My Twitter: https://twitter.com/tweetsauce Kevin's Field Day video: https://www.youtube.com/watch?v=1zARMZ08ums Field Day: https://www.youtube.com/channel/UCRPktNf5vnBR1J4e7t1RUVg Chocolate illusion: http://mathandmultimedia.com/2014/07/22/explanation-infinite-chocolate-bars/ Chocolate illusion video: https://www.youtube.com/watch?v=dmBsPgPu0Wc related Numberphile videos: sizes of infinity (includes diagonal argument): https://www.youtube.com/watch?v=elvOZm0d4H0 infinity paradoxes: https://www.youtube.com/watch?v=dDl7g_2x74Q Countable & uncountable definitions: http://mathinsight.org/definition/uncountable https://en.wikipedia.org/wiki/Countable_set https://en.wikipedia.org/wiki/Uncountable_set Banach-Tarski on wikipedia: https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox Banach-Tarski proofs: http://math.uchicago.edu/~may/REU2014/REUPapers/Robinson.pdf https://www.math.hmc.edu/~su/papers.dir/banachtarski.pdf http://people.math.umass.edu/~weston/oldpapers/banach.pdf Banach-Tarski explinations online: http://www.irregularwebcomic.net/2339.html http://www.kuro5hin.org/comments/2003/5/23/134430/275?pid=5#10 http://skepticsplay.blogspot.co.uk/2010/05/doubling-sphere.html http://austinrochford.com/posts/2014-05-14-banach-tarski-paradox.html http://www.math.cornell.edu/~mec/Summer2009/Whieldon/Math_Explorers_Club%3A__Lesson_Links/Entries/2009/7/28_Lesson_6%3A__Whats_an_Anagram_of_Banach-Tarski.html http://rachellevanger.com/index_files/BT%20Animated%20Presentation%20Web.pdf http://quibb.blogspot.co.uk/2013_03_01_archive.html http://blog.computationalcomplexity.org/2011/04/what-did-banachs-wife-think-of-banach.html https://geopolicraticus.wordpress.com/tag/banach-tarski-paradox/ http://dgleahy.com/p47.html https://www.math.hmc.edu/funfacts/ffiles/30001.1-3-8.shtml Cayley graph animated gif: https://twitter.com/GIFsofWikipedia/status/624202342259240960 Hilbert's hotel on wikipedia: https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel types of infinity: http://www.xamuel.com/levels-of-infinity/ set theory and quantum physics: http://link.springer.com/article/10.1007/BF02213427#page-1 LHC gif: http://cms.web.cern.ch/news/lhc-data-be-made-public-open-access-initiative Zermelo-Fraenkel axioms of mathematics: http://mathworld.wolfram.com/Zermelo-FraenkelAxioms.html Is math invented or discovered?