Thursday, September 21, 2017

Intrepid Math

Anthony Bonato’s “The Intrepid Mathematician” blog has caught my attention several times this week:

1) Interesting post on some neuroscience of math versus language:

2)  He’s  posted two interviews this week with wonderful mathematicians:
Maria Chudnovsky HERE and
Ken Ono HERE

3)  And today, this news on Ramsey Theory:

4)  I’m not much of a film buff myself, but if you are, you may want to additionally read his post on math and science in the movies here:

Read up!

Wednesday, September 20, 2017

A Sphere In Any Other Dimension Is Still A Sphere

Can spheres be spiky? According to Matt Parker yes they can, once you escape your puny 3-dimensional world:

Sunday, September 17, 2017

Healthy Mathematics

This Sunday reflection from Ian Stewart in the 2nd edition (1992) of “The Problems of Mathematics”:
“Some observers have professed to detect, in the variety and freedom of today’s mathematics, symptoms of decadence and decline. They tell us that mathematics has fragmented into unrelated specialties, has lost its sense of unity, and has no idea where it is going. They speak of a ‘crisis’ in mathematics, as if the whole subject has collectively taken a wrong turning. There is no crisis. Today’s mathematics is healthy, vigorous, unified, and as relevant to the rest of human culture as it ever was… If there appears to be a crisis, it is because the subject has become too large for any single person to grasp… today’s mathematics is not some outlandish aberration: it is a natural continuation of the mathematical mainstream. It is abstract and general, and rigorously logical, not out of perversity, but because this appears to be the only way to get the job done properly. It contains numerous specialties, like most sciences nowadays, because it has flourished and grown. Today’s mathematics has succeeded in solving problems that baffled the greatest minds of past centuries. Its most abstract theories are currently finding new applications to fundamental questions in physics, chemistry, biology, computing, and engineering. Is this decadence and decline? I doubt it.”

Wednesday, September 13, 2017

Measuring Infinities

Fantastic article from Quanta Magazine (Kevin Hartnett) about new findings/proof of the equivalency of two variant infinities — actually findings published a year ago; am amazed it’s just now reaching the wider press (at least I’d not heard about this ’til now!):

Part of what makes the proof interesting (IF I understand matters correctly) is that it didn't require any re-statement of fundamental set theory, but only a bringing together of disparate math models that had not been linked up before. Even if you (like me) don't understand the details of the finding, just recognizing that a 50+ year problem has been resolved is very exciting. The solvers, Maryanthe Malliaris and Saharon Shelah, received the Hausdorff Medal for their work earlier this year.

…In a bit of irony, the above article got tweeted out yesterday on the very anniversary of the death of David Foster Wallace whose book on infinity, “Everything and More,” I've discussed earlier here:

Tuesday, September 12, 2017

Quantitative Literacy

According to a recent study, 36 percent of college students don’t significantly improve in critical thinking during their four-year tenure. 'These students had trouble distinguishing fact from opinion, and cause from correlation,' Goldin explained.
The above words from mathematician/statistician Rebecca Goldin come near the beginning of this new piece in Quanta Magazine:

The title of the piece is “Why Math Is the Best Way To Make Sense of the World.” I fear the title may be the very sort that turns people away from it, or at least many of those who most need to read it — just mention 'math' in some sort of positive light and a lot of the ‘I-was-never-any-good-at-math’ folks will turn away out of disinterest :(
And if college-bound students aren’t gaining critical thinking skills over their 4-year sojourn, what can we expect of the non-college crowd who may have even less opportunity to be exposed to critical-thinking skills?
But critical thinking shouldn’t even begin with college; it should begin back in elementary school with language skills, which are themselves fundamentally entwined in critical thinking. Nonetheless, the above article (and interview with Goldin) is excellent and focused on the societal value of math and science at the university level -- there are several lines in it I’d love to quote, but just go read it for yourself and take to heart this central message: “…if we don’t have the ability to process quantitative information, we can often make decisions that are more based on our beliefs and our fears than based on reality.
Interestingly, this article appears at a time that topics like critical thinking, quantitative reasoning, innumeracy and the like are getting a fair amount of discussion in society, though I’m not confident that we’re even close to dispensing such skills to the population-at-large, nor to upcoming generations. In fact I fear quite the opposite; it may be too little too late in a digital world of speed, simplification, and reality-manipulation... hope I'm wrong, but the Machiavellians who plotted the path of our current Oval Office interloper knew all-too-well that appeals to base instincts could overcome appeals to critical thought. :(

