The Radical Brain Teaser That Stumped Everyone, And Changed Math Forever

Video Description

Before Ramanujan was famous, he challenged mathematicians with this problem. He waited for more than 1.5 years for anyone to solve it, but no one provided an answer. Finally he submitted a solution himself. Learn about the brain teaser that is still inspiring mathematicians over 100 years later. 0:00 intro 1:53 problem 1 5:16 general 1 7:13 problem 2 8:43 question 10:11 fairness 11:10 proof Wiki https://en.wikipedia.org/wiki/Srinivasa_Ramanujan#Pursuit_of_career_in_mathematics https://commons.wikimedia.org/wiki/File:Srinivasa_Ramanujan-Add._MS_a94_version2_(cropped).jpg CC BY 4.0 volume 3 problem J. Indian Math. Soc, 3 (1911), p. 90 https://babel.hathitrust.org/cgi/pt?id=umn.319510002394343&seq=642 volume 3 problem cover April 1911 https://babel.hathitrust.org/cgi/pt?id=umn.319510002394343&seq=601 volume 4 solution J. Indian Math. Soc, 4 (1912), p. 226 https://babel.hathitrust.org/cgi/pt?id=chi.63388476&seq=252&view=1up volume 4 cover Dec 1912 https://babel.hathitrust.org/cgi/pt?id=chi.63388476&seq=227&view=1up Putnam Competition 1965-1984 (book) https://bookstore.ams.org/view?ProductCode=PRB/30 27th Putnam 1966 A6 (not official) https://prase.cz/kalva/putnam/psoln/psol666.html alternate proofs https://www.jstor.org/stable/2301294 https://www.ias.ac.in/article/fulltext/reso/001/12/0060-0062 https://www.isibang.ac.in/~sury/ramanujanday.pdf https://www.tandfonline.com/doi/abs/10.1080/00029890.1935.11987745 https://math.stackexchange.com/questions/7204/evaluating-the-nested-radical-sqrt1-2-sqrt1-3-sqrt1-cdots https://math.stackexchange.com/questions/3119631/ramanujans-radical-and-how-we-define-an-infinite-nested-radical https://www.sciencedirect.com/science/article/pii/S0377042704001906 Members get early access to videos YouTube members https://www.youtube.com/channel/UCHnj59g7jezwTy5GeL8EA_g/join Patreon members https://www.patreon.com/mindyourdecisions Support the channel with a one-time donation https://www.paypal.com/donate/?hosted_button_id=REZRY3QRQPYQA Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address at end of many videos). I may not reply but I do consider all ideas! If you purchase through these links, I may be compensated for purchases made on Amazon. As an Amazon Associate I earn from qualifying purchases. This does not affect the price you pay. Book ratings are from January 2025. My Books (worldwide links) https://mindyourdecisions.com/blog/my-books/#worldwide My Books (US links) Mind Your Decisions: Five Book Compilation https://amzn.to/2pbJ4wR A collection of 5 books: "The Joy of Game Theory" rated 4.2/5 stars on 564 reviews http://amzn.to/1uQvA20 "The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" rated 4.2/5 stars on 55 reviews http://amzn.to/1o3FaAg "40 Paradoxes in Logic, Probability, and Game Theory" rated 4.2/5 stars on 81 reviews http://amzn.to/1LOCI4U "The Best Mental Math Tricks" rated 4.3/5 stars on 148 reviews http://amzn.to/18maAdo "Multiply Numbers By Drawing Lines" rated 4.5/5 stars on 57 reviews http://amzn.to/XRm7M4 Mind Your Puzzles: Collection Of Volumes 1 To 3 https://amzn.to/2mMdrJr A collection of 3 books: "Math Puzzles Volume 1" rated 4.4/5 stars on 138 reviews http://amzn.to/1GhUUSH "Math Puzzles Volume 2" rated 4.2/5 stars on 45 reviews http://amzn.to/1NKbyCs "Math Puzzles Volume 3" rated 4.3/5 stars on 38 reviews http://amzn.to/1NKbGlp 2017 Shorty Awards Nominee. Mind Your Decisions was nominated in the STEM category (Science, Technology, Engineering, and Math) along with eventual winner Bill Nye; finalists Adam Savage, Dr. Sandra Lee, Simone Giertz, Tim Peake, Unbox Therapy; and other nominees Elon Musk, Gizmoslip, Hope Jahren, Life Noggin, and Nerdwriter. My Blog https://mindyourdecisions.com/blog/ Twitter https://twitter.com/preshtalwalkar Instagram https://www.instagram.com/preshtalwalkar/ Merch https://teespring.com/stores/mind-your-decisions Patreon https://www.patreon.com/mindyourdecisions Press https://mindyourdecisions.com/blog/press