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Monday, July 25, 2016

Three to Expect a Lot From

An interesting piece on 3 leading, young European mathematicians,  Peter Scholze,  James Maynard, and Sara Zahedi, who are "surprisingly young -- and very down-to-earth(h/t to Egan Chernoff for this one):


Sunday, July 24, 2016

"mathematics is permanent"

This  week's Sunday reflection from Freeman Dyson:
"...it’s the beauty of mathematics, as opposed to physics, that it’s forever. I published my selected papers recently in one volume, and I found out that when you publish your selected papers most of the physics is ephemeral, that you don’t want to publish stuff that was written 10 or 20 years earlier, but the mathematics is permanent. So essentially everything I’ve ever published in mathematics is there, whereas only about a quarter of what I published on physics was worth preserving."

Wednesday, July 20, 2016

"an extreme sensitivity to numbers"

Am largely taking vacation from blogging for a couple of weeks (’til political conventions are over), and will again skip Friday potpourri over at MathTango, but put up an occasional post here (and still be on Twitter) -- between the two blogs I've averaged over 5 posts per week for the last 6 years so won’t feel too guilty taking a vacation ;-)
Anyway, passing along this interesting recent piece from the Christian Science Monitor on a supposed real life “Good Will Hunting” Chinese migrant (Yu Jianchun) using a creative/imaginative approach to solve a long-standing problem involving “Carmichael numbers” :
…alternatively, this coverage from the Washington Post:
With all the reporting on Ramanujan in recent months (including in these articles), Yu's story sounds a bit familiar. According to one professor, “All he has is an instinct and an extreme sensitivity to numbers.” And Yu himself says, “I made my discoveries through intuition.”

I love this almost inexplicable notion of math prodigies and savants possessing a “sensitivity to numbers,” whatever that means, and connecting to mathematics more through intuition than pure deduction. In some way it harks back to the Platonist/non-Platonist divide in mathematics. Are such gifted individuals intuitively in touch with some Platonic realm of math that exists apart from humans, and that most of us lack direct access to, or are they merely in touch with some special corner of their own working brains? Are they discovering math or creating it? And what is it like to be “sensitive” to something as abstract and ethereal as numbers?

It all makes me think a bit of physicist Max Tegmark's controversial view that all there is in the Universe is mathematics (or mathematical structure), and ultimately nothing more. But then how would such mathematical structure evolve into human brains capable of looking back on itself with objective analysis? And are the philosophers and cognitive scientists who tackle such questions simply caught in some sort of infinite regress or word loop... explaining an explanation by an explanation of an explanation of... (that really explains nothing!).
Anyway, go read about the "package delivery worker" Jianchun who, after 8 years of emailing prominent mathematicians "to no avail," finally got someone to take note.

Sunday, July 17, 2016

Of Politics and Science

"...there is a fundamental difference between science and politics. In fact, I've come to view them more and more as opposites.
"In science, progress is possible. In fact, if one believes in Bayes' theorem, scientific progress is inevitable as predictions are made and as beliefs are tested and refined. The march toward scientific progress is not always straightforward, and some well-regarded (even 'consensus') theories are later proved wrong -- but either way science tends to move toward the truth.
"In politics, by contrast, we seem to be growing ever further away from consensus. The amount of polarization between the two parties in the United States House, which had narrowed from the New Deal through the 1970s, had grown by 2011 to be the worst that it had been in at least a century."

-- Nate Silver (from "The Signal and the Noise")

Tuesday, July 12, 2016

Sunday, July 10, 2016


For today's Sunday reflection, an interview interchange between Jerry Seinfeld and Judd Apatow from Apatow's book, "Sick In The Head" (no math, but somehow it appealed to me ;-):
JerryI used to keep pictures of the Hubble [Telescope] on the wall of the writing room at Seinfeld. It would calm me down when I would start to think that what I was doing was important.

JuddSee, I go the other way with that. That makes me depressed.

Jerry:  Most people would say that. People always say it makes them feel insignificant, but I don't find being insignificant depressing. I find it uplifting.

Thursday, July 7, 2016

Memories... (and Sparks)

I've occasionally thought about asking here about people's earliest memories of being attracted to mathematics. What problem/puzzle, parent/teacher, or book or event, do you remember spurring an early interest in numbers/math? 
A tweet yesterday inspires me to finally try the question out. 
"15yo has an interesting question this morning: What's the first major news story you can remember living through as a child?"
...and got a huge response from folks bringing forth early historical memories from their lives. Of course I don't expect such an outpouring for math memories, but still might be interesting.

One of my own early memories, which I've written about here before, was viewing a large, glass-encased "Galton board" at the Field Museum in Chicago (1950s), and being mesmerized, as a child, by the individual balls falling "randomly" or unpredictably from the top, yet attaining a specific pattern (Bell Curve) time and time again once all balls had settled at the bottom. Didn't really know what it meant, but knew it was something deep.

What early memories do others have that helped spark your journey to mathematics???

