Category Archives: math

norbert blum P vs NP attack goes CYBER-SCIENCE-VIRAL!

⭐ 💡 ❗ 😀 😎 ❤ hi all! want to write a lot on this, have all kinds of impressions and things to say on one of my favorite topics in the world for 2½ decades now and which this blog is partly dedicated to, but am starting out by just collecting some links vacuumed up mostly today for others to check out, the top locations for commentary. unf there is not really a key/ central place so far where all the action is happening. will be adding to this post as time goes on. its very hard to figure out when to time a post wrt very fast moving developments like this, but my trigger just hit mostly right after RJLipton[a10] blogged about it. oh yeah, that comment by gowers that “I think it may reach the level where the experts feel that it needs to be checked” is highly triggering for me too (referring ofc to himself in 3rd person, maybe being more than a bit )( coy about this— doncha just love hardcore mathematicians! which reminds me of the joke about shoelaces…) … oh and then theres also fortnow who literally wrote the book on it! (oh yeah wrt that theres this by RJL too!) 😛

it looks like the Norbert Blum paper[a14][a15] basically went “pop/ scientific viral” today or so probably after mentions on Reddit[a8][a9] and Hacker News.[a11] of the experts Trevisan[a1] was the first to wager a reaction along with some curious onlookers like Baez[a2] and verging-on-jester-or-gadfly-or-even-troll Motl[a5] who along with some mild conspiracy theory about CS research(ers) (lol!) says, wrt the #1 top problem in TCS…

Except that unlike the case of string theory, there exists absolutely no rational evidence that there exists something stunning waiting to be discovered.

@#$% 😡 👿 ❗ whoa, fighting words and/ or near-sacrilege there! excuse me, what is “stunning” is that the problem with $1M prize over 1½ decade has eluded/ stymied/ thwarted the worlds greatest scientific minds for almost ½ century now! and the proof either way, in whatever shape or form, will be assuredly stunning to anyone who isnt jaded or a nihilist! hey physics bozo! think of a great experiment that guaranteed leads to an extraordinary answer either way! arent there any examples like that in your field anyway? or is maybe someone looking a little envious over there? or out of the loop or maybe dont even know how to flirt at all? :mrgreen:

the TCS stackexchange post by a n00b newbie (who didnt know enough to not ask! hows that for “zen beginners mind”?) is now up to 136-4 votes and 28K hits (thursday eve 8/17).[a3] (joy that the lame heavyhanded/ constricting/ dictatorial policy of the self-appointed cyber spoilsports and partypoopers also long criticized here in this blog, is overruled by striking mass opposition!) that post slipped my radar for a few days! found the paper on the 1st day (monday this wk) but thought it might stay “unviral” (you know, like those killer viruses locked in the… thawing… arctic, right?) based esp on the last Hauptmann attempt.[a12][a13]

discovered the big commotion today via reddit myself and spent excited hours poking through sites! but my hits on the Hauptmann blog post had been creeping/ climbing up massively all week, merely from google searches (many from germany), and figured it was due to questions on the Blum attempt. turns out theyre both profs at the same university! (Bonn/ Germany) pardon me but wtf?!?… some kind of story there eh? are any reporters listening?

cyberspace is such a joy sometimes, in my quasi-bipolar days, mostly-sometimes seemingly very flat for days, weeks, months, even years at a time, this is a massive manic spike for me… the adrenalin is flowing! didnt sleep as well this week! there is so much cybersynchronicity to this, must admit, its a very rare event, am myself (and defensively, some others are too) having a bit of a mini-cyber-orgasm so far… 💡 😮 o_O 🙄 ❗

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Mirzakhani math superwoman 1977-2017

205EAEF2-F2D9-4809-87A5-4AA8A211C433-641-0000007822AA4645😦 😥 ❤ a few years ago Mirzakhani was credited in this blog with her striking bolt-from-the-blue achievement, and now its with major regret to write this “postscript” in this case also a “postmortem”. (“bolt from the blue” is a turn of phrase used by Heisenberg to describe the Einstein EPR1935 paper and Bohrs response to it, which historical echo seems somewhat fitting/ apt here. coincidentally, it just now occurs to me, Turings amazing paper introducing or even “solving” the undecidability problem was released one year later in 1936. two problems that have been particular extreme focii of attn for me over the years, and is there maybe some deeper resonance that could be observed beyond superficial connections?)

ironic or a bit eerie that Mirzakhani died at age 40, exactly the cutoff age for the fields medal, a topnotch prize with a rare age limit (over the years, not without some element of professional/ expert questioning verging on controversy). on the other hand esp in “winner take all capitalism”, the golden rule is he who has the gold, makes the rules…

have long thought the fields medal prize value ought to be much higher. its status is far higher than the numerical reward in dollars. ($15K, ~1.5% of a Nobel despite being called the “Nobel of mathematics” or ~0.5% of the Millenium prize won by her cohort Tao [a8]—who btw apparently still has said absolutely nothing about his award(s) in all his copious blogging and advice pages and elsewhere!)… but maybe the comparatively micro-money-prize is fitting for mathematicians who tend to profess to be unmotivated by material rewards? or maybe better to avoid such “calculations”? 😮 🙄

