The abc Conjecture may have been proven by a Japanese mathematician – but what is it? More links & stuff in full description below ↓↓↓ Feeling brave and want to read the papers by Shinichi Mochizuki – http://www.kurims.kyoto-u.ac.jp/~motizuki/papers-english.html (scroll to the bottom) This video features Dr James Grime who tweets at https://twitter.com/jamesgrime NUMBERPHILE Website: http://www.numberphile.com/

Four circles of equal size are inscribed in a square as shown in the video diagram. Inside of the four circles is a smaller square tangent to each of the four circles. If the large square has a side length equal to 4, what is the area of the small square? Watch the video for

0! = 1 Dr James Grime tries to explain why this is the case – follow James on Twitter at https://twitter.com/jamesgrime More links & stuff in full description below ↓↓↓ Regarding the equation at the end – James says it should be e^-t dt NOT e^-n dn … sorry for the mix-up! NUMBERPHILE Website: http://www.numberphile.com/

15-year old Joseph Rosenfeld thought he spotted an error in the Boston Museum of Science. The exhibit Mathematica has a sign that says the golden ratio is (√5 – 1)/2. He remembered and checked online that the golden ratio is supposed to have a positive symbol, (√5 + 1)/2. He left a note for the

How accurately can we calculate Pi using hundreds of REAL pies? More links & stuff in full description below ↓↓↓ Extended version of this video (director’s slice) at http://www.youtube.com/watch?v=x4kyFKyCMv0 This video features Matt Parker: https://twitter.com/standupmaths Matt believes this is the world’s most accurate pie-based Pi calculation. More Pi videos: http://bit.ly/W4oDN1 Filmed and edited by Brady

I majored in math at Stanford, but this geometry problem stumped me and I had to look up the solution. A square is inscribed in a circle. A smaller square is drawn; one side is shared with the inscribed square, and the other two corners touch the circle. What is the ratio of the large

How do we know there are an infinite number of primes? More links & stuff in full description below ↓↓↓ Dr James Grime explains, with a bit of help from Euclid. Follow James at https://twitter.com/jamesgrime NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Videos by Brady Haran Patreon: http://www.patreon.com/numberphile Brady’s videos

I have seen this puzzle in a few places. Most recently I came across it in Peter Winkler’s “Mathematical Puzzles: A Connoisseur’s Collection” http://amzn.to/1DcPE4V The Race to 15 Game Theory Puzzle. Alice and Bob take turns selecting cards numbered 1, 2, .., 9 without replacement. (Alice goes first, then Bob picks a remaining card, and

The Josephus Problem, featuring Daniel Erman from University of Wisconsin-Madison. Winning at Dots and Boxes: https://youtu.be/KboGyIilP6k More links & stuff in full description below ↓↓↓ Correction: Around 9:40 that should be L less than 2^a NOT 2a — Sorry, typo in editing! But you got the point hopefully. Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website:

We now have a Tumblr: Tumblr: http://numberphile.tumblr.com This paper on ebay: http://www.ebay.co.uk/itm/221197137799? More links & stuff in full description below ↓↓↓ Just how hard was the second problem cracked by Will in Good Will Hunting? Matt Damon! And who doesn’t love Homeomorphically Irreducible Trees? This video features Dr James Grime – http://singingbanana.com/ Music by Alan

Happy Pi Day! At 3/14/15 at 9:26 the time will be accurate to pi for 7 decimal places. What’s your favorite fact about pi? Links to proofs and more below in the description. 1. The definition 00:10 Related: the area of circle intuitive explanation 2. Pi is irrational 00:47 Proof (video) Proof (blog post) http://mindyourdecisions.com/blog/2013/11/08/proving-pi-is-irrational-a-step-by-step-guide-to-a-simple-proof/

Hippocrates of Chios solved this, nearly 100 years before Euclid even wrote The Elements, and before we knew the exact formula for the area of a circle. This is said to be the first precise mathematical of the area between two curved lines. Learn how he solved for the area of a crescent-shaped lune (same

The AKS Test has been a major break-through in the search for Prime Numbers. More links & stuff in full description below ↓↓↓ See the previous video about Fermat’s Prime Test at: http://youtu.be/jbiaz_aHHUQ The video features Dr James Grime – http://singingbanana.com The AKS Test paper: http://bit.ly/primetest Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile

We mark the date 12/12/12 with a video about the merits of the dozenal/duodecimal system. More links & stuff in full description below ↓↓↓ Numberphile regular Dr James Grime makes the case. More about James at http://www.singingbanana.com/ NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Videos by Brady Haran Patreon: http://www.patreon.com/numberphile

A tetrahedron and a pyramid have edges of equal length. If they are glued together on a triangular face with the vertices aligned, how many faces will the new shape have? This question is trickier than it looks! It stumped the test-makers. Playable demonstration: Steve Phelps has made a Geogebra worksheet that you can try

A chat about some of the ways legendary physicist Richard Feynman cracked safes (filing cabinets) at Los Alamos during the Manhattan Project. More links & stuff in full description below ↓↓↓ Discussed by Professor Roger Bowley. My Favourite Scientist on Feynman: http://www.youtube.com/watch?v=qoYWfytx5QA Feynman Diagrams: http://www.youtube.com/watch?v=3bbJeMBHq0g Enigma: http://www.youtube.com/watch?v=G2_Q9FoD-oQ NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile

Thanks to Reio in Romania for emailing me this fun problem! What is the area? This puzzle was shared with the tagline “you should be able to solve this.” Solution to 5th grade Chinese challenge problem My blog post for this video https://wp.me/p6aMk-82G Reference Math problem from anime Steins;Gate https://math.stackexchange.com/questions/798367/area-of-a-part-of-a-square Playlist to watch all videos

Here is the biggest (?) unsolved problem in maths… The Riemann Hypothesis. More links & stuff in full description below ↓↓↓ Prime Number Theorem: http://youtu.be/l8ezziaEeNE Fermat’s Last Theorem: http://youtu.be/qiNcEguuFSA Prof Edward Frenkel’s book Love and Math: http://amzn.to/1g6XP6j Professor Frenkel is a mathematics professor at the University of California, Berkeley – http://edwardfrenkel.com The Millennium Prize at

This problem went viral after it appeared on a Math Olympiad test for talented students in Singapore. It’s not a trick question! Here’s the problem, which I have very slightly re-worded for clarity. Blog post (detailed text explanation): http://mindyourdecisions.com/blog/2015/04/14/when-is-cheryls-birthday-answer-to-viral-math-puzzle/ Source: https://www.facebook.com/kennethjianwenz/photos/a.173663129479243.1073741827.167504136761809/385751114937109/?type=1&theater Official Solution: http://mothership.sg/2015/04/p5-logic-question-is-actually-a-math-olympiad-question-for-sec-3-and-4-students/ Albert and Bernard have just become friends with Cheryl, and they

Can you solve 97 x 96 in your head? Learn the trick in this video! This is how NFL player Ryan Fitzpatrick’s son was able to multiply two numbers in the 90s wowing the media audience. If you like my videos, you can support me at Patreon: http://www.patreon.com/mindyourdecisions Connect on social media. I update each

Marcus du Sautoy discusses Gödel’s Incompleteness Theorem More links & stuff in full description below ↓↓↓ Extra Footage Part One: https://youtu.be/mccoBBf0VDM Extra Footage Part Two: https://youtu.be/7DtzChPqUAw Professor du Sautoy is Simonyi Professor for the Public Understanding of Science and a Professor of Mathematics at the University of Oxford. Professor du Sautoy’s book as mentioned… In

Every year some NBA team seems to make the playoffs with a losing or barely even record. This video considers how extreme the example can go. WATCH how an NFL team with 0 wins could make the playoffs: https://www.youtube.com/watch?v=3xXyauro_kc Worst nba playoff teams: http://www.sbnation.com/nba/2014/4/4/5581984/nba-playoffs-history-bulls-spurs-knicks-cavaliers NBA scheduling: http://www.nbastuffer.com/component/option,com_glossary/Itemid,0/catid,44/func,view/term,How%20the%20NBA%20Schedule%20is%20Made/ If you like my videos, you can support

Professor David Eisenbud on the infamous Collatz Conjecture, a simple problem that mathematicians may not be “ready” to crack. More links & stuff in full description below ↓↓↓ Extra footage from this interview: https://youtu.be/O2_h3z1YgEU Prof Eisenbud’s 17-gon: https://youtu.be/87uo2TPrsl8 Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub

Can you calculate 85 percent of 24 in your head? This is not as hard as it sounds. If you know how to halve numbers and divide by 10 you can probably do this in your head. This video explains how to calculate many percentages as a combination of ones that are easier to compute.