Wednesday, July 6, 2016

When Will I Ever Use This...

Well, in the event you become a space scientist/engineer you might just use math to embark a man-made spacecraft on a journey to a world far, far away....

No explicit mathematics today, but just thought these videos from NASA's Jet Propulsion Laboratory ought be shared, if you missed them.  First, is the jubilation of workers upon spacecraft Juno attaining orbit around Jupiter after its momentous 5-year voyage. Followed by a little more background info on the project in the second video. Amazing!:

How petty and irrelevant our localized politics and day-to-day affairs seem when shown what some humans are actually capable of accomplishing!

Sunday, July 3, 2016

An Incidental Remark...

Sunday reflection:

"In [his 1859 paper], Riemann made an incidental remark -- a guess, a hypothesis. What he tossed out to the assembled mathematicians that day has proven to be almost cruelly compelling to countless scholars in the ensuing years...

"...it is that incidental remark -- the Riemann Hypothesis -- that is the truly astonishing legacy of his 1859 paper. Because Riemann was able to see beyond the pattern of the primes to discern traces of something mysterious and mathematically elegant at work -- subtle variations in the distribution of those prime numbers. Brilliant for its clarity, astounding for its potential consequences, the Hypothesis took on enormous importance in mathematics. Indeed, the successful solution to this puzzle would herald a revolution in prime number theory. Proving or disproving it became the greatest challenge of the age...

"It has become clear that the Riemann Hypothesis, whose resolution seems to hang tantalizingly just beyond our grasp holds the key to a variety of scientific and mathematical investigations. The making and breaking of modern codes, which depend on the properties of the prime numbers, have roots in the Hypothesis. In a series of extraordinary developments during the 1970s, it emerged that even the physics of the atomic nucleus is connected in ways not yet fully understood to this strange conundrum. ...Hunting down the solution to the Riemann Hypothesis has become an obsession for many -- the veritable 'great white whale' of mathematical research. Yet despite determined efforts by generations of mathematicians, the Riemann Hypothesis defies resolution."

-- John Derbyshire, from the dustjacket description of Prime Obsession 

==> p.s... check out my new interview with science/math writer Brian Hayes over at MathTango:

Wednesday, June 29, 2016

A Name to Know; Work to Be Aware Of

From Erica Klarreich at Quanta, a fascinating piece about a fascinating young mathematician, his fascinating work in number theory, making fascinating, groundbreaking connections between disparate areas of math:


Did I mention this is fascinating stuff....

Peter Scholze is a 28-year-old German wunderkind, probable Fields Medal candidate, and by several accounts, "one of the most influential mathematicians in the world," who works at the intersection of number theory and geometry. That might sound simple, but it is cutting edge, and for most, unexplored territory. Yet Peter seems to possess a strong intuitive sense for it (the article is aptly titled, "The Oracle of Arithmetic"). 

A couple of quick sentences from the piece:
"'I’m interested in arithmetic, in the end,' he [Scholze] said. He’s happiest, he said, when his abstract constructions lead him back around to small discoveries about ordinary whole numbers."

Almost makes it sound as if we rookies could understand what he does ;-); but that'll be the day. He's delving into deep, rich, abstract areas of mathematics, that most of us will never encounter, but the article makes clear he is also open, generous, and patient in his willingness to explain it to those who are able to take the leap.

Klarreich writes that Scholze "avoids getting tangled in the jungle vines by forcing himself to fly above them," which reminded me so much of Keith Devlin's early metaphor of reaching the top of a mathematical woodland canopy where he could look down and suddenly see that the whole forest was inter-connected.
Part of Scholze' work deals with what is called "reciprocity" and its linkage to hyperbolic geometry, including "perfectoid spaces," all of which leads to the Langlands Program and "frontiers of knowledge" which may eventually unify the field of mathematics (slightly akin to the so-called "Theory of Everything" searched for in physics).

But I can't do Scholze or Klarreich's writing justice here, so go read her article NOW!

Monday, June 27, 2016

Don Knuth Explains the Surreals

Wonderful new video from Numberphile, of Donald Knuth describing where "surreal numbers" came from:

If you missed it, less than a year ago Jim Propp ran this great post on the surreals at his MathEnchantments blog:


Sunday, June 26, 2016

40 Years Ago, But So Timely...

Another no-math Sunday reflection; just a hackneyed piece of movie nostalgia (1976) with "Howard Beale," that now seems all too prescient:

(movie: "Network" screenplay: Paddy Chayefsky)

Friday, June 24, 2016

Political Navel-gazing

So Stephen Hawking, Terence Tao, Scott Aaronson, and Leonard Susskind have all now weighed in very publicly to essentially denounce Donald Trump (and many others have voiced shorter, but similar, sentiments through Twitter, Facebook, Google+, and the like). Four folks I'd never feel too bad being in agreement with ;-)

I'm still not convinced Trump will get his party's nomination (is the Republican Party establishment reeeeally that craaaazy? -- granted, in the near-term they may wreck their party either way: nominating Trump or denying him the nomination; their best hope is for him to become disabled, forcing another choice)... but if he does get nominated, the lengthy parade of brilliant minds springing forth to castigate him may be unlike anything ever seen in American politics... not merely because he is obviously narcissistic, misogynistic, bigoted, incompetent, hedonistic, naive, dishonest, inconsistent, simplistic, egocentric, and ignorant... but, because many surmise he is mentally-ill in some psycho-or-socio-pathic sense, and dangerous (...but hey, nobody's perfect!). 

