent "Riddler" postings over at FiveThirtyEight blog:
Say (you know just for the sake of imagination), that you’re the President of the U.S. and you’re panties are in a wad because there are too many leaks coming from your Administration. So of course you wish to catch the sniveling culprit and axe them from your staff. Thus, you hatch a plan: You will give, at different times, different stories out to each of your 100 staffers and watch to see what bits end up in the press — we’ll assume there is just one leaker and they always leak what they know to the media. How many different concocted stories, minimum, do you need to feed to your staff of 100, in what manner, over time to be able to identify the leaker?
.answer below
7 stories are required IF you release them sequentially as follows:
The first story is told to half your staff (50 people) and withheld from the other 50 staffers. If it is leaked, you immediately know the leaker is among the first 50, or, if it doesn’t leak, the leaker is in the other half. Whichever 50 staffers are still suspects, give 25 of them a new story, and withhold same from the other 25. Repeat this process and you get a sequence like this: 100, 50, 25, 13, 7, 4, 2, 1, such that within 7 steps you’ve narrowed the search down to one culprit.

[p.s…: any resemblance between this process and our current Administration is probably not just coincidence.]

Sunday, August 20, 2017

Math Was Never the Same Again

Sandro Contenta provides this Sunday reflection from a profile of Canada’s Robert Langlands:

“In 1966, [Robert] Langlands almost abandoned mathematics. Deep mysteries in number theory discouraged him. He decided on a change of scenery and applied for a job in Turkey.
‘The decision itself freed me and I began to amuse myself with mathematics without any grand hopes or serious intentions,’ he said in written answers to a 2010 UBC interview.
Inspiration struck during the Christmas break, in an empty, grand old building on the Princeton campus, as Langlands gazed at a garden through leaded windows.
He described his revelation in a Jan. 16, 1967 letter to Andre Weil, a giant in the field of number theory: ‘If you are willing to read as pure speculation,’ he wrote Weil, I would appreciate that; if not — I am sure you have a waste basket handy.’
"Three years later, after he’d returned from Turkey, Langlands published his two theories, called functoriality and reciprocity, under the title ‘Problems in the Theory of Automorphic Forms.’ Math would never be the same again.”

Thursday, August 17, 2017

It Was a Wiles Wednesday

Two pieces on Andrew Wiles showed up yesterday… with little overlap ;)
Ben Orlin and his round-faced friends here for your light read:

…and Peter Cameron delving into the Langlands Program here with some heavy going:

And even if you've seen it before, always worth watching again:

Wednesday, August 16, 2017

If I Had A Hammer... I'd Hammer Out a Warning

Sorry, I’m in a mood (someone put me there), so just a bit more music for the moment (‘cuz as bad as the 60’s were, they seem glorious compared to today):

Sunday, August 13, 2017

American Tune...

“And I don't know a soul who's not been battered
I don't have a friend who feels at ease
I don't know a dream that's not been shattered or driven to its knees
But it's alright, it's alright, for we live so well, so long
Still, when I think of the road we're traveling on
I wonder what's gone wrong, I can't help it I wonder what's gone wrong”

Category Theory via Eugenia Cheng

For Sunday reflection, Eugenia Cheng describing 'category theory':
"This is how category theory arose, as a new piece of math to study math. In a way, category theory is an ultimate abstraction. To study the world abstractly you use science; to study math abstractly you use category theory. Each step is a further level of abstraction. But to study category theory abstractly you use category theory."

Thursday, August 10, 2017

"the psychology of unspeakable truths"

I hope you've already seen it, but in case not, Scott Aaronson's latest post is both a thoughtful tribute to A.N. Kolmogorov and a somewhat stoic commentary about the world we  find ourselves in:

...an important read, though not for any math.

