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.