Again, plenty to choose from....
1) David Brooks (no, not THAT David Brooks) continues his search for interesting sequence-generating integers:
http://aperiodical.com/2015/10/guest-post-sequence-numbers/
http://sequencenumbers.blogspot.co.uk/
2) Chess fans, fabulous post from Jason Rosenhouse reviewing the new Bobby Fischer docu-drama ("Pawn Sacrifice"), and including other Fischer anecdotes, as well:
http://scienceblogs.com/evolutionblog/2015/10/03/the-big-bobby-fischer-movie/
3) Interesting post on password algorithms from DataGenetics:
http://datagenetics.com/blog/november22012/
4) Max Tegmark expounds on his 'mathematical universe' for Aeon:
http://nautil.us/issue/29/scaling/life-is-a-braid-in-spacetime-rp
5) Making pi, the Futility Closet way:
http://www.futilitycloset.com/2015/10/04/easy-pi/
6) Deborah Mayo re-blogs about 'evidence' and 'junk science':
http://errorstatistics.com/2015/10/04/will-the-real-junk-science-please-stand-up/
7) Alex Bellos writes about James Stewart of calculus fame (and riches):
http://tinyurl.com/obsp4ol
8) Interesting "rich tasks" from Cavmaths:
https://cavmaths.wordpress.com/2015/10/05/playing-with-jigsaws-is-the-way-forward/
9) I was never one of those to say "I can't do math," but am not ashamed to say I've never heard of, nor comprehend, most of the proposals made here for future Polymath projects! :-(:
http://mathoverflow.net/questions/219638/proposals-for-polymath-projects
10) h/t to Evelyn Lamb for calling attention to this relatively new blog from a CUNY math grad student:
http://www.math3ma.com/
...and a second doff-of-the-cap to Dr. Lamb for this explication of calculus's fundamental (if not terribly popular) treatment of limits:
http://blogs.scientificamerican.com/roots-of-unity/the-subterfuge-of-epsilon-and-delta/
11) Shinichi Mochizuki's "impenetrable proof" ('abc conjecture')... will it be resolved?:
http://www.nature.com/news/the-biggest-mystery-in-mathematics-shinichi-mochizuki-and-the-impenetrable-proof-1.18509
12) Latest issue of Chalkdust Magazine with good stuff:
http://chalkdustmagazine.com/
13) Lastly, for visual delight (or confusion), a few days back Cliff Pickover tweeted out this older story about a janitor's awesome maze-drawing:
http://tinyurl.com/ou3mmdf
Potpourri BONUS! (extra NON-mathematical links of interest):
1) As always, another wonderful edition of NPR's "RadioLab" last week, this time on conversing with animals, in 3 segments of which the second (18-min.) was probably my favorite (related to John Lilly's dolphin research):
https://www.wnyc.org/radio/#/ondemand/535162
2) And sticking with NPR, this week's episode of "This American Life" included an old segment (17-min.), for those who are old enough to enjoy some nostalgia from The Ed Sullivan Show:
http://www.thisamericanlife.org/radio-archives/episode/568/human-spectacle-2015?act=3#play
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