Tuesday, August 8, 2017

In Case I’m Banished to a Gulag

People love… and... hate, lists… at least they’re a fun time-and-space-filler, so I've been thinking about which books I’d grab off the shelf if Donald Trump, in his wisdom (spelled “p-a-t-h-o-l-o-g-y”) decided to banish me to a remote Gulag, only letting me take along 10 of my math-related books; which ones might I grab quickly for sustenance and entertainment? In no particular order, here’s what I chose (some aren’t particularly mathy though):
a) The Colossal Book of Mathematics  — Martin Gardner (...so much fun and games and puzzlement!)
b) How Mathematicians Think — William Byers  (...a long time favorite of mine about ideas permeating and underlying mathematics)
c) The Outer Limits of Reason — Noson Yanovsky  (...my favorite volume from the last few years, weaving together so many important subjects)
d) How Not To Be Wrong — Jordan Ellenberg  (...popular best-selling treatment of mathematical thinking)
e) Things To Make and Do In the Fourth Dimension — Matt Parker  (...jaunty, wise, diverse, instructive topics)
f)  Love and Math — Ed Frenkel  (...fascinating bio and intro to the Langlands Program)
g) Math In 100 Key Breakthroughs — Richard Elwes  (...succinct overview of key math topics)
h) The Music of the Primes — Marcus du Sautoy  (...'cuz I gotta have one volume devoted to the Riemann Hypothesis)
i)  Metamagical Themas — Douglas Hofstadter  (...some of the best stuff from Hofstadter's fertile mind)
j)  Beyond the Hoax — Alan Sokal  (...not math, but rich overview of critical thinking and much more)
Oddly two of my favorite math expositors, Keith Devlin and Ian Stewart, didn’t quite make the cut, though I’ve happily read more of their books than any of the above authors. Nor does it include the single volume I still most frequently recommend to lay people: Strogatz’s “The Joy of X.”  And a lot of other wonderful picks, including some older classics, go unmentioned as well.
Admittedly, an eclectic list, framed to my interests, that wouldn’t satisfy many of the math-folks likely beside me at the Gulag. Oh well, at the very least I suspect I'd have the company of Devlin, Ed Frenkel, and John Allen Paulos along to help entertain me! ;) (...and probably many more of you as well; hey, maybe even Andy Borowitz would be there to keep us all in good humor).

Monday, August 7, 2017

Sunday, August 6, 2017

Math Methods Versus Math Tricks

This week's Sunday reflection comes from Jim Propp in a recent Web piece:
"Mathematicians are people who like solving problems, and have the persistence to work on problems that take time to solve, and have collected a mental tool-kit consisting of methods that have helped them solve problems in the past. Some mathematicians distinguish between methods and tricks. A method is a tool that solves more than one problem, while a trick is a tool that applies to only one. Under this definition, I’d say that there are no tricks in math, and part of the discipline of getting good at math is to study every trick you encounter until you see the method hiding inside it."

Thursday, August 3, 2017


James Grime is a bit deranged in this recent Numberphile episode (or maybe he's a bit deranged in any Numberphile episode… and I mean that in a good way!):

Monday, July 31, 2017

Claude Shannon… & Guest Posts Anyone?

Newly out, “A Mind At Play,” a biography of Claude Shannon:
(the title seems to be a play on Siobhan Roberts very successful/excellent bio of John Conway entitled “Genius At Play”)
Also, John Horgan has posted a piece on the bio and on Shannon’s life (including an old interview):
Meanwhile... I’m having limited time to devote to blog posts at moment with too many summer things intervening, but if anyone is interested in writing a math-themed “guest” post for either here or MathTango, let me know [sheckyr[AT]gmail…] and I’d consider that to pick up some of the slack! Just let me know what you have in mind (...please, no proofs of the Riemann Hypothesis, P vs. NP, etc. ;)

Sunday, July 30, 2017


From a recent Michael Harris essay:
“The ideology of mathematical certainty and objectivity is our most potent weapon; we should not allow it to be used to undermine democracy. With regard to mathematical modeling, we should constantly remind anyone who is willing to listen that a model is not objective or scientific just because it is mathematical.”

Thursday, July 27, 2017

Michael Harris Asks "Do Mathematicians Have Responsibilities?"

