number theory news/ highlights: prime bias, Diffie-Hellman, Zhang-Tao, Wiles, Riemann

😮 💡 ❗ 😎 😀 ❤ hi all. big news in number theory last few months and years. this is a tribute to a few years of top breakthroughs and exciting developments. the general theme is “primes” but there are a few detours.

in a breakthru/ rare event, a new statistical property of primes was discovered related to frequency of occurrence digits in base-n expansions. it was discovered by Oliver/ Soundararajan and has led to a huge amount of media attention and notice by top scientists. some of it was uncovered with dear-to-my-heart computer empirical/ experimental approaches.[e]

yet its somewhat reminiscent of another similar discovery only ~7yrs ago in 2009 by Luque/ Lacasa.[e6]

big discoveries like this sometimes make one think that maybe we havent even “scratched the surface” of theory of primes. [a2], a long-held/featured link on this site (on main sidebar) points out connections with quantum mechanics by Sautoy, an authority on the Riemann hypothesis (Dyson/ Montgomery 1972).

speaking of Riemann, and apropos/ befitting/ in observation/ reverence of todays date, it was claimed to be proven by a Nigerian recently. and it turns out not surprisingly Nigerian mathematics is not all so different than illustrious Nigerian business ventures advertised on the internet.[g]

alphaGo victorious 4-1 over Sedol in SKorea, NKorea crushes Warmbier 15-0

hi all the go match was very eventful and turned out to have massive media coverage worldwide, with huge interest from technology publications, and theres a sizeable AI/ ML/ singulatarian crowd on the internet that follows these types of developments quite avidly.

wish that google would transcribe the press conferences. there was a lot of interesting details but it takes a long time to watch them and the midstream translation interruption (korean to english, english to korean) slows down the presentation also.

saw some interesting press questions in the post-3rd match conference iirc that tie in with some angles explored on this blog.

battle of the brains midmatch pause: alphaGo 2-0 over Sedol

hi all. feeling blog-overwhelmed by recent Turing Machine-type events but just cannot resist blogging again at this historic moment (my blog frequency is up lately and some at expense of other activities). caught some of the 2nd match live late wed eve. do not know go heads from tails myself but found the commentary by Redmond quite engaging. it was interesting in postgame analysis that Sedol felt at no time was he winning, but Redmond saw the game as fairly even even far into the middle. but near the end something shifted, possibly a single move, and Redmond said that Black (alphaGo) had a major ~10stone advantage based on rough count.

the long ~4hr match made me feel a bit sorry for the commentators attempting to say something meaningful the whole time sometimes when the moves were very slow. there was a ~30m delay in the midgame as sedol pondered a weird/ unusual move by alphago. at one point Redmond called alphago a “he” and they reacted briefly on that, redmond said it seemed natural to him. (at my job a guy also sometimes talks about computational processes in terms of “he”…)

this game is quite interesting in that, for apparently nearly even positions (which are possibly frequently the case in very advanced level games) one does not know clearly if one is winning or losing and single moves can significantly tip the balance. the single moves seem to be about unifying separate regions and strengthening major separate areas such that they reinforce each other. it seems to be about simultaneously playing out multiple strategies in separate regions and then tying them together in the end.

the game seems to me to have a strong fractal quality, apparently not noted by many. explaining exactly what this means is not quite possible at this moment in scientific history. fractals are very difficult to describe.

battle of the brains! real vs artificial! google AlphaGo vs top human Go at it next week

next wednesday march 9th is the 1st match between an improved google Go and the top human player Lee Sedol. it will be livestreamed on youtube with commentary by several experts.[a1]

as has been noted in a lot of articles on the subject, the recent match between european champion Hui tested a human at ELO ranking 2750. Sedol is ranked at 2940. Hui is ranked 633rd in the world, Sedol ranked 5th. Sedol [and other cohort experts] is already on record as saying he is confident he will win at least this 1st match based on analysis of the prior Hui match and apparent mistakes in the computer gameplay. the prior Hui match would seem to definitively show the Go machine is already playing substantially better than ELO 2750.

but Sedol maybe seems not to have realized/ anticipated/ acknowledged that Google is already throwing significantly more hardware and software improvements (obtained via reinforcement learning) in the new match, therefore the new system will not be the same as the prior one; it will presumably be substantially improved and maybe even its style of play will diverge some.

google deepmind attacks Go and AlphaGo attacks top human

hi all, it was a very big week for AI news. google deepmind published a paper in Nature demonstrating world competitive level performance in the game of Go.[a] there were several articles and an excellent/ cool 7 minute video produced by the site. experts thought this could be ~5-10 years away. the google team was relatively small with only 15 employees. however, their combined salaries were surely not that low, could that figure probably easily approach over a million dollars annually? (we are talking about silicon valley rates here.)

google will be challenging the top world player in march for $1M, Lee Sedol. more edge-of-seat excitement!

so, this is a great excuse or milestone to write up my last batch of links. and boy is it a big pile. its only been ~½ yr since last writing on this subject.

and am going to take some big credit here. (along with wired) pointed myself to the game of Go as a ripe terra incognita for new algorithms and development. maybe a few people really do actually read this blog, eh? and this breakthru also cuts across many categories long covered on this blog.

another big cybersynchronicity, AI pioneer and near-gadfly Minsky died this week.[b]

also since the last post, Musk announced a billion dollar AI fund and they are also committed to an open source approach.[d]

google announced open sourcing its AI engine, TensorFlow.[l]

there are dramatic weekly, nearly daily advances in the field.[g] eg emotion recognition on faces etc.[i] vision algorithms are continuing to evolve rapidly and getting very sophisticated.[k]

a brilliant book by the brilliant Domingos on “the master algorithm” was released and made some media waves.[e] there actually have been a plethora of AI books at the bookstores within the last few years & am planning on reviewing about 5 of them soon. (the google Go breakthrough caught me in the middle of that.)