Wednesday, September 6, 2017

ABC... A Baez Commentary

ICYMI, the more hardcore among you may want to see John Baez's recent commentary (and the comments that follow) on Mochizuki's "proof" of the ABC conjecture:

Mathematician Go Yamashita has written a 294-page "summary" of Mochizuki's 500-page inscrutable(?) proof... if that's any encouragement to you ;)

Here's a few lines of the summary as quoted by Baez:
"By combining a relative anabelian result (relative Grothendieck Conjecture over sub-p-adic felds (Theorem B.1)) and "hidden endomorphism" diagram (EllCusp) (resp. "hidden endomorphism" diagram (BelyiCusp)), we show absolute anabelian results: the elliptic cuspidalisation (Theorem 3.7) (resp. Belyi cuspidalisation (Theorem 3.8)). By using Belyi cuspidalisations, we obtain an absolute mono-anabelian reconstruction of the NF-portion of the base field and the function field (resp. the base field) of hyperbolic curves of strictly Belyi type over sub-p-adic fields (Theorem 3.17) (resp. over mixed characteristic local fields (Corollary 3.19))."
...Have at it!

Sunday, September 3, 2017

Springtime For...

We’ve ended another wrenching week with this current unfit, anti-science, truth-warping, money-worshipping, law-disrespecting, ignorant, imperious, corrupt, coarse, Kafka-esque, foul, faux-Christian, scam-loving, dysfunctional, despotic, deplorable, delusional, democracy-dismantling, ill-principled, nepotistic, police-state-leaning, patronizing, power-grasping, plutocratic, pompous, prissy, prevaricating, pathological, piggish, petty, Putin-obeying, phony, pathetic, prickish, press-bashing, cerebrally-challenged, pseudo-American, scared little, self-absorbed, simple-minded, non-stable, tweet-obsessed, whistling-in-the-dark, roguish, Russian-colluding, Alpha-malevolent, amateurish (and impeachable?), Aryan-embracing, routinely-ridiculed-as-clueless, tin-pot dictatorial, pussy-grabbing Regime (...but you didn't hear any of that from me), and somehow I feel compelled to again run this classic Jacob Bronowski clip:

...BUT, so as not to end on too sad a note, we'll close out sliding from Bronowski to Brooks:

Tuesday, August 29, 2017

Collatz… So what’s the history of it???

I see the always-intriguing Collatz conjecture going around a bit again on Twitter (as it seems to every few months), but just started wondering what the history/background of it is, which I’ve never seen much about, other than that it originated with Lothar Collatz maybe in the 1930s(?).
The simple statement of it, is that you take any positive integer and apply the following 2 rules iteratively:
  • If the number is even, divide it by two, or
  • If the number is odd, triple it and add one. (Then repeat.)
Doing so successively you will always conclude with a sequence of integers ending at 4, 2, 1 (...or so goes the conjecture).
People write a lot about the conjecture and continue to work on it, but what I’m wondering now is how did Collatz stumble upon those two specific iterative rules to begin with out of essentially an infinite number that might be imagined (even if many would pretty obviously not lead to anything interesting)? Or, you could even come up with 3 iterative rules! Or, or, or… Did he try LOTS of others… have other people since tried LOTS of others? Is there something unique about his two rules, as opposed to ANY others that might be concocted and have some interesting result?
Anyone know, or can point to some informative links?

...And for anyone who's missed it, here's a nice Numberphile introduction to the Collatz conjecture:

In the comments below Brian Hayes responds with this link to an old piece he wrote for Scientific American on the subject. Like other pieces, it’s largely analysis of the conjecture, written in Brian’s always-superb exposition, but there is a bit of history on page 12. He also references a piece by Lothar himself, but what I found most interesting in tracking it down, was seeing a number of folks say that though Lothar explored many iterative functions, he never actually claimed specific credit for the so-called 3N+1 problem that took on his own name!

And with all that said, what I’m still not clear about is whether the two conjecture rules involved in 3N+1 were arrived at primarily by sheer trial-and-error, or was there a more methodological/quantitative approach to hitting upon them?