STEM people often leave politics outside their public personae, viewing it as a private matter held separate from their profession. This year could be very different. Albert Einstein  famously spoke out on various political and philosophical fronts. Perhaps the time is long overdue for today's prominent scientists to also be more actively/loudly involved. Maybe they'd just be preaching to the choir... but just maybe enough Americans will listen when their most brilliant, creative, productive, insightful minds speak up in concert, out of genuine concern for their nation's future.

Muppet Beaker (via Wikipedia) refusing to release his tax returns

ADDENDUM:  I wrote the above yesterday for posting this morning... and now wake up to find 'Brexit' approved in Britain. Incredible! World stock markets are expected (at least temporarily) to plummet. David Cameron is resigning. Uncertainties about other EU members now become quickly more real. The anger of the 95% against the 5% is worldwide, and reminiscent of 1930s German mentality, looking for scapegoats as targets for that anger. 
Some even speculate this all helps Trump's campaign... shake things up, just for the sake of shaking things up, because hey, trying to do things rationally hasn't exactly been a booming success... so goes the visceral logic of the masses.  ANY change is better than the status quo.
When the 2008 crash happened I told friends I believed we were in for essentially a 20+ year recession; it seemed clear it would require a generation to correct the long baked-in maladies of our banking and corporate system. But perhaps I underestimated the degree and scope of the problems. In fact, maybe what we call "recession" is simply the new "normal."
We live in bizarre times. Rocky days ahead. But at least have a good weekend! ;-)


Wednesday, June 22, 2016

Putting Lipstick on a Pig

"Any sufficiently crappy research is indistinguishable from fraud"... that's the gist of a recent post from Andrew Gelman taking off on Arthur C. Clarke's 3rd Law, in the realm once again, of research papers displaying poor statistical analysis (be it incompetency or deliberate deception): 


The post gets quite a bit of commentary in follow-up (mostly backing Gelman up): 

And in a funny bit of timing, I came to Gelman's post very shortly after seeing a political cartoon on the Web showing Paul Ryan putting lipstick on a pig drawn as Donald Trump. Just struck me as an odd juxtaposition... how often politicians put lipstick on pigs, and, so too, researchers.

ADDENDUM:  just this morning "Retraction Watch" tweets out this abstract from a John Ioannidis group indicating that the majority of randomly-controlled studies evaluating "efficacy and safety" are sponsored by industry, and, lo-and-behold, 95+% of published results favor the sponsor:


Sunday, June 19, 2016

Hard and Easy Problems...

For today's Sunday reflection, Steven Pinker (from "The Language Instinct"):

“The main lesson of thirty-five years of AI research is that the hard problems are easy and the easy problems are hard. The mental abilities of a four-year-old that we take for granted – recognizing a face, lifting a pencil, walking across a room, answering a question – in fact solve some of the hardest engineering problems ever conceived…. As the new generation of intelligent devices appears, it will be the stock analysts and petrochemical engineers and parole board members who are in danger of being replaced by machines. The gardeners, receptionists, and cooks are secure in their jobs for decades to come.”   

Friday, June 17, 2016

James Propp Explores Ramanujan

"What can you say about a thirty-two-year-old mathematician who died?  That he loved numbers and equations.  That he had a mysteriously intimate understanding of infinite numerical processes...
so begins a brand new post from James Propp on Indian savant mathematician Srinivasa Ramanujan.

Ramanujan, of course, has been much in the news of late, due to a major motion picture on his life, and also a Ken Ono bio of him; now comes along the best single post I've ever seen on him from Propp, that provider of once-a-month thought-provoking, "enchanting" posts:


This is just a great, succinct compendium of Ramanujan's life and work (if I were you, I'd print it out and keep on hand, just for inspiration!). Not only is there a bit of the wonderful life story in brief, but lots of the math wonderment for which Ramanujan was famous. Jim too goes a little into the mysterious connection between Ramanujan and his family Hindu "Goddess" Namagiri Thayar (who supposedly provided him his math insights), as I did in an earlier post here.

This is a not-to-be-missed post! (with lots of good links and endnotes as well). And next month Jim will be doing a followup specifically on the current film biopic of Ramanujan's life ("The Man Who Knew Infinity"). His take should be very interesting.

Anyway, a great post to take you into the weekend.

Sunday, June 12, 2016

Inspired By Escher

For a different Sunday reflection today re-running this lovely 3-yr.-old Cristobal Vila film-short in tribute to M.C. Escher (always worth seeing again):