H/T to Peter Woit for pointing out this provocative piece from Michael Harris (author of "Mathematics Without Apologies") on Reuben Hersh, politics, Embodied AI, and mathematics: 

Tuesday, July 25, 2017

Replicate THIS

If you missed it, last week’s NPR’s “On The Media” show included a nice segment (number 2 out of 4) on the ongoing replication problems in psychology:

Sunday, July 23, 2017

Real Numbers... not simple at all

a reflection on the reals...:

"The metaphor of the real numbers as a line... is very simple and self-evident. In fact, the identification of the real numbers with the picture of a line is almost too simple because it gives people the impression that the real number system itself is simple and easily understood. Yet real numbers are not simple at all -- in fact, real numbers are one of the most complex creations of the human mind. Even today, all kinds of questions about real numbers are not understood, and remain unresolved."

-- William Byers in "The Blind Spot"

Thursday, July 20, 2017

Prime Stuff...

Always elusive prime numbers...

1) Super piece from Kevin Hartnett in Quanta today about the work of Kaisa Matomäki on prime factors and related ideas:

2) ...and timely, as it follows up on a new Numberphile video yesterday with James Maynard on prime gaps:

3)  And earlier in week Evelyn Lamb pointed out this fun li'l excursion into prime numbers I'd missed from a few weeks back:

Wednesday, July 19, 2017

Robert Langlands

Wonderful piece on Robert Langlands... not sure what the date on it is (I assume recent?), but h/t to Graham Farmelo for pointing it out on Twitter:

Sunday, July 16, 2017

In Memoriam

For Sunday reflection, this from Maryam Mirzakhani in a prior Guardian interview (re-published from the Clay Mathematics Institute):
“…the most rewarding part is the ‘Aha’ moment, the excitement of discovery and enjoyment of understanding something new – the feeling of being on top of a hill and having a clear view. But most of the time, doing mathematics for me is like being on a long hike with no trail and no end in sight…. 
“I don't think that everyone should become a mathematician, but I do believe that many students don't give mathematics a real chance. I did poorly in math for a couple of years in middle school; I was just not interested in thinking about it. I can see that without being excited mathematics can look pointless and cold. The beauty of mathematics only shows itself to more patient followers."
[also see yesterday's posting ]

Saturday, July 15, 2017

"A Light Was Turned Off Today..."

VERY sad news today in the math world with the announcement of mathematician/Fields Medalist's Maryam Mirzakhani death from cancer at the all-too-young age of 40. When I see some more lengthy tributes to her posted I’ll add some links below. For now I'll pass along Erica Klarreich's profile from a few years back... and, a Neil Diamond oldie:


Terry Tao posted this:

This from Stanford University where she was a professor:

The New York Times obituary now here:

This from The Guardian:

And Evelyn Lamb weighs in here for Scientific American:

And John Baez on Google+:

The wonderful Siobhan Roberts in the New Yorker:

Sunday, July 9, 2017

Fearing the Wrong Things

Sunday reflection from David G. Myers in John Brockman’s volume “Know This”:
“News-feed images can make us excessively fearful of infinitesimal risks. And so we spend an estimated $500 million on anti-terrorism security per U.S. terrorist death but only $10,000 on cancer research per cancer death. As one risk expert explained, ‘If it’s in the news, don’t worry about it. The very definition of news is ‘something that hardly ever happens’…. 
“Media researcher George Gerbner’s cautionary words to a 1981 congressional subcommittee ring true today: ‘Fearful people are more dependent, more easily manipuated and controlled, more susceptible to deceptively simple, strong, tough measures and hard-line postures.’ 
“Ergo, we too often fear the wrong things. And it matters.”

Sunday, July 2, 2017

Read This Sentence.

"This sentence contains ten words, eighteen syllables, and sixty-four letters."

(a Sunday reflection via J. vos Post)

Tuesday, June 27, 2017

The Yingying Zhang Case...

Newest updates are at the top in reverse chronological order...
Sorry the more extended post below has become a bit messy/disorganized by now, but don’t have time to reorganize it.

