hi all havent written on misc math topics for quite awhile. was reminded of the area by the recent fields medal award to Birkar and the wild theft imbroglio.[a13-15]
these are a collection of fascinating/ fun links.
highlights for me: wiles abel prize.[a11] but do think its a real pity it took ~2½ decades to award! ouch! alas, it shows how conservative prize committees are. it seemingly wasnt awarded until they were convinced his heroic effort had more applications in math and could be built on by others. to me solving a 3½ century open math problem eluding the worlds greatest mathematicians of ages deserves a large prize in a short amt of time, but this also reflects some of the larger math community conservativism: eg Collatz is open ¾ century but is not taken that seriously by mathematicians at large. gauss wrote evasively about FLT centuries ago and one might say the semi-stigma never went away…
my favorite area is auto thm proving and theres misc developments in the area, but alas nothing earthshaking as hoped and not even much of a discernable increase in momentum.[e] but, have learned to be very patient in this area and think fortunes will change. esp notable was the Yedidia-Aaronson paper on constructing a small Turing Machine that verifies ZFC very similar/ related to some of my own research into TM compilers.[e7][e8]
the abc conjecture resolution complexity seems to have gone on several years now with no end in sight and is a bit scandalous, now rather singular in the history of math.[b] to me it shows partly how complex modern math has become where new deep results may span hundreds of pages. as noted numerous times in this blog over the years there are a lot of analogies between math and computer code and that seems to be tightening in the 21st century. the ongoing abc work is sort of the “mother of all code reviews”. have also said here “math is like algorithms that run in human brains”.
deep links between the riemann conjecture and physics are very intriguing, feel like someone really should write a book on this or at least a huge survey.[c] there are other connections that show up.[d] have blogged on these yrs ago but it deserves another highlight.
😦 😥 ❤ 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.
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.
hi all. AI technology is really exploding in the last few years. the last big post/ compilation on the subj here was ~½ year ago and the links piled up in a blur since then. the main trigger for this post: the game of poker now seems to have “folded” to computer supremacy. a new paper was published on Deepstack and its highly competitive play, and Libratus is $800K up in a recent match against top experts (top players). my understanding is that there is still some weakness in multiplayer games and that the new breakthru is for 1-1 games, human vs computer, but presumably that razor-thin human edge might also melt away quickly.[a]
poker was a very good game for humans wrt our inherent/ evolved psychology. we (top humans that is) seem to have an intuitive grasp of how to bet based on the strength of cards, including the use of bluffing. it took computers until the 21st century to master this stuff. but it looks like they just passed the threshhold again. in a small surprise, it wasnt done by Deepmind but which is behind many other near-monthly, even verging on weekly breakthroughs.[c]
maybe not by total coincidence, the winning Libratus algorithm involves training a neural network to accurately estimate the search tree, quite similar to the Deepmind Go strategy that made huge headlines just a year ago. the media hasnt picked up on the poker competition as much as it did with Go… is it because cautious/ publicity shy academics have less PR instinct than google? or less budget? but maybe that “relatively low profile” will change in the weeks/ months ahead. hopefully there will be a very high profile contest that again captures widespread public interest/ imagination.
it seems the top poker competitions are typically held in Las Vegas afaik… what would it take to get the computers in that? wouldnt be cool if say Vegas (or some other high profile gambling center) decided to publicize it to attract attn/ tourism? but would the computer algorithms be competitive in the top multiplayer games? there have been increasing/ huge audiences for poker over last few years, not sure what all the factors are in in this surge (internet gambling might play a role…)
its neat to see academia still at the top of competitive research in AI. but that seems to be thinning somewhat over last few years as the massive corporations Google[b], Microsoft, Apple,[g] Facebook, Intel [f] and misc other corps [e] are snapping up AI talent like its a feverish arms race, and to some degree it is. theres also very fast/ dynamic startup/ other merger activity going on, and new research laboratories being founded.[h]
➡ ❗ ⭐ 😎 😀 💡 hi all sparkfun 2016 was last wknd sat sep 17th. what a blast! got the big robot fix and geek (over?)dose for a long time.
as mentioned before in this blog (last summer), sparkfun is an amazing company with a lot of really dedicated/ passionate members. its grown massively in only about a decade. they have very impressive warehouse/ facilities with nice features such as several classroom areas.
a huge unexpected highlight for me (got there just in time) was the presentation by Casey Kuhns (aerospace engineer!) and Zachary Goff of the POISON ARROW battlebot. their robot is built incredibly well in short timeframes. they have to glue snap connectors together otherwise they break apart during collisions that have as much kinetic energy as in car crashes. they showed a highlight of launching another 250LB robot 8ft in the air. they also had a flying drone that could shoot down flames. it was impressive to watch but seemed to have a lot of trouble honing in on targets.
to a large room/ ~50 count rapt audience with lots of kids, they detailed the fascinating building and insider/ behind the scenes aspects/ figures of its creation. lots of great/ riveting slides/ videos. they revealed the ABC battlebot cage cost $3M. builders got $10K from the show, and they didnt mention much prizes on the show, it didnt seem to be much of a consideration for them.