Monday, August 28, 2017

Too Good Not To Pass Along

By now we've probably all seen plenty of Richard Feynman videos. But h/t to Paul Halpern for tweeting out this old clip (that I don't recall viewing previously) of Feynman and Fred Hoyle in brief conversation (3+ mins.) about scientific revelation:

Sunday, August 27, 2017

Logical Consistency/Objectivity

This week's Sunday reflection taken from Michael Guillen's “Bridges To Infinity” (1983):
“…the world of today’s mathematician is one not only in which truth is not synonymous with logical proof but also in which merely trusting in the validity of a logical proof is itself a matter of faith. This is because Gödel not only showed that any logical system is unable to prove all the mathematical statements that are actually true, but also that any system of logic is unable to prove its own logical consistency. Believing in logic, in other words, is no less subjective a frame of mind than believing in, say, a secular or mystical principle of faith, because even logic itself cannot be verified logically or objectively.”

Wednesday, August 23, 2017


Recently on Twitter @mathematicsprof asked for suggestions on who ought be commemorated if a statue of a native-born American (U.S.) mathematician was to be erected in Washington D.C. Of course famous mathematics names (including several that were mentioned) have a tendency to be British or otherwise European, so it’s not surprising that many different names arose to the tweet, without any one standing out above all others. Among those getting at least one mention were the following (in no particular order):
David Mumford
Paul Cohen
Ken Ribet
John Milnor
Ed Witten
John Nash
Julia Robinson
Martin Gardner
Katherine Johnson
Raymond Smullyan
Claude Shannon
William Thurston
John Tate
Jim Simons
Stephen Smale
Ronald Graham
Donald Knuth
Persi Diaconis
Alonzo Church
Definitely a tough choice! I very slightly lean toward Thurston, but good arguments can certainly be made supporting many of these choices (Nash, Witten, Shannon, Milnor were among those with multiple votes). And I'd throw Barry Mazur into the mix as well. Also, was a little surprised that several popular math writers didn’t seem to get a mention: Reuben Hersh, Morris Kline, Philip Davis, James Newman, Ed Kasner, Paul Lockhart.  A bit odd too, that despite responders citing a great many non-U.S. born mathematicians (mostly European) I don't recall Grothendieck or Perelman coming up -- political bias or mathematicians just not wanting to be represented by social outliers? (or perhaps repliers simply knew the latter two were foreigners, while unaware that many others named, some of whom were naturalized Americans, were born elsewhere.)
Anyway, interesting to think about... (ya know, in case any of you were hoping to replace some Robert E. Lee monument with a mathematician) ;)

Tuesday, August 22, 2017

A Total Parody of Bonnie Tyler

Long-time readers here may recall my affinity for self-reference and recursion, so in that vein (and just for fun), this outlandish rendition of Bonnie Tyler's classic hit, "Total Eclipse of the Heart" which many folks tweeted yesterday in honor of the celestial show:

[p.s.: apparently her original 1983 hit became the #1 popular streaming song this week as eclipse-viewers re-fell in love with it]

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 your 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: 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 ( 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  ( 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.

9/8:  Brendt Christensen's current attorneys were taken off the case (at their request, due to lack of funds of the defendent), and a public defender was assigned to Christensen. It's also rumored that before the end of October the Feds will bring an indictment for murder against Christensen (currently he is still only charged with kidnapping). Still no word of Yingying Zhang's body.
6pm. EDT. 8/28: At today's pre-trial hearing the start date for Brendt Christensen's trial was moved from Sept. 12 to Feb. 27 of next year. This is probably almost incomprehensible to Yingying's family and friends back in China. So much for the 'Constitutional right to a speedy trial' ;(
It is possible that before then, additional charges (beyond kidnapping) will be brought and presented to another grand jury.
4pm. EDT. 8/22: Still following this case in hopes of greater resolution. Yingying Zhang's family and boyfriend (all staying in Champaign) held a heartbreaking hour-long news conference today, wishing for more progress, but essentially having nothing new to report that hasn't already been reported publicly. They both made statements and took questions-and-answers, and plan to remain in the U.S. as long as it takes to find Yingying. Must be very difficult for them to comprehend the workings of the American legal and criminal system. Still no news on Yingying's body/remains? If video of the conference becomes available on the Web I'll link to it here. [ it is now here: 
Meanwhile, I assume the pre-trial hearing scheduled for August 28 will go on as scheduled, though won't be surprised if defense attorneys ask for a delay.
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:’s-creepy-how-he-walked.html

[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: