Lightning calculation and other "mathemagic" | Arthur Benjamin

www.ted.com In a lively show, mathemagician Arthur Benjamin races a team of calculators to figure out 3-digit squares, solves another massive mental equation and guesses a few birthdays. How does he do it? He'll tell you.
TEDTalks is a daily video podcast of the best talks and performances from the TED Conference, where the world's leading thinkers and doers are invited to give the talk of their lives in 18 minutes -- including speakers such as Jill Bolte Taylor, Sir Ken Robinson, Hans Rosling, Al Gore and Arthur Benjamin. TED stands for Technology, Entertainment, and Design, and TEDTalks cover these topics as well as science, business, politics and the arts. Watch the Top 10 TEDTalks on TED.com, at
www.ted.com/index.php/talks/top10

[@NateBagley]

I've never rooted so hard for someone to do a math problem.

[@TeamRetox]

That cracked me up

[@escargoux]

***** I was thinking the same thing. It was very suspenseful, like close soccer game. I would watch mathematician competitions on TV, lol

[@daniel01231]

@@escargoux whoosh

[@oscara.3981]

Hahahaha rooted

[@Durzo1259]

This guy's pre-frontal cortex must be a quad-core.

[@wazif1786]

his brain is a supercomputer

[@wazif1786]

+Durzo heh... Well Damn..

[@bestredditstories1158]

Durzo It's as simple as he has more blood flow to his brain than the average person.

[@abhideepsingh4484]

octa core!

[@markengamer5649]

r/iamverysmart

[@kwilson5832]

"I know as a magician, we're not supposed to reveal our secrets, but I'm not too afraid that people are going to start doing my show next week" Classic!

[@GMYC7774]

Yeah, not even 15 years later. Legendary!

[@chesseswar]

Oh, the days before everyone had a calculator on their phones.

[@arthurwoster4856]

teacher: no calculators allowed in tests me: brings arthur benjamin teacher:

[@xw591]

More than just impressive, he seems like a genuinely great guy, great humor.

[@rrahman12]

A fantastic guy. Really deserves a standing ovation.

[@johnnytheyoungmaestro]

He got one at the end of this video!

[@HemoStopRomania]

I just love this guy. He's incredible.

[@Renato404]

loved it when he showed no problems in revealing his methods. Amazing!! Dam good!!!

[@kimnabi3988]

Damn

[@Jalanko13]

This guy is great! it's one thing to be a math genius...it's another to know how to work a crowd.Seriously, the way he keeps the audience enthralled and inserts light humour "Let me re-cap *puts cap back on*" is a great way to ease the audience.Wow. Great Going Art :)

[@DisKeda]

What I liked about this that the guy was actually funny. You wouldn't expect it from this kind of person. Very good!

[@isabellajimenez7072]

My sister has his "the Great Courses: The Secrets of Mental Math" She is absolutely amazing! She can finally square 5-digit numbers in her head, though it takes roughly 2-3 minutes.

[@SpiritMolecule]

***** sarcasm?lool

[@isabellajimenez7072]

Wow you're so classy... She goes to math competitions and wins, thank you. That's how she applies this knowledge.

[@isabellajimenez7072]

Well that's obvious, but for now, it's quite useful...

[@94D33M]

@@isabellajimenez7072 are you still there mate

[@groundshaker333]

Saw this live today, he came to our school and he truly is amazing!!! Amazing work !!!!

[@HelloDapp]

this guy has to have that talent where he can remember every detail of his life

[@mariah98nelson]

I got the book. He's phenomenal!

[@theplayersplay1984]

1:27 He almost said the word stupid

[@WalterKingstone]

+ThePlayersPlay Lol

[@AvastarBin]

+ThePlayersPlay Oh My god! Yes ! LOL

[@KirubaEbenezer]

He was about to tell 624 i think so....

[@scorpiuscosplays7972]

true

[@tsundereshark5945]

STU- 594!!!! Give her a round of applause!

[@vika09]

It's a mind blowing application of the (a+b)^2 and (a-b)^2 formulas. Still a damn genius.

[@anshulgoel007]

Nice viewing.. But two mistakes 457^2 = 208849 [Not 208549], 722^2 = 521284 [Not 513284] I guess the people with the calculators on stage doubted themselves / were embarassed to point it out. But still amazing to do this in so short a time.

[@blahblaah4474]

For 457 squared I heard him say 205849 but my calculator gives me 208849.

[@Ishaanstube]

Were the people with the calculators retards or something, couldn't read out the correct answer or were too shy to correct him.

[@foya7404]

Anyhow, his performance is still absolutely remarkable as he only did two mistakes in over 50 calculations

[@CaseysBeats]

Oops, I see a carry coming.

[@PolochAngriff]

When he asked the audience what 5 squared was, I blurted out the wrong answer..

