Support Vsauce, your brain, Alzheimer's research, and other YouTube educators by joining THE CURIOSITY BOX: a seasonal delivery of viral science toys made by Vsauce! A portion of all proceeds goes to Alzheimer's research and our Inquisitive Fellowship, a program that gives money and resources directly to growing STEM channels here on YouTube! https://www.curiositybox.com

Q: "What's an anagram of Banach-Tarski?"
A: "Banach-Tarski Banach-Tarski."

twitter:   / tweetsauce  
Instagram:   / electricpants  

Kevin’s Field Day video:    • After The Upload | Kevin Lieber from ...  

Field Day:    / @fieldday  

Deep dream animation by   / nadermakki  

If you like it, you'll love this video also by Nader:    • Look Closely - by Nader Makki  

Chocolate illusion: http://mathandmultimedia.com/2014/07/...

Chocolate illusion video:    • Video  

related Numberphile videos:

sizes of infinity (includes diagonal argument):    • Infinity is bigger than you think - N...  
infinity paradoxes:    • Infinity Paradoxes - Numberphile  

Vi Hart on types of infinity:    • How many kinds of infinity are there?  
Countable & uncountable definitions:

http://mathinsight.org/definition/unc...
https://en.wikipedia.org/wiki/Countab...
https://en.wikipedia.org/wiki/Uncount...

Banach-Tarski on wikipedia: https://en.wikipedia.org/wiki/Banach%...

Banach-Tarski proofs:

http://math.uchicago.edu/~may/REU2014...
https://www.math.hmc.edu/~su/papers.d...
http://people.math.umass.edu/~weston/...

Banach-Tarski explinations online:

http://www.irregularwebcomic.net/2339...
http://www.kuro5hin.org/comments/2003...
http://skepticsplay.blogspot.co.uk/20...
http://austinrochford.com/posts/2014-...
http://www.math.cornell.edu/~mec/Summ...
http://rachellevanger.com/index_files...
http://quibb.blogspot.co.uk/2013_03_0...
http://blog.computationalcomplexity.o...
https://geopolicraticus.wordpress.com...
http://dgleahy.com/p47.html
https://www.math.hmc.edu/funfacts/ffi...

Cayley graph animated gif:   / 624202342259240960  

Hilbert’s hotel on wikipedia: https://en.wikipedia.org/wiki/Hilbert...

types of infinity: http://www.xamuel.com/levels-of-infin...

set theory and quantum physics: http://link.springer.com/article/10.1...

LHC gif: http://cms.web.cern.ch/news/lhc-data-...

Zermelo-Fraenkel axioms of mathematics: http://mathworld.wolfram.com/Zermelo-...

Is math invented or discovered?

http://phys.org/news/2013-09-mathemat...
http://www.scientificamerican.com/art...

more deep dream images:   / deepdream  

BOOKS:

The Pea and the Sun: http://www.amazon.com/The-Pea-Sun-Mat...
The Outer Limits of Reason: http://www.amazon.com/Outer-Limits-Re...
Why Beliefs Matter: http://www.amazon.com/Why-Beliefs-Mat...
Things to Make and do in the Fourth Dimension: http://www.amazon.com/Things-Make-Fou...

Music by    / jakechudnow   and
http://www.audionetwork.com