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.
hi all. blade runner 2049 came out a few mos ago, liked it a lot. it did medium business at the box office worldwide and was something of a domestic underperformer. hey, the 1st one was too right?
am a neon collector and got some of the idea from this movie. isnt it neat that neon has a nearly 1-century long history at this point, and showed up in a big way in a scifi movie. a motif for the future.
one of the highlights for me of the new movie was the las vegas exterior desert scenes. amazing! mesmerizing!
another big highlight for me was the virtual gf character “joi” played by ana de armas. it was said in 1 of the original reviews that “the cyborgs/ replicants are more human than the human characters.” was thinking that about joi. it seemed she had more empathy/ emotional intelligence than anyone else in the movie.
so here is maybe some small )( discrepancy between geek taste and mass cultural taste. think lots of the movie was geek nirvana.
theres a scene where the blade runner buys a emanator instead of a emulator (the latter of which is a decades old real software engr technology). just a few letters make all the difference. the emanator gives joi a 3d body. sort of like dynamic 3d printing? seems completely physically impossible but thankfully that never stopped a great scifi concept.
hi all Google Deepmind has pulled another rabbit out of the hat and won 3-0 against the worlds reigning Go champion Ke Jie who coincidentally is also Chinese, only about 1yr since last historic match.[a] the 19year old was reportedly literally in tears.[a17] quite a different reaction than kasparov ~2 decades ago! looks like emotions really run the gamut eh? last years match with Lee Sedol had him apologizing for/ to humanity at the end! reminds me of the so-called “5 stages of grief” concept from psychology… where the “loss” is one of mankinds most priceless/ treasured possessions, its uniqueness wrt intelligence/ mind!
theres a brand new AlphaGo movie/ documentary on the prior history, cant wait to see it, has anyone else?[a8] what do you think? how does google/ deepmind top this? apparently they cant and actually theyve announced theyve decided to avoid any further human media/ spectacle matches! or is that just my interpretation? Hassibis is quoted as saying AlphaGo will stop/ retire, but not sure exactly what he means by that, its a big question mark, and the funky/ choppy chinese translation certainly isnt helping any.[a17] doesnt it make some sense to continue to refine it some, or release parts or all of it, do some maintenance, etc? it seems even after it beats the top human there is some small )( suspense left. (have always thought it a bit of a historical loss verging on tragedy that IBM Deep Blue chess hardware/ code was “decommissioned” and maybe never archived or released to the public.)
various alignments and massive themes going on here. the Chinese have funneled billions of dollars into AI research and yet this match was not really publicized much or celebrated within china, in stark contrast to last years international Korean media extravaganza, verging on near-media-circus! the state censorship system apparently decided to cut off the live feed of the match ~30m into it after uncertain/ unknown reasons, and/ or it became clear that maybe their human player would not dominate. and then theres the trickiness of Google having withdrawn from china in the prior few years due to their hacking, and wanting back into the gargantuan market. but oops! chinas semi-state-sponsored companies compete directly with google services. as the teenagers say, AWKWARD! 😳
hi all. have been waiting for an opportune moment to unleash this post, collecting links for probably close to 2+yrs. VR/ virtual reality is a massive gamechanger/ disruptive technology. as a teenager several decades ago (ugh) fantasized about VR, and now its finally here. the final designated trigger for this post: was wandering around a great mall & walked into the gamestop and sony VR (PS4) was sitting around in boxes, and also samsung (gear) VR was in the best buy cell phone store. (old geezer me remembers a time when best buy didnt sell cell phones!) we’ve certainly come a long way!
tried out oculus rift demo about a year+½ ago. tried out gear VR a few mos ago. its all fantastic. may buy the sony VR for ps4 fairly soon, am debating. might buy it just for the battlezone game! actually it was probably mostly battlezone by atari released ~1980 that started my near-pre-adolescent VR dreams aflutter.
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.