6pm. EDT, 7/20: At Brendt Christensen's arraignment today the suspect (as expected) pled 'not guilty.' A pre-trial hearing is scheduled for August 28, before a start date for the trial of September 12. There was no further news about the crime itself, nor the search for Yingying Zhang's body.
6pm. EDT, 7/19: Just a reminder that tomorrow the arraignment of Christensen takes place (3pm. in Urbana, IL.). I presume, in line with previous indications, that he will plead ‘not guilty’ to kidnapping and related charges (no murder charge brought as yet). I’m assuming it’s too early for any plea bargaining to have occurred yet, but I don’t know that much about legal procedures, so will update tomorrow once we know more.
Still no news of official searches for Yingying Zhang, let alone finding her body. Her distraught parents remain in the U.S. (from China) awaiting any further outcome to this sad, senseless case.
4:30pm. EDT, 7/14:  In a morning news conference, Champaign CrimeStoppers with the Zhang family officially announced that the reward for information leading to Yingying Zhang was raised to $50,000 (also the FBI has its own separate reward). No real additional news given.
This week the FBI took Zhang’s name off its “missing persons” listing, indicating how strongly they must feel their knowledge of her demise is (a person ‘in absentia’ is more normally dropped from a missing persons’ listing after 7 years, not a few weeks).
I have my own scenario in mind now of how this crime played out, and where the victim’s body may be, but purely speculative on my part so no need to spell out. But I do hope police don’t let another week go by without an update. And again, Christensen's official arraignment is set for next Thursday, July 20th. (I'm also a bit curious as to whether prison guards have him under any sort of suicide watch?)
5pm. EDT, 7/12: Today, a Federal grand jury returned an indictment charging Brendt Christensen with kidnapping visiting scholar Yingying Zhang; arraignment yet to be scheduled, but the originally-scheduled July 14th preliminary hearing is now cancelled.
Search for Zhang's body presumably continues. [ADDENDUM: according to Chicago Tribune article, arraignment is now scheduled for July 20, where Christensen will enter a plea (previously rumored he would plead innocent).]
8pm. EDT, 7/9:  Well, I was wrong on that (prior) hunch… NO significant news released over weekend thus far. Plenty of speculation and ideas swirling around the Web about this strange case, but I’ll probably wait for some sort of official, substantive info before posting news here.
9pm. EDT, 7/6:  nothing of significance to add today, except that press has been told that the accused will plead innocent at preliminary hearing; not at all unusual early on. I'll be surprised if this case gets through the weekend without some major further break or the victim's body being found (but merely a hunch on my part). Oh, and Brendt Christensen is now being jailed in my old hometown of all places, about an hour from Champaign-Urbana.
5pm. EDT 7/5:  Latest local news article (with some new information) following another brief hearing for Brendt Christensen (in which he was denied bail). It is possible he will enter a plea at a July 14th hearing:
Still no recovery of the victim's body.
5:30pm EDT 7/4:  Not that this really means anything, but just learned that Christensen graduated about 4 yrs. ago (undergraduate) as a double major in physics and math at the University of Wisconsin/Madison. So, in some weird sense maybe this case isn't as completely unrelated to this blog as I've previously said!
There will be another court hearing for Christensen tomorrow afternoon, though doubtful we'll learn much new.
And still no word of active searches for the victim Yingying Zhang...?

morning 7/3:  At a 9-minute hearing today Brendt Christensen was read his rights and was represented by a Champaign law firm, with additional hearings scheduled for July 5 and 14th. No pleas or new information given.
Also, stiiiiiiiiill no information on the search for Yingying Zhang's body.
There are MANY more pertinent links (including Christensen’s social media postings) to this case by now, but I won’t link to more at this point unless there is a major new development in the case. Having said that, I will leave this post up for awhile because there remain several oddities about the case that need resolving before assuming the story is known. (Once I’m satisfied the story, though obviously not the trial, is largely over, I’ll likely scrap this post from the blog.)
[below are the "updates" from 6/27 to 7/2]:

==> UPDATE!!!! (5pm. EDT, 6/27):  The black Saturn Astra described below HAS now been located by law enforcement; Ms. Zhang has not been found at this time (not much more info currently being given, but hopefully later tonight we'll know more):

6 am. EDT, 6/28: No further news overnight in the case. The official (somewhat oddly-worded) FBI statement on finding the vehicle is HERE. They have the car but continue to seek public help in their search for the suspect and Zhang. No news even, on where the car was found, or in what condition. Hope we'll know more today.

