A Bump in Cost...

 John Baez on "the social cost of greenhouse gases":

https://johncarlosbaez.wordpress.com/2021/02/27/the-social-cost-of-greenhouse-gases/

ABC... A Baez Commentary

ICYMI, the more hardcore among you may want to see John Baez's recent commentary (and the comments that follow) on Mochizuki's "proof" of the ABC conjecture:
https://plus.google.com/+johncbaez999/posts/P7AN48F9pC7

Mathematician Go Yamashita has written a 294-page "summary" of Mochizuki's 500-page inscrutable(?) proof... if that's any encouragement to you ;)

Here's a few lines of the summary as quoted by Baez:

"By combining a relative anabelian result (relative Grothendieck Conjecture over sub-p-adic felds (Theorem B.1)) and "hidden endomorphism" diagram (EllCusp) (resp. "hidden endomorphism" diagram (BelyiCusp)), we show absolute anabelian results: the elliptic cuspidalisation (Theorem 3.7) (resp. Belyi cuspidalisation (Theorem 3.8)). By using Belyi cuspidalisations, we obtain an absolute mono-anabelian reconstruction of the NF-portion of the base field and the function field (resp. the base field) of hyperbolic curves of strictly Belyi type over sub-p-adic fields (Theorem 3.17) (resp. over mixed characteristic local fields (Corollary 3.19))."

...Have at it!

John Baez Ruminates

John Baez is one of those fellows virtually incapable of writing a dull post!
A couple of recent challenging ones from him; not easy reads, but interesting:

1)  This one on "surprises in logic" focuses on "a complexity barrier built into the very laws of logic," with some Chaitin, some Gödel, some Kolmogorov, some Kritchman-Raz all rolled in together, before closing out with Joel Hamkins and the "computability of incomputable functions" (also includes lots of good links):
http://math.ucr.edu/home/baez/surprises.html
(this is mainly for logicians, but generalists can find bits of interest as well)

2)  and this one, completely different, from his personal blog ("Azimuth") on "Diamonds and Triamonds" which leads to mention of one of his "favorite entities," the E₈ lattice, and closes out with 5 puzzles:
https://johncarlosbaez.wordpress.com/2016/04/11/diamonds-and-triamonds/
(again a challenging read)

A Little Bedtime Reading…

…okay, NOT really!

This is probably the most heavy, dense mathematical piece (on the Riemann Hypothesis, quasicrystals, Freeman Dyson, and more) I've ever linked to, and I don't comprehend it… but, all things Riemannian fascinate me, and even without following the mathematics here I think this very long piece from John Baez communicates the beauty and profundity of methodical, thoughtful, mathematical analysis. Simply put, it is, I think, a beautiful piece of mathematical exposition (not at all unusual for Baez)….

http://golem.ph.utexas.edu/category/2013/06/quasicrystals_and_the_riemann.html#more

It starts off thusly:

"Freeman Dyson is a famous physicist who has also dabbled in number theory quite productively.  If some random dude said the Riemann Hypothesis was connected to quasicrystals, I’d probably dismiss him as a crank.  But when Dyson says this, it’s a lot more interesting.  So I’ve been trying to understand his remarks on this.  And it’s been productive, in that I’ve learned some interesting things, and I now feel closer to seeing why the Riemann Hypothesis is a natural and important conjecture."

 ...On a side-note, I also find it interesting that Freeman Dyson advanced this original quasicrystal notion, which has generated a lot of interest (like so many things Dyson has advanced over the years), at the ripe young age of 85! Who says mathematics must be a young man's game!

Talk Mathy To Me! ;-)

2 interviews to pass along today…

Over at mathblogging.org, their latest transcribed interview is with the always interesting mathematical physicist John Baez of Azimuth blog: 

http://mathblogging.wordpress.com/2013/01/18/john-baez/

And Sol Lederman now has up his second podcast interview with some fellow named Keith Devlin, who he first interviewed almost a year ago -- guess he's giving this Keith guy another chance to try and get it right this time… ;-))

http://wildaboutmath.com/2013/01/22/keith-devlin-%E2%80%93-inspired-by-math-17/

but… seriously… in it, Keith talks almost exclusively, and extensively, about MOOCs, "massive open online courses" (too late now, but I wish someone had dreamed up a better name for these ventures!) …his experience with them and their future. It's a long (100 mins.!) 2-part interview. Very interesting; very worthwhile stuff. I especially enjoyed the last 30 mins.-or-so where Keith discusses the future of education (and Sol points out that until recently online degrees and education were very much looked down upon, while Keith is predicting a very bright and expansive future ahead for digital education with the MOOC model). Also, at the end Dr. Devlin hints about a new, separate learning project he has underway that will be publicly debuting in about 3 weeks!