Math

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/
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Albert Einstein was challenged with a simple riddle in a 1934 correspondence with the psychologist Max Wertheimer. Can you figure it out? Thanks to all patrons! Special thanks to: Shrihari Puranik, Richard Ohnemus, Michael Anvari, Kyle. We are the only channel to feature math topics suggested by people around the world. Support on Patreon to
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Fields Medallist and math “celebrity” Cédric Villani is famous for wearing ornate spiders on his lapel. More Villani videos: http://bit.ly/Villani_Videos Cédric Villani website: http://cedricvillani.org His book Birth of a Theorem (Amazon): http://bit.ly/BirthOfATheorem Villani talks about his Fields Medal: https://youtu.be/Vp3sgYKULp0 Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by
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Featuring Professor Howard Masur from the University of Chicago. Filmed at the Mathematical Sciences Research Institute (MSRI). Part 2 of this interview: https://youtu.be/AGX0cLbHaog Patreon: http://www.patreon.com/numberphile Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of
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The famed Poincaré Conjecture – the only Millennium Problem cracked thus far. More links & stuff in full description below ↓↓↓ Ricci Flow (used to solve the problem): http://youtu.be/hwOCqA9Xw6A Riemann Hypothesis: http://youtu.be/d6c6uIyieoo Extra interview footage with Jim Isenberg: http://youtu.be/7eJleW0JcKg Grigori Perelman’s paper: http://bit.ly/perelmanpaper Discussed here by Katie Steckles and James Isenberg. Support us on Patreon:
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People around the world have asked me this and similar problems. Learn how to solve using only geometry (and a little bit of algebra). There are many other ways to solve the problem too https://www.mathalino.com/reviewer/plane-geometry/02-area-common-arcs-quarter-circles Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I consider all ideas though can’t always reply! Like many
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This problem is adapted from an Oxford University admissions question. They say if you can solve this in your head, you are a genius 😉 Alex Bellos’s column on The Guardian https://www.theguardian.com/science/2021/jul/12/did-you-solve-it-oxford-university-admissions-questions 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!
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Tadashi Tokieda puts $20 on the line… More links & stuff in full description below ↓↓↓ More Tadashi videos: http://bit.ly/tadashi_vids Paperclips: https://youtu.be/wGkvyN6s9cY Video by Brady Haran and Pete McPartlan (animations by Pete) 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 Numberphile is supported by the Mathematical
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Three squares are placed in a row. Connect the bottom left corner of each square to the top right corner of the third square, forming angles with measures a, b, c with the horizontal. What is the sum of a, b, and c? Many people requested this problem, and I thank Roberto O. and Cardist
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Johnny Ball on Russian and Egyptian Multiplication. Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓ More on Johnny Ball, including his books and live shows: https://www.johnnyball.co.uk Russian multiplication is also known as Ethiopian multiplication. Why Use Binary? (on Computerphile) – https://youtu.be/thrx3SBEpL8 Discuss on
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An exciting paper about gaps between prime numbers – a step closer to proving the twin prime conjecture. More links & stuff in full description below ↓↓↓ Extra footage at http://youtu.be/D4_sNKoO-RA The proof was published by Yitang “Tom” Zhang from the University of New Hampshire. We’re discussing it in simple terms with Numberphile regulars –
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Students in the UK faced a similar question to this one. Don’t give up–U can solve it! Adapted from [GCSE Edexcel Further Math] How would you solve for x? from HomeworkHelp 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
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Archimedes’s famous Cattle Problem had a truly epic solution. Featuring Alex Bellos. More links & stuff in full description below ↓↓↓ Alex Bellos: http://www.alexbellos.com More Alex videos on Numberphile: http://bit.ly/Bellos_Playlist So You Think You’ve Got Problems by Alex Bellos Amazon: https://amzn.to/2KR9Get Signed copies via MathsGear:http://bit.ly/BellosProblemsSigned More Alex books: https://amzn.to/2KQTc5Y The Cattle Problem by AH Bell:
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I received many requests for this challenging problem. Can you solve it? Thanks to Toli for the suggestion! Geometry solution in method 1 http://128.192.17.191/EMT668/EMAT6680.F99/Estes/15degrees/15degreesgeometric.html Another geometry solution http://128.192.17.191/EMT668/EMAT6680.F99/Estes/15degrees/solution2.html Trigonometry solution http://128.192.17.191/EMT668/EMAT6680.F99/Estes/15degrees/15degreestrigonometric.html Go Geometry discussion https://gogeometry.blogspot.com/2009/11/problem-395-square-15-degree.html https://drive.google.com/file/d/1A0Az5nJ9wGBwcM2F4gQY2dSfeKJZ1gSS/view 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