[@BlessedOne686]

😂😂😂

[@davidweng2160]

Ok boomer

[@cher4057]

David Weng you’re using it wrong...

[@davidweng2160]

Chen H would you be so nice as to teach me then?????

[@triple7marc]

David Weng It’s not funny regardless of how you use it. But it’s especially not funny when it makes literally no sense, like how you just used it.

[@NectarineSoup]

This man is banned from all casino's in the state of Nevada.

[@CodingMazaa]

why?

[@nickbirrer]

kumropotashify He would destroy the house every goddamn time.

[@preciousdoe6813]

Why?

[@wooty2745]

@@preciousdoe6813 he can count for example: cards and odds. but ofcourse hes not banned.

[@whiterajah2072]

Not if he's performing there 🤪

[@claudees]

Truly appreciate Arthur Benjamin's efficiency, intelligence and eloquence. Thanks for sharing this video. Best wishes.

[@mateharris]

Art, you rock! Art Benjamin is a professor where I went to college, Harvey Mudd College. Despite knowing him for years, I am still in awe at his mental math ability.

[@StayQrious]

Interestingly, in the trick, 8649 is a multiple of 9 which means that any multiple of it will also be a multiple of 9. The test for divisibility for nine is that all the digits added will still give a multiple of 9 if done recursively and so we can just add the remainders with 9. (ie. 81(8+1) , 8649 ( 8+6+4+9 = 27, 2+7 = 9) . We don't have to even go this far in addition. We can keep subtracting 9 as the sum becomes greater than 9 and that's all he does with his showmanship of course, eg. He took 8649 because it was convenient, (he says six digits in "any order" because the order of the sum of the digits hardly matters. A middle school student knows this. person 1 -1,9,7,0,4,0 - (find the sum subtracting 9 every time the sum exceeds 9 and you get 3 - so the number to be added to this to reach 9 would be 6 and that's what he says. person 2 - 4,4,8,7,5,2 - circular sum = 3 therefore answer = 6 Person 3 - 0,7,9,0,4,4 - circular sum = 6 . Ans = 3 Person 4 - 2,6,3,9,7,2 - circular sum = 2. Ans = 7. Loved the way he pulled off a middle school question with all that showmanship.

[@Bobstew68]

Nice work figuring this out! I was hoping the comments would contain something like this.

[@youvegottobefukin]

aanand srinivas Yeah I go that too. Nice trick though

[@Keyakina]

aanand srinivas didn't even get this

[@mattt3942]

It is not a random coincidence that 8649 is a multiple of 9, either. The way he got these numbers was by calling 4 people in a row, with the last being on the end. He did the exact same procedure in another video I've seen him do this trick. Again, the last choice was a girl on the end of the row who served him up a number divisible by 9. This is a trick which I think is beneath this man. All of the other calculations he does are completely legitimate and can be learned from. This trick only works when his "plant" in the audience serves him up a number divisible by 9.

[@omak7084]

an easier way dude, is to just add all the numbers, and subtract it from the next multiple of 9. example: 1 + 9 + 7 + 4 + 0 + 0 = 21. 27 - 21 (next multiple of 9) = 6.

[@audimute]

I was impressed... yes with "the show/ presentation" but more so, how fast my 2kids picked up mental math as a game. You gotta get this guys book! It makes math very "useful" for everyone. I wonder why schools have not picked up some of his methodology. It is so musch easier than how traditional math is tought. When you look past the showmanship of this video, there is real science, genious, and surprisingly FUN. Very impressive Mr. Benjamin. Best of luck to you.

[@brandon7477]

I don't know if this is how he did the missing digits trick or if it was just a coincidence: the number he chose, 8649 is divisible by 9 and I know this because if you add all the digits, you get 27 which is 9*3. The is the divisibility rule for any multiple of 9. If you multiply 8649 by a 3 digit number, it will still be a multiple of 9 and thus the rule still applies. For example, if they told you that 6 digits were all 1's, then you would know that the last digit is a 3.

[@theraymondchou]

That's exactly what he did. Notice how he picks the one number that is divisible by 9. The day of the week thing he uses an algorithm for, though he said 1824 is hard implying he's using "anchor dates," which is really inefficient imo, there are better ways. The three digit squares he talks about in his book, and he's so well versed in it it becomes almost lightning like.

[@jimmierustler5607]

Ray Chou Might have been because 1824 was a leap year

[@mikelincoln8395]

This is just like knowing all the necessary moves to manipulate a Rubric cube, then practise practise practise.

[@alisonhernandez7189]

My class invites you to our school. I have showed this video so many times to so many classes. Every year my students are amazed. Some of them say you are their idol because of your mental math skills.