9pm. EDT, 6/28: Over 24 hours since FBI announced finding the black Astra, yet no further details or information given on this crime. No sign of Yingying Zhang. All very strange. Still hoping for a good outcome in days ahead.
noon EDT, 6/29: Oddly, stiiiiiiill nothing new being reported, and for more reasons than I’ll report, the case seems increasingly peculiar. The resolution, positive or negative, may not be what people expect.

9:30pm EDT, 6/29:  No more news today. CNN did run this story on the case this morning (but nothing new that wasn’t already known):
(While newspapers have had some coverage of the crime, national TV and radio have carried remarkably little about it. Strange.)
8:30pm EDT, 6/30: Still nothing new today from officials on the case. We're now at the 3-week point since the alleged kidnapping.
If no news by tomorrow morning, I may continue with a new post tomorrow about some of what I find odd.

==>BREAKING:  9:30pm EDT, 6/30: Wow, local (Illinois) news reporting Brendt Christensen, 27, at Stonegate Apts. in Champaign arrested for kidnapping of Zhang who at this moment has not been found, and very sad to report, "law enforcement agents believe that Ms. Zhang is no longer alive." Await confirmation of all information.
Turns out suspect is a grad student in "condensed matter physics." [correction: he graduated in May with his Master's degree, and left the PhD. program]
The full "criminal complaint" (with several details leading to his arrest) against Christensen is here:
This site/page summarizes much of the info from the criminal complaint, as well as having additional material about Christensen:

5am. EDT, 7/2: recent timeline article from the local News-Gazette newspaper:

[the original blogpost, from 6/27/17, below]:

A major diversion today:
Wouldn’t normally use the blog for such a purpose (especially given how many unsolved crimes are out there), but a recent assumed broad-daylight kidnapping at the University of Illinois (where several of my friends attended) and near where I grew up, has grabbed my attention. 
If you’re not aware of it, it is the Yingying Zhang case; a Chinese visiting scholar who disappeared on June 9th and has not been seen since, but was last viewed on camera getting into a black Saturn Astrathe one below:

This model car was only produced a couple of years (~2008-9) and there can’t be all that many still on the road (relative to other car models). Be on the lookout for it! (by now an abductor could be far, far away from the point of the crime, Champaign-Urbana, Illinois; and could've also changed vehicles for that matter).
You can call 911 or Champaign Crimestoppers: 217-373-8477 or the FBI numbers: 217-522-9675 or 800-CALL-FBI with any information... SOMEone out there must know this individual (white male).
This is a high-priority case for the FBI with a major reward.

Here’s one news story on the crime (obviously you can google for much more):  

Surprised at how little national news coverage this case has received (I only learned of it myself by chance on the Web). The crime is already over two weeks old, so time is of the essence. One can only imagine the agony for Yingying's parents who've come here from China to aid in any way they can (a GoFundMe campaign on their behalf has surpassed its initial goal).

....On a complete (less serious) side-note:  at one crime website, I noticed a commenter bemoaning that since discussing this case they were now getting repeated ads for Saturn Astras on their computer screen! ...can’t help but shake my head; this is what the supposedly vaunted algorithms of Facebook, Google etc. bring to our attention! I’ve complained before that most (by which I mean 98%+) of the digital ads I get are of no interest (or even antithetical) to me! yet someone is paying Web powerhouses big (wasted) bucks to annoy me with them. Unlike some folks, I’m not that opposed to advertising, but how about turning me on to products/services I’m actually seeking, instead of turning me OFF to products/companies. 
So just to be clear, something I have NO interest in purchasing is a: black Saturn Astra, black Saturn Astra, black Saturn Astra, Saturn Astra, black Saturn Astra, black Saturn Astra, Saturn Astra, black Saturn Astra, black Saturn Astra, Saturn Astra, black Saturn Astra, black Saturn Astra, black Saturn Astra, black Saturn Astra. 
Good (instead of lazy-ass) algorithms are hard to write, but it is possible.