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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
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A triangle with sides of 4, 3, and 5 is drawn inside a square as shown. What is the length of the square’s side? It’s a fun little geometry problem! Sources https://www.instagram.com/p/Btw9ZfyBz5w/ http://mathhelpforum.com/geometry/236852-area-square-right-triangle-inside.html Egyptian Proverb http://oaks.nvg.org/egyptian-proverbs.html Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I consider all ideas though can’t always reply! Why
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This was asked to students in 1801, but it is still a challenging and fun problem to solve to this day! Source See page 5, problem 24 https://archive.org/details/cambridgeproblem00cambuoft/page/4/mode/2up 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 buy from
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This video features Dr Hannah Fry (more links below) ↓↓↓ Check out Brilliant.org: https://brilliant.org/numberphile (20% off premium subscription) That circle cutting problem on Brilliant: https://brilliant.org/NumberphileSandwich Hannah Fry on Twitter: https://twitter.com/FryRsquared Read about Hannah’s Xmas book (and buy a copy to show her some support!): http://www.bradyharanblog.com/blog/hannahs-book More Hannah videos on Numberphile: http://bit.ly/hannah_vids Animation by Pete McPartlan
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Happy #PiDay! When two of the hardest tests in the world cover the same problem, you know it’s a big deal. References Wikipedia article https://en.wikipedia.org/wiki/Proof_that_22/7_exceeds_%CF%80 Putnam exam 1968 A1 https://prase.cz/kalva/putnam/putn68.html JEE Advanced 2010 Paper Solutions Part-1 | IIT-JEE | Strategy, Tips, & Tricks | Paper Discussion (see around 55:30) https://youtu.be/Zz4buu5y7_8?t=3330 Proving 22/7 is greater than
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Not all jokes are in base 10… More links & stuff in full description below ↓↓↓ With thanks to Audible – http://www.audible.com/numberphile (book details below) More jokes explained at: http://youtu.be/JJQWtGm3eIs Animation by by Pete McPartlan – http://www.petemcpartlan.co.uk Explanations by Matt Parker – http://www.standupmaths.com This video was posted during YouTube Comedy Week: http://yt.be/comedyweek Leave more joke
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Three chords are drawn in a circle, spaced 30 degrees apart from the same vertex. If the left chord is 10, and the right chord is 12, what is the length of the middle chord? Wow! The channel “Freedom Mathematics” did a general case of the chord progression puzzle. The general problem is quite complicated!
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Partitions are a major part of the Ramanujan story (as shown in the new film about his life) – but what are they? More links & stuff in full description below ↓↓↓ Dr James Grime tackles the issue. Extra footage: https://youtu.be/ksHqQW94KlE More James Grime on Numberphile: http://bit.ly/grimevideos Young Tableau: https://youtu.be/vgZhrEs4tuk Shuffling: https://youtu.be/AxJubaijQbI James discusses Good
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Langton’s Ant – starring Katie Steckles (and Audrey). More links & stuff in full description below ↓↓↓ Extra footage: https://youtu.be/oTssNuDEkSc The 104-steps: https://youtu.be/xU072T4V12A John Conway videos: http://bit.ly/ConwayNumberphile Support us on Patreon: http://www.patreon.com/numberphile Katie Steckles website: http://bit.ly/stecks_web Audrey: https://www.facebook.com/AudreyAdorable One of many online simulators: http://rossscrivener.co.uk/projects/langtons-ants/ Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook:
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This is adapted from the Mathematics Olympiad of Nepal (MOON). Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address in video). I consider all ideas though can’t always reply! Like many YouTubers I use popular software to prepare my videos. You can search for animation software tutorials on YouTube to learn how to make videos. Be
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Beautiful Dragon Curves, Fractals and Jurassic Park. Featuring Rob Eastaway. More links & stuff in full description below ↓↓↓ Rob’s website: http://www.robeastaway.com/ Thanks to Matthew Ward and Faraz Barzideh who helped Brady out with some curves! The book Jurassic Park is by the late Michael Crichton. NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets:
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University entrance exams and job interviews have asked questions similar to this problem. What is the area of the rectangle? What is the minimum area of the large triangle? Special thanks this month to: Jamal Jackson, Mike Robertson, Michael Anvari, Robert Zarnke, Fiona Harper, Kyle. Thanks to all supporters on Patreon! http://www.patreon.com/mindyourdecisions Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send
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Sequence guru Neil Sloane on a sequence which puzzled him – until he spotted the mistake! More links & stuff in full description below ↓↓↓ More Neil Sloane videos: http://bit.ly/Sloane_Numberphile The OEIS: https://oeis.org Hanny’s Voorwerp: https://youtu.be/RDr6bSB6Vlg Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile We are also supported by Science Sandbox, a