[@alexrobertsfcim]

The first time I remember seeing this video was in my pre-calc class junior year of high school back in 2010-'11. The video is so good that I keep coming back to it now several years since I finished school.

[@Repented]

Wow, amazing! He's well articulated, talented, and entertaining as hell.

[@highflyer7652]

This is so awesome, I am really at awe. I''ve bought his book before I saw this video, now I'm gonna read it

[@vivoai2831]

how is your mental calculation ability now?

[@ishansinha1336]

HOW YOU DOIN COMRADE ?

[@johnnytheyoungmaestro]

Wow, a standing ovation! Arthur Benjamin is really talented, and he's so great at adding humor to all of this! :)

[@GuardsmanBass]

I'd love to see this live.

[@pablopablopablo22]

"someone give me a 3-digit number." "100."

[@mantingfoo8697]

He must have eaten a calculator when he is 1 year's old

[@bestcovercollection9012]

😂😂😂😂😂😂

[@IamFlaem1]

Did u eat a joke book when you were 1 year’s old

[@ajayprasanna9217]

that standing ovation atlast gave me goosebumps

[@jasmineswen]

AMZING!! just unbelievable! My math teacher also impressed!

[@m12mikeful1]

"let me re-cap"....... ahhaah lol nice one. XD

[@opalseekingthetruth7620]

This was amazing to watch. - Definitely not the same as this video, but sometimes I give my son math problems just on a whim to solve, and I gave him 97+49 ...He gave me the answer from his head before I could. :P He's 7. lol You would think I'd be embarrassed to tell that story, but nope. Too proud of him to care. :P If he's a natural mathematician, I will definitely support and encourage his development in that subject.

[@spacedtime6597]

Sounds right, These guys put so much work into a small tricks like this.

[@RadheadFilms]

This guy is my math teacher at Mudd. He's awesome.

[@michaelmcclung4193]

Lol, same exact thing in another TEDx Talk

[@cmanw]

That was awesome! Wish I could just do the 2 digits in my head!! :)

[@owenthompson3323]

I can

[@quleughy]

Agreed. Makes me wish I enjoyed algebra more in school.

[@sharmanedeleon831]

I salute this man,,,he's so smart!

[@anncervales1492]

I actually watched this clip more than twice.

[@Mike-dy8sj]

Ann Cervales more than twice? You can't count higher than that?

[@DjGreydanus]

8:00 For day of the week trick

[@Givicencio]

Just awesome.

[@NebraskaBear]

I just saw his show in Kearney. It was the best show I've ever seen!

[@pop12Viper]

First I said: wow he is a math genius. Then I said: wow he is a time traveler.

[@redmed10]

everybody in the audience are in on it.

[@leonlian007]

He is great in mental math, there is no question about that. I had that experience when I was in grade 5 in China. wht i remember was doing addition and subtraction instead of multiplication, nothing very tricky, coz u still have to memorize all the procedures and number in it.

[@riccardoportelli4065]

This show's script if identical to his Ted talk 5 years later it's almost insane. I can't believe he did the exact same show over and over for that long.

[@marcellocapone4925]

I get a hint this gentleman is good at maths. Just a hint though...

[@anncervales1492]

I like him, he's so smart and funny as well!

+Ann Cervales are you attracted to him sexually or just like we men are amazed how he is good

[@anncervales1492]

Of course not sexually! Lol

[@nathan791]

+pako pako That's a nice thing to say to someone.. :/

[@101toheedahmad]

fantatic mindblowing,he has extrawordinery skills , and commond on the mathematics amazing

[@Abjecttestament]

Utterly incredible

[@an.gie.gie0811]

I need him as my next math teacher...

[@KumareshRamesh]

What if someone had left out 0 or 9?

[@MagicianBrendanRodrigues]

i was priviliged to see arty live a few times, he is very entertaining,

[@ibethguagalango4253]

Incredible

[@dany3241291]

hax, VAC banned.

[@alperozcan1097]

he uses fuckin' p90

[@Kairogue13]

dany3241291 csgooooo let's go man

[@user-cw2py6wh8l]

why no one ever pick zero?

[@AlyRose2012]

Mine did too. Love this guy

[@SpiritMolecule]

AMAZING

[@frankhomer9323]

This guy shows some amazing abilities, but can he take out the trash ?

[@SpiritMolecule]

lool

[@ShephineShaji]

at 3:42 he made a mistake... 457^2 is 208849 and not 205849 as he said!

[@AddzyKishoore]

Yeah!

[@phanduong6170]

Yeah! The 4 guys in the platform had some gestures like disagreeing with him, but he didn't mind. But this it's just a little mistake. ^^

[@Grejegando]

Also 722

[@Daniel-pd2zn]

This guy is so good. Definitely, definitely.

[@GosuVu]

Incredible.