Returning to a serious note, please help to solve this case if you can.  Law enforcement is very tight-lipped about their progress on the crime (one hopes they know much more by now than they are saying), but certainly continues to seek input from the public.
ADDENDUM:  I’ll add further notes here as I think warranted:

1)  Obviously, folks should probably take note of any black Saturn Astras suddenly being put up for private sale recently… or, any being re-painted, or otherwise altered in appearance.

2)  The perpetrator in this case may have already ditched the vehicle, but IF still driving it, must be stopping for gas on occasion, and other necessities… gas stations, grocery stores, Walmarts, are among locales to be on lookout for the vehicle.

3)  Some additional webpages:

Two Twitter feeds with news:

The Univ. of Illinois Police Dept. website may be the best place to get ‘official’ updates on the investigation:
They also have a Facebook page here: 


Monday, June 26, 2017

Chaos Versus the Multiverse

“Science predicts only the predictable….It is only the way we look at the universe that gives us the illusion of structure.”

Dr. Noson Yanofsky authored my favorite book of 2013, “The Outer Limits of Reason” (and in fact one of my favorite books of all time!), and now has a new provocative Nautilus article out weaving together more interesting topics, including number systems, the octonions, multiverse theory, and the way our perception acts as a sieve for the patterns we recognize and structure that may be an illusion. I recommend both physicists and mathematicians give it a whirl:

Sunday, June 25, 2017


An old bit today from Paul Watzlawick's 1976 volume, "How Real Is Real?":
"There is a joke, known to most psychology students, in which a laboratory rat says of its experimenter, 'I have trained that man so that every time I press this lever, he gives me food.' Obviously the rat sees the S-R (stimulus-response) sequence quite differently than the experimenter does. To the experimenter, the rat's pressing the lever is a conditioned reaction to a preceding stimulus administered by him, while to the rat, the pressing of the lever is its stimulus administered to the experimenter. To the human, the food is a reward; to the rat, a reaction. In other words, the two punctuate the communicational sequence differently. Ordering sequences in one way or another creates what, without undue exaggeration, may be called different realities."

Friday, June 23, 2017

Sunday, June 18, 2017

Prove or Disprove

John Allen Paulos, from his older volume, “Once Upon a Number”:
The joke about the mathematics professor who gave a test consisting of four problems is apt. The first three problems required proofs of theorems and the last one was a statement prefaced with the directions ‘prove or disprove.’ One student toiled for a while and then came up to the professor’s desk and asked, ‘On that last problem, do you want me to prove it or disprove it?’ The professor responded, ‘Whichever is the right thing to do.’ ‘Oh,’ replied the student, ‘I can do either one. I was just asking which one you preferred.’ The interchange, of course, would not be a joke if the subject were history or literature.”

Wednesday, June 14, 2017

Puzzles To While Away Time

In the event you need something to distract you from the news-of-the-day, a few puzzles from the week…

1)  First some puzzle site suggestions via AMS:

2)  Jim Propp begins his own series of video math puzzles here (you know it’ll be good):

3)  And from Futility Closet this 1976 prime number puzzle:

4)  And lastly, not exactly a puzzle, but a game using a variation on Tic-Tac-Toe to make it more interesting (or maybe not):

Sunday, June 11, 2017

The Infinite and Perfect, Studied by the Finite and Flawed

Today's Sunday reflection comes from Bruce Schechter's biography of Paul Erdös, "My Brain Is Open":
"Mathematicians are finite, flawed beings who spend their lives trying to understand the infinite and perfect. That kind of thing is bound to result in problems and misunderstandings. Trends and fashion, politics and pig-headedness all affect the lurching progress of  mathematical knowledge. None of them, however, affect the validity of mathematical knowledge. 'There are many ways,' [Edward] Rothstein writes, 'to show that the ratio between the circumference of any any circle and its diameter is always the same, a number known as pi. The priests, farmers, and builders who first used that ratio may have had various intentions and goals. And the ratio may be given names like pi or zed or Milwaukee, for that matter. But the number and its meaning are unaffected by cultural apparatus and influence.'"