(brief tangent, inserting prize trivia or nontrivia depending on your pov, am reminded some of the TCS $5k Godel and Knuth prizes. extremely prestigious, rather tiny by Trumpian standards. another interesting case study is the Turing prize which was apparently unfunded for ~¼ century, was $¼ million ($250K) for ~½ decade, and went to $1M the same year Mirzakhani won, 2014. yeah as iconoclast Kary Mullis observed, prize money awards are one of the most irrational things around… near miss with Nobel himself, long story…)

am not familiar with Mirzakhanis work in particular but the identification of it as “science fiction mathematics” is personally meaningful/ delightful (have myself admittedly consumed vast quantities in written/ visual/ hollywood form of the literary genre, no intention of pulling/ holding back on that in future). as regular readers know, there is a lot of flavor of dynamical systems analysis in these pages lately wrt Collatz conjecture, and there can be regarded as some rough/ abstract connection.

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Royen proof of gaussian correlation inequality

hi all theres been a recent shock of awareness of the Royen proof of gaussian correlation inequality, pop-sci publicized by Wolchover for Quanta, a big milestone… this is a nearly ½-century-open problem![a] Quanta funded by Simons institute is one of the top outlets for scientific/ mathematical writing around today. a real community resource/ treasure!

the Royen proof is not exactly my area so cant write a lot on it but do note that its a key case study in dynamics of scientific peer review, and seems like it has some parallels to the ongoing mochizuki proof analysis.[b] it took over ~1½ year for “community” to begin to grasp the correctness of this proof and Wolchover has a nice historical timeline for how others began to notice/ accept it, a mapping of the spread of awareness. it did not help that Royen was somewhat isolated and did not seem to personally contact any cohorts for peer review. he published openly but it got lost in the noise. it shows how community acceptance is sometimes far from a black/ white binary decision, esp for “big problems”.

is there any way to improve peer review? its definitely a bit of an achilles heel of the scientific process. my feeling is that there is no way to improve it very much except maybe to try to increase transparency somehow. its very similar to the problem of “fake news”. how do you measure quality in content? we live in the vast Information Age but as has long been noted, theres a big difference between Information and Wisdom, and in a way peer review is the major mechanism that is designed to separate/ discriminate the two.

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math celebration 2016: pythagorean triples empirical attack conquest

310516_proofsupercomputer_1

actual U Texas Stampede supercomputer where proof was run [a2]

➡ 💡 ❗ ⭐ 😎 😀 hi all. RJLipton recently covered the amazing/ brilliant breakthrough of solving the pythagorean triples problem by empirical work namely a reduction to SAT and analysis by a supercomputer by Heule, Kullmann, Marek and its a nice pivotal trigger/ tipping point for my own writeup along with related stuff.[a] (have been waiting for opportune time to write this up since may.) proofs like these are a complex or “complicated relationship” for mathematicians (aka facebook-speak), a love-hate affair. (did the extraordinary/ breakthrough/ revolutionary/ paradigm-shifting 4-color computer proof ever win any awards? and how much despair/ handwringing and further effort has there been over it over the decades?)

the breakthrough is celebrated but mathematicians would like to see shorter proofs that are human-comprehensible, so there are mixed/ ambivalent feelings about it within the community. have written on this topic quite at length in this blog even since its beginnings, and this latest breakthrough is delightfully affirmationally crosscutting across many of this blogs categories, and think this is the tip of the iceberg of 21st century mathematics in a way not yet fully recognized. its a dramatic, vivid realization/ materialization of an idea suggested a few years ago here called “SAT induction.” think that these types of proofs will lead to new theory that is indeed human comprehensible but some of the isolated theorems will be claimed first by computer analysis before the more thorough theory catches up to integrate them.

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Ramanujan film, the man who knew infinity

ramanujan.jpghi all. ramanujan is one of the great/ inspiring/ legendary characters out of the pantheon of math heroes and they just released a major hollywood movie on his life starring Dev Patel and Jeremy Irons. its been a few great years lately for geeks of all stripes such as with the facebook movie, google movie, and the Turing movie (just a few that immediately come to mind). am really enjoying this moment in the spotlight or sun. if you are curious about such things, the etymology of geek vs nerd and the relation of “semantic drift” is now documented on dictionary.com, but the short story is that what was once a stigma is now an accolade/ badge of honor.[b15] and lets face it, mathematicians are long close to the stereotypical ultimate geeks. which reminds me of old joke:

Q. how can you tell if a mathematician is extroverted?

A. he looks at your feet while talking to you.

the movie is based on a book by Kanigel now about ~¼ century old (1992).[b14] bought the book as soon as it was available but never did read it! am delighted that the public has rediscovered this great intellectual hero/ prodigy, and some aspects of his story are being played up in the modern age such as the “diversity” angle. we also have a huge mix of indian culture into the US, and indians seem to be overrepresented in the technology field, although have not seen many mention this. india is also a world powerhouse in software outsourcing, although maybe that wave while still moving/ in motion is not as strong after over a decade of very intense rampup. cities such as Bangalore and Hyderabad are miniature foreign Silicon Valleys although ofc the latter is distinctly singular worldwide.

another great ref on Ramanujan is some essays in the amazing book World of Mathematics, 1956.[b13] think may have heard 1st of ramanujan from this book found while browsing the math section of different libraries.

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