[@konstantingeist3587]

A few weeks ago I attempted to multiply a 4-digit number by a 2-digit number... in my dream. I actually remembered my way of calculating it when I woke up and it was correct, but it wasn't finished, unfortunately

[@opalseekingthetruth7620]

+KonstantinGeist I think dreams could be used as powerful tools if we practice it. ("Practice dreaming?" - I don't know if you're familiar with lucid dreams, but it's where in a dream you KNOW you're dreaming. Therefore could do practically anything you want.) In one of mine, I could speak and understand fluent French. Like it was the most natural thing to do. It'd be amazing if we could tap into this ability. : )

[@WinstonKnows]

Opal SeekingtheTruth I love that concept! I would recall things that I had forgotten(while awake), in my dreams. There has to be a way to tap into our subconscious and draw out ideas, thoughts, memories, data, etc...

[@nts0011]

damm killer cpu

[@devashishjoshi4134]

Spectacular!

[@Laxmikanthb1]

Me returns from grocery store Mom: where is the remaining money? Me: 13:56

[@WordsandNumbers1]

One mistake sir, 1824, June , 6th was actually sunny ⛅. Lol

[@DoLLfaceEMME]

Wow This was the most incredible thing I've ever seen!!!! What a gift!!!!

[@IFrancyISantosI]

why a gift? he had the passion and trained it. we are just too lazy

[@Osminiscool]

I just saw this guy on the Colbert Report lol He's pretty damn cool!

[@bishololo]

Mother of MATH !!!!!!!!!!!!!!

[@rubic64]

722^2=521284 and not as he claimed 113284 4:01

[@WalterKingstone]

rubic64 You mean "as he claimed 513284" but you're right! He got it wrong!!??

[@Grejegando]

And the first 3-digit number he also got it wrong

[@WalterKingstone]

987 squared does equal 974169

[@Grejegando]

Sorry, I meant the second one. 457^2 = 208,849 He said 205,849

[@corvoattano8426]

+Grejegando he said it wrong. The rest were the same.

[@deepak201]

Thousands still do it in India. Shakuntala Devi is a famous and much venerated Indian mathematician who is considered a genius and is popularly known as the Human Computer. In 1977, Shakuntala extracted the 23rd root of a 201-digit number mentally, 12 seconds faster than the Univac-1108. She even occupies a place on the 1995 Guinness Book of Records for her skills.

[@WasifAli96]

Same here it's awesome.

[@poketosonic88834]

He just visited our school! :D AMAZINGGG

[@laxmanselvam]

This is insane. I was actually going to bed. then I thought, lets watch a TED talk. I am fresh now. *Standing Ovation*

[@Navigatorbythestars]

this is Amazing!

[@polarbits]

This guy was at my Mathcounts event a year ago!

[@sachinjagarwar]

what happened to cookie though .did anyone eat it🤭🤭🤭

[@aboveaverageinsanity8128]

"It will take me a little bit of time" it would take me a year.

[@robinsonpeter7942]

Hvis du har brug for hjælp bare besked mig om WhatsApp på [phone]

[@TheSmurf1973]

That is impressive!!

[@FalconRTA]

...just amazing

[@poketosonic88834]

His intro: Exact same wording he used at our assembly today. :O

[@thepussygrabbingfamilyvalu557]

3:41 he's asked about 457*457 and he says 205,849... btut it's actually 208,849

[@MarkCliffeIsGay]

I love your username.

[@HelloDapp]

back in the day it use to be 205,849 , then they updated maths

[@rayawira]

Nobody's perfect

[@naybobdenod]

very entertaining especially the re-cap lol

[@Tino81295]

doing revision for my maths exam next week...this is the best procrastination so far...

[@brennahill5449]

my math teacher was in a conference with Arthur Benjamin and beat him at the 24 game

[@jordanrogerson4499]

No magics just mathematics.

[@sagitswag1785]

Jordan Rogerson well, most of these routines are described in mentalism books...

[@lilyvingdead]

Watched this in Math Club and my seat mate who was a fast calculator was mind-blown.

[@czhiting]

BRILLIANT

[@EZKATKA527]

2018??

[@shahaddaood9468]

he is a human calculator nothing beats him

[@pen.4381]

I like the phrase the improbable

[@shahaddaood9468]

no lah I copied u

[@Andrei-si9yl]

awesome

[@shahaddaood9468]

***** he is a real man

[@stylinsandwich]

Lets pit him against my 4090 in tensor calculations

[@Raykon9]

i cant even do a double digit and this guy is......no words, simply amazing

[@AshrayMalhotra]

Whohoo, Arthur Benjamin rocks!!!

[@megakeenbeen]

the answer for 722 squared was actually wrong.

[@nathanoshea4356]

Still can't deny he's amazing!