Monday, June 5, 2017

Be On the Watch!

I hardly have time anymore for all the excellent, polished math videos that are showing up these days. Hopefully, anyone reading this blog is already well-aware of these wonderful presenters: 

Infinite Series (from PBS)

A few others I’ll mention are:
Singing Banana from James Grime, well-known from Numberphile, but still also going strong on his own site (similarly, another Numberphile contributor, Matt Parker, has his own site for fun math at StandUpMaths).
Mind Your Decisions, Presh Talwalkar’s less fancy and more recreational site.
PatrickJMT and ProfRobBob, teachers with plenty of basic instructional videos.

Finally, this Pinterest site has links to tons more math-related videos of varying quality/interest:

With the rapidly-rising quality of such video presentations it makes one wonder exactly what the future holds for the role of live human teachers in the classroom! Like brick-and-mortar shopping, brick-and-mortar education likely has major changes coming.

We’ve advanced a long way since Khan Academy, which continues with its own evolving site (...and give Salmon Khan credit for early on recognizing/promoting the value of free, widely-distributed learning videos). Amazing to think of the youngsters (and adults) worldwide who weren't previously exposed to good schools, teachers, or textbooks, but now do potentially have 24/7 access to entertaining and instructional resources. Sometimes I think/fear we're in a race between fascism sweeping across the globe or good education (perhaps an antidote) sweeping across the globe!

[...As if math videos weren't time-consuming enough, there are also math audio podcasts, a handful of which I list in the right-hand column to this blog, but many more available. These are usually less instructional, but still covering topics or people of interest.
One for book-lovers, that I only recently discovered, though it's been around for quite awhile, is "New Books In Mathematics."]

Sunday, June 4, 2017

The Day the Light Dawned

For Sunday reflection, this from Paul Halmos (and h/t to Jim Propp for bringing this quote to my attention):
“The day when the light dawned… I suddenly understood epsilons and limits, it was all clear, it was all beautiful, it was all exciting… It all clicked and fell into place. I still had everything in the world to learn, but nothing was going to stop me from learning it. I just knew I could. I had become a mathematician.”

Thursday, June 1, 2017

A Few Book Notes

Princeton University Press is working hard to keep all of us math fans happy!:

Two of my favorite PUP books from 2015 are newly-out in paperback:
Marc Chamberlain’s “Single Digits,” a fun read covering lots of examples/ideas, and Michael Harris’s thought-provoking, quirky, even unique, “Mathematics Without Apologies.” If somehow you’ve missed these, no better time to catch up then when the paperback arrives.

A book I’m not familiar with is Oystein Linnebo’s “Philosophy of Mathematics,” but among many choices in this genre this looks like it ought be a good introduction.

I’ve already mentioned “Power Up” by Matthew Lane, a lively read on math and video games, a topic not geared to my interests, but which is getting good buzz from the many who do hold such an interest.

I also previously mentioned “The Probability Lifesaver” by Steven Miller, a massive (700+ pgs. volume I’m just dabbling in as time permits), specifically for those with a penchant obviously for probability; loads of problems/examples/explanations. Miller spends an entire introduction basically trying to make the book seem user-friendly and less imposing/intimidating than it appears. Likely a must-have for the stats-crowd.

The last 3 volumes above I would say are more suitable for niche audiences (that will love them), while the first two books (from Chamberlain and Harris) are more appropriate for a wider, lay and professional crowd of math fans.