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I had a lot of fun solving this one, and I think you will too! 0:00 Problem 0:49 Hints 4:12 Solution 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 buy from the links below I may receive a
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A number of galactic proportions… See more #MegaFavNumbers on this playlist – https://bit.ly/MegaFavNumbers – and read below to contribute your own. More links & stuff in full description below ↓↓↓ See our full collection of video on the sum of three cubes at: http://bit.ly/SumOfCubes (*) the cube (which we depicted quite loosely and artistically, of
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Can you solve this geometry problem? Thanks to Lucas from Brazil for the suggestion! Kangaroo Maths 2020 https://www.matematica.pt/en/docs/kangaroo/enunciados/2020/2020_Grade9-10.pdf Proof of inscribed angle theorem https://www.khanacademy.org/math/geometry/hs-geo-circles/hs-geo-inscribed-angles/a/inscribed-and-central-angles-proof 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 buy from the links below I
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Thanks to Devesh from India for the suggestion! A version of this problem was given in an Olympiad qualifying test. Socratic https://socratic.org/questions/a-root-a-b-root-b-183-a-root-b-b-root-a-182-find-9-5-a-b Math StackExchange https://math.stackexchange.com/questions/2405256/find-the-value-of-frac95ab-given-that-a-sqrtab-sqrtb-183-and-a Brainly https://brainly.in/question/3901575 Quora https://www.quora.com/Suppose-a-b-are-positive-real-numbers-such-that-a%E2%88%9Aa-+-b%E2%88%9Ab-183-a%E2%88%9Ab-+-b%E2%88%9Aa-182-How-do-we-find-9-5-a-+-b 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 buy
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Johnny Ball on the “often missed” Hippocrates of Chios. Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓ More on Johnny Ball, including his books and live shows: https://www.johnnyball.co.uk See Johnny discuss Russian multiplication: https://youtu.be/HJ_PP5rqLg0 Numberphile is supported by the Mathematical Sciences Research Institute
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This challenging geometry problem appeared on one of the hardest math competitions (the Putnam exam), and there is a neat way to solve it! The Putnam Exam has legendary difficulty: the average (median) score is usually 1 out of a possible 120 points. No calculators allowed though, and you have to prove everything very carefully.
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Can you solve this incredibly difficult calculus question? I had a lot of fun solving this one! Special thanks this month to: Kyle, Mike Robertson, Michael Anvari. Robert Zarnke, Fiona Harper. Thanks to all supporters on Patreon! http://www.patreon.com/mindyourdecisions Adapted from Comment from discussion PhysicsHelpBernoulli’s comment from discussion "[12th grade math] What number would n have
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Can you solve this geometry brain teaser? Note: I was emailed a similar problem but I am unable to locate the original source. It seems to be in the style of Bright Side quizzes, but often those are based on problems circulating. Please let me know if can identify the original source and I will
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The ancient Babylonians used a number system with base 60 (sexagesimal). More links & stuff in full description below ↓↓↓ Tablet image courtesy of Bill Casselman and Yale Babylonian Collection – more at http://www.math.ubc.ca/~cass/Euclid/ybc/ybc.html This video features Thomas Woolley – he tweets at https://twitter.com/#!/thomasewoolley NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe:
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John H Conway on his love/hate relationship with his most “famous” invention. Conway playlist: http://bit.ly/ConwayNumberphile More on how he invented it at: http://youtu.be/R9Plq-D1gEk More links & stuff in full description below ↓↓↓ 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 Numberphile is supported by the Mathematical
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More links & stuff in full description below ↓↓↓ Brady’s Movember Page: http://bit.ly/BradyMo See full description for list of Connect 4 links. John Tromp’s page: http://bit.ly/TrompNumberphile James Allen’s Connect Four book: http://bit.ly/AllenBook James Allen: http://james.fabpedigree.com/ OEIS: https://oeis.org/A212693 Victor Allis paper: http://bit.ly/AllisPaper 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
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George Dantzig, William Sidis, Srinivasa Ramanujan? Who was the real Good Will Hunting? More links & stuff in full description below ↓↓↓ Maths in Good Will Hunting: http://www.youtube.com/watch?v=iW_LkYiuTKE This video features Numberphile’s very own mathematics superstar – Dr James Grime. 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
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Can you solve this interesting geometry problem? References Solution by “WAY TO GOVT JOB” on YouTube Stretched length of band https://www.thestudentroom.co.uk/showthread.php?t=1936482 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 buy from the links below I may receive a
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