Finally, and also from PUP, is the new 500+ page “Unsolved” by Craig Bauer, on unsolved cryptographic messages; some famous, others lesser known — little direct mathematics in it, but of course the actual methodologies for solving cryptograms involve very-largely mathematical thinking, and who among us didn't enjoy cryptograms sometime in our youth. 
I’m close to finished with it and have to admit much of it was more spellbinding than I’d expected. For lovers of cryptography certainly another must-have. Since the majority of examples in the book are unsolved messages (from various times/places) you have plenty of work to attempt if you so choose, or just enjoy reading the mysteries. There's also a website that ties into the book with additional material.  I'll say more about the volume in the near future.
As usual, thanks to Princeton U. Press for such a wonderful, ongoing and varied array of mathy offerings.

My impression, thus far, of this year in popular math books, is that there are more 'specialty' books aimed at specific interests, and fewer general interest math offerings showing up than usual, but the year isn't even half-over so we'll see what happens.

Sunday, May 28, 2017

Life Lessons From One Who Succeeded

From Edward O. Thorp's “A Man For All Markets”:
“Education has made all the difference for me. Mathematics taught me to reason logically and to understand numbers, tables, charts, and calculations as second nature. Physics, chemistry, astronomy, and biology revealed the wonders of the world, and showed me how to build models and theories to describe and to predict. This paid off for me in both gambling and investing.
 “Education builds software for your brain. When you’re born, think of yourself as a computer with a basic operating system and not much else. Learning is like adding programs, big and small, to this computer, from drawing a face to riding a bicycle to reading to mastering calculus. You will use these programs to make your way in the world. Much of what I’ve learned came from schools and teachers. Even more valuable, I learned at an early age to teach myself. This paid off later on because there weren’t any courses in how to beat blackjack, build a computer for roulette. or launch a market-neutral hedge fund.”

[...and over at MathTango this morning I have a further look at Thorp's recent volume.]

Wednesday, May 24, 2017

Ben and Jim Deliver (good Wednesday stuff!)

These are both toooooooo good to hold them until the Friday potpourri, so passing them along now:
1) Ben Orlin, a bit more serious than some Wednesdays, on “the three phases of the mathematical life” (competition, mentorship, and collaboration):
2)  Jim Propp on “Math, magic, and mystery” in this 36-min. video describing math being “liberated from (physical) reality”:

A couple of pieces I think might also make good adjunct readings to Jim’s talk are this Evelyn Lamb piece from a couple years back on epsilons and deltas:
…and this old Terry Tao piece on rigor and intuition in math:

Tuesday, May 23, 2017

Cantor Weirdness

Fantastic treatment of the fractal Cantor Set and the “Devil’s Staircase” (Cantor function) from PBS’s “Infinite Series." Is it any wonder Cantor was driven to a sanatorium!:

Sunday, May 21, 2017

Math Melancholy

For Sunday reflection, this from Marcus du Sautoy’s “The Great Unknown”:
“The importance of the unattained destination is illustrated by the strange reaction many mathematicians have when a great theorem is finally proved. Just as there is a sense of sadness when you finish a great novel, the closure of a mathematical quest can have its own sense of melancholy. I think we were enjoying the challenge of Fermat’s equations so much that there was a sense of depression mixed with the elation that greeted Andrew Wiles’s solution of this 350-year-old enigma.”

Wednesday, May 17, 2017

Happy 15th Anniversary for Stephen Wolfram

When Stephen Wolfram’s tome, “A New Kind of Science,” came out 15 years ago, I saw more critical reviews of it than positive ones, but its sheer size (~1200 pgs.) and technicality made it a very difficult volume to review adequately at all.
Now on the 15th anniversary of his opus, polymath Wolfram, who’s accomplishments are multi-fold, is out with a long post reviewing matters. PLENTY to consider and chew on here, including “computational equivalence” and the “computational universe,” machine learning, neural networks, artificial intelligence, language design, and the nature of mathematics and physics.  You’ll need to set aside some significant time to read and digest it all: