Math Magic



The above video is just amazing. Dr. Arthur Benjamin performs feats of math in his head and even tries to explain some of the methods he uses to arrive at the answers. Just watch it. I guarantee you will be as amazed as I was.

Via Ted

    • Mahdi
    • January 1st, 2008

    Great stuff. Pls shoot Shandooga someone. He was a failure in school maths and wouldnt beenrolled in the local amateur magic class. He is just envious.

  1. @Al,

    I wouldn’t say this guy is garbage. Daniel Tammet is amazing, but he’s a savant. His brain is wired differently than yours or mine or Dr. Benjamin’s. Daniel sees numbers in his mind as colors, shapes and sounds. He does math in his head by just reading the “landscape” in his mind.

    Further, Dr. Benjamin can *teach others* how to do what he does. Daniel Tammet cannot. I don’t think anyone could be taught to think the way that Daniel Tammet does. I mean, c’mon the guy’s not only a wiz with numbers, but he learned Icelandic in just around seven days!

    Cheers and happy new year!
    Chris

    • Steven
    • January 2nd, 2008

    Sorry Chris, but Icelandic isn’t terribly difficult. It’s just Old English. If you’ve studied any old English at all, Icelandic becomes a snap. (Shakespeare is considered Modern English). I think your idea of how he turns things to colors, shapes, and sounds is a poetical way of doing it. If I spent 5 hours a day every day for the next month learning how to square numbers, I’m sure I could do just as well.

    What gets me about the video is that none of the people with the calculators caught his 2 mistakes. Were they really random people, or people whom he chose beforehand so as to avoid the embarrassment in case he did make a mistake. But it’s hard to say. In one case (of the 2 mistakes) you can see the second person to the left shaking her head… was she doing it because she caught his mistake but was too polite to say anything, or she had been coached prior to the airing to say anything?

    Anyways, I think he’s got a lot of stuff memorized. It’s like a chess player memorizing openings, the board, etc., to the point where they can play the game without looking at the board and pieces. If I could visualize and keep in my memory the numbers, it wouldn’t take me long to square 3 digit numbers. It’s a matter of will power, persistence, and determination to acquire a skill like that, in my opinion.

    • Daryll
    • January 2nd, 2008

    hmm, this is quite clever. Multiplying numbers by drawing lines… It’s nothing as fast as Art but hey it’s pretty cool none the less.

    http://memorymentor.com/blog/mental-tips-tricks/multiplying-using-lines/

    Like Steven said, persistance and time on your hands and you could do *amazing* things too!

    Anyone ever hear of the Knight’s tour??

    • Traveller
    • January 3rd, 2008

    @ Steven other than coming across as patronising (which I am sure was not the intent) Your critique of Chris seemed to miss the point.

    If Mr Daniel Tammet is a savant then it is not unfair to state that “I don’t think anyone could be taught to think the way that Daniel Tammet does”

    Furthermore, knowing the root influences of a language does not make learning it any easier to be honest. Apptitude in a subject allows ease not the knowledge that ‘oh yes, that’s an olde english form there’

    And I might also suggest you take a look into synethesia.

    • Lori
    • January 3rd, 2008

    What a gift, how wonderfully entertaining and inspiring! I do not think him arrogant any more than someone who is good at painting sells his art!

    • Steven
    • January 6th, 2008

    @traveller “Genius” is about effort. I knew a mentally handicapped kid who spent all his time studying maps and memorizing where cities, lakes, rivers, and mountains were. As it so happens, you could tell him any city and he could point it out to you on the map. Was he born with it? no. He worked at it obsessively. Some people sit on their butts watching TV all day. These are the people who look at others and put labels on it such as ’savant’ as if they were born with it rather than what it really took: an obsession to learn how to do something and a lot of time to make it happen. Talent is 99% myth.

    Look at Mozart. Known to all as one of the greatest. From the time he was 2 years old his dad forced him to learn how to play the piano. I met one kid, 6 years old, who was memorizing botanical terms. From the time he was a toddler his mother started reading books to him, showing him videos, etc. Is it no surprise that the kid is going to become a ’savant’?

    • vcapo
    • January 6th, 2008

    I thought he was supposed to do magic? These are just math tricks.

    • Dave
    • January 7th, 2008

    I have a cat named Mr Package. What’s your cat’s name?

    • Mary
    • January 7th, 2008

    My cat is called DEBUSSY
    My dog is called OFENBACH

  2. Great, excellent

    • Jonas V
    • January 11th, 2008

    Leaving out a digit is very very simple if you choose the right number to multiply with. There is a reason why he chose 8 649 and not one of the three other.

    • TisJustMe
    • January 12th, 2008

    FANTASTIC…
    WHAT HE IS DOING IS ENTERTAINING.
    WHY ADD ANYTHING ELSE TO HIS ENTERTAINMENT?

  3. Numbers don’t exist :) It’s a concept, therefore it was invented by humans. 3 oranges exist, and yes there is 3 of them, but there is no 3 :)

  4. for the bit about guessing the extra digit he uses a number which is a multiple of 3, 8649*(random number) 354 = 3061746
    now take 6 in any order, 0,7,1,3,6,6 (leaving 4) sum them you get… 7+1+3+6+6=23, 2+3 = 5
    This means either 1, 4 or 7 has been left over. As for any multiple of 3 the digital root must be 3, 6 or 9.

    That’s as far as I get :) Hope someone else can work the rest out.

    • IgnominiousJoe
    • January 12th, 2008

    @ Steven – It is possible to see numbers as colours and shapes. It’s a well documented phenomenon called synesthesia, and furthermore, Daniel Tammet actually has it. It means parts of your brain develop unusual connections, so some people with synesthesia see colours when they hear a word, or can taste sounds. Don’t be patronising when you don’t even know the background.

  5. I NEED THIS GUY FOR THE LOTTERY

    • cheater….
    • January 13th, 2008

    what a cheater, he has an ear-piece… figure it out…

    • Thomas Tew
    • January 14th, 2008

    He said 457 squared is 205849. That’s wrong! It’s 208849.

  6. Magic is tricks. Your job is to find out how he does his tricks. Don’t ask me; I don’t know and I don’t care. Even if he is legit, what good is it? Now that we have calculators his ’skill’ is pretty much useless unless he can get people to pay to watch his ‘magic’.

    • Lingo South
    • January 15th, 2008

    This man is gifted and is willing to share it…
    Absolutely amazing…
    Wish I could do that…
    The worl is filld with ilitterits…as is witnessed above
    Religious people (opposite of Christian) tend to be filled with pride and judge negatively those of us who have achieved…..makes them mindless, skeptic, etc

    • Lingo South
    • January 15th, 2008

    AND we also have a large number of idiots….
    They do not like hard working smart people

    • Sarah
    • January 16th, 2008

    Vedic maths seems to be what this maths is all about, and here is method everyone should learn
    http://memorymentor.com/vedic-maths/30/

    My six year old can do this.

  7. Omg he’s amazing, he has a calculator in that little head! a 12 digit calculator…Shandooga (the guy ALL the way up), i think you need to go out and knock sum sense in. Thats like impossible to b honest, who the fuck would be able to do that except some crazy big calculators. The person with the calculator didn’t even had the time to press buttons. I do admit that he’s gifted, believe it or not. Though I think your jealous because you can’t b like him.

    • mac
    • January 18th, 2008

    well it just shows what can be done , peaple that choose
    to saythat they cant show there ngnoreance

    • Stimulated
    • January 18th, 2008

    This man has done more than you give him credit for. Look at how many of you are so curious that you have gone to your calculators to figure it out. That is called stimulation. If someone can stimulate you to make an effort to learn, even if you are trying to disprove his actions, he has made an improvement in you. Your lives have been enriched if you don’t recognize it. He is greater than you think!

    • Steven
    • January 19th, 2008

    “Don’t be patronising when you don’t even know the background.” I guess it would be patronizing if I corrected your spelling. In any case, it’s a romanticism, a poetic way to help people try to conceptualize something. Benjamin said nothing of colors when he was trying to share his mental process. He was using a mnemonic device. He probably has some algorithms coordinated with words and certain number combinations. Like everything else, once you get the few kinks of any trick figured out, it’s usually pretty simple.

    I have a terrible memory for numbers. So, whenever I get a telephone number I convert it to a word or two. For instance, right now my number is Applilab. It’s almost like Apple lab. Ask me the number, I can’t tell you without looking at the key. I’ve had 935-Babe. There’s nothing genius about relating words to numbers.

    There’s probably not a person here who couldn’t learn how to do what he does, providing you can put down the TV remote long enough to figure it out.

    • Azita
    • January 21st, 2008

    This man has an amazing gift for Math, and on top of it he is entertaining and likes to perform in front of crowds. More power to him….

    • Adam Birchfield
    • January 22nd, 2008

    Thats pretty good but some of his calculations are wrong. 457^2 is 208,849 not 205,849 and 722^2 is 521,284 not 513,284. I am sure the calculator helpers were probably just embarrassed to correct him

    • Steven
    • January 23rd, 2008

    “I am sure the calculator helpers were probably just embarrassed to correct him” either that, or they were plants.

  8. For those who can’t see the ear piece, enlarge the video to full screen. In the first couple seconds of the vid, when his name “Arthur Benjamin” appears on the screen, notice in his right ear, there’s the ear piece. I’m not, by any means, implying that he’s cheating, I’m merely pointing out that the piece does exist. I know this is quite possible; I’ve a good friend who can do similar tasks, not nearly as quick but can still do them none the less.

    • shirl
    • January 27th, 2008

    I THINK THIS IS SO UNBELIEVEABLE!!!!!!!!!!!
    SUPER!!!!!!!!!!!!!!!!!!!!!!!!!!!

  9. The following is an essay I wrote on my meth card game.
    ———————————————————

    Marsh Kaminsky
    Copyright 2004

    THE STORY OF MATHINO

    “I don’t like math, and I’m not good at it.” Those annoying words are uttered all too often today by children and adults alike. Americans frequently say them with pride, accompanied by a smirk, as if being a math wimp was some kind of badge of honor. As a Certified Public Accountant, my livelihood depended on math. Much of my life revolved around my ability to understand, nurture and massage numbers. How could I prepare tax returns without knowing math?

    With that in mind, I sat on the edge of my four year-old son’s bed one evening, preparing to read him Green Eggs and Ham. As I looked at the book, I wondered whether he would grow up to dislike numbers and become a certifiable math wimp like so many others. The thought made me cringe. After stewing about this for a week, I made a decision that is forever etched in my memory. “I will teach Daniel mathematics!” I remember shouting those words to no one in particular. My son probably wondered what his silly Daddy was yelling about.

    The next day a little voice in my head asked me a reasonable yet disquieting question: “Okay, big shot, what do you know about teaching math to a little kid?” I wanted a way to teach him math that would ignite his interest in the subject. Knowing my son and his very short span of attention, I knew my project was doomed unless he really enjoyed what he was doing. So how do I proceed?

    A few days after my teaching decision, I went to Harrahs casino in Reno for some much needed rest from enduring yet another murderous tax season. I soon found myself watching my money slowly disappear at a 21 table. It must have been fated, because I began to think about how one cannot play 21 unless one can do simple addition. I did not know it at the time, but Harrahs just showed me the way. Card games are the answer!

    I started by acclimating my son Daniel to the look and feel of playing cards and the numbers on them. I did this by teaching him the simple game of War. While War reinforced the concept of more or less, it did little else in teaching him math. Worse yet, because the outcome of a game of War is determined by pure luck, there is never any strategic thinking involved. But on the plus side, I saw how much he enjoyed our uninterrupted time together. In fact, I was enjoying it too. Furthermore, I could not fail to notice how much he enjoyed competing with me. His competitive nature and desire to win turned out to be crucially important factors in the lessons that would soon follow.

    Next, I thought back and remembered a card game called Casino my father taught me when I was a teen. While I sensed that Daniel was not quite ready for quadratic equations, I figured he could handle a card game that involved simple addition to the number ten. Well, if he ate up War, he soon gorged on Casino.

    The object of Casino is to “capture” as many cards as possible, particularly those with point values such as the four aces. One way to capture a card is by a simple match — a player matches a card in his hand with one on the table. Hence, a player can capture a five if he has a five in his hand. It took about two minutes to explain that to him. There are, of course, other ways of capturing cards which, as one might guess, involve addition. A player, for example, can capture a 3 and a 5 with an 8 in his hand. What’s more, a player can “build” numbers — a procedure that creates mathematicians. Building is exciting as it involves a strong element of risk. I might put a 3 on a 4 and build 7s. If Daniel had a 7 in his hand, he could capture my build. Furthermore, in an attempt to steal my 7s build, he could change it to a card he had in his hand. To illustrate, he could add a five from his hand and change my 7s to a 12. Nothing gave him more pleasure than that.

    From the onset, my major goal was not to stuff my son’s head full of math facts. Sure, I wanted him to know the basics, like the addition and multiplication tables by heart. But I did not want him to learn math (algebra in particular) as I did in high school by memorizing meaningless formulas where I’d plug in some numbers. Overall, I guess I wanted him to be enthralled with mathematics and, of course, to think mathematically. I know kids will learn if they are bored, but they will learn so much more if motivated by a sense of joy and fun. That’s how kids are. Now that I think about it, adults are like that too.
    .
    We played Casino constantly — maybe a few hundred games over the next four or five months. Because of the constant practice, Daniel became quite adept at simple addition.

    One day I had a brainstorm that changed everything. If a player, I wondered, could put a 2 on a 5 and build 7s using addition, why couldn’t he/she build 3s instead by using subtraction? I taught Daniel the new “rule” and he accepted it immediately. Not yet six years old, Daniel had no idea that subtraction was a school subject. He thought it was just another rule of the game. After a few months of playing with both addition and subtraction, he asked me, “Any more new rules, Daddy?” His words were music to my ears.

    “The new rule is called multiplication. Want to try it?”

    Since multiplication is just a fancy way of adding the same number more than once, I approached him with that strategy. “Daniel, five times three is simply a way to add the number three, five times.” After a few days of practice with this new intriguing rule, he got the idea.

    Adapting multiplication to Mathino (somewhere along the line we changed the name) was a problem since the largest number in the game is twelve. The trouble was . . . the product of a two number multiplication is frequently more than twelve. However, my knowledge of a tax depreciation method called “summing of the digits” provided a solution. In short order, Daniel learned that 8 x 8 really equals 10 because the sum of the digits of the product (64) equals 10. He was enthralled with this new rule.

    Now I was on a roll! After a few months of practice with multiplication, I gradually began to introduce four more new rules: division, powers, roots and negative numbers.. I suspect that if I could have incorporated integral calculus into the game, his competitive spirit would have prompted him to learn that too.

    Mathino is a deceptively easy game. Played at its simplest level with just addition, a five year old child can easily pick up on the play of the game in less than an hour. But at its most sophisticated level with addition, subtraction, multiplication, division, negative numbers, powers and roots all being played in tandem, Mathino would challenge a college math professor.

    During a game, I never allowed Daniel to use a calculator. Instead, I provided him with hard copy multiplication and power tables. Daniel sometimes spent five or more minutes going through mental math calculations before deciding on a favorable move. I never hurried him as I knew that this constant mental practice was acclimating his brain to the world of mathematics. I was also fascinated by his grasp of intricate strategic nuances. Whether he knew it or not, he was also learning odds, percentages, logical thinking skills, along with the importance of a good memory

    Besides all the other things that Mathino taught him, I used the game to show him how to win graciously and how to lose without having a snit.

    The following incident happened when Daniel was in the first grade. His teacher called and told me that they were discussing the number five in class when Daniel raised his hand and piped in with, “A five is not just a five. It is also a two plus three, a seven minus two, a negative two plus a positive seven, a five times one, ten divided by two, and the square root of twenty-five!” The teacher said she almost fell over. Such is the power and magic of Mathino.

    END

    Postscript

    Throughout the last twenty years I must have decided at least ten times to market Mathino. From years of teaching the game to many young students and teachers, I knew it would be a great success. But somehow, something always happened to interfere with those plans.

    One of those happenings was a case of Multiple Sclerosis. Now at sixty years old and confined to a wheelchair, I no longer have the strength to market the game. But on the other hand, I know that Mathino is far too good a math teaching tool to just let it wither and die. Accordingly, I have decided to freely give the game away to parents and teachers. That way, I know the game will never die.

    Marsh Kaminsky

    • Bob Haft
    • January 28th, 2008

    My grandson Mark Biundo is my personal mathmagician and I will forward this to him for evaluation. The performance was very impressive.

    • nj kid
    • January 28th, 2008

    Marsh…God bless you and make your last years fruitful and peaceful.

    • Terry
    • January 29th, 2008

    LOL…Not good at math,it’s my worst subject…

  10. He is wrong on some of his calculations. IE 722 x 722 = 521284 not 513284. Follow along yourself if you don’t believe me!

    • Alan
    • January 31st, 2008

    As Josh pointed out, Dr. Benjamin made a couple mistakes with the three digit numbers, but that didn’t detract from an amazing show. His couple of quips added to the pleasure of witnessing his performance.

    Perhaps the best thing I got from this was Marsh Kaminsky’s comments. He made up a great game for his son, and even taught him some of life’s lessons along the way !
    While teaching Junior High math for 33 years, I too learned a few things about making it FUN. It only took me about 20 of those years to learn that little fact, but it made my last teaching years even more rewarding than “just” setting the district record with 100’s on regents etc. I wish I had known about “Mathino”, because I’m sure that the early adolescent that I was teaching/learning with, sure would have enjoyed the challenge of that game.
    Sad [for me] that not all comments were positive about this show, because of my love for math. But I’m very glad that I noticed, and read the comments, because Marsh has also taught/reminded me of one of life’s BIG lessons. You know the one: the one about TODAY IS A GIFT, tomorrow is a mystery and yesterday is history. So thanks Marsh for your inspiring comments!!

    • epi
    • February 1st, 2008

    yo, Shandooga. Die. ur making us worse off. some one found something that they are good at and you turn that against them.

    heaven: why the heck do you think God is against #’s? there are many many things out there that are worse and He’s not against them. and whatever happens to this guy, he should not die.

    steve: ur backwards

    Dr. Benjamin is simply amazing. I want to be that good.

  11. Benjamin is indeed good, not only at the math skills but at the showmanship. He is right to emphasize the “magic” (performance) connection. It’s conceivable that he’s cheating with the earpiece. That’s a psych question, not math, but it would so completely undercut his showmanship that I think it’s very unlikely he’s cheating — especially so obviously.

    As for his techniques [nerd commentary on a nerd performance ;-]:
    #1. He probably knows all the 2-digit squares by heart. (I know a lot of them, and I don’t even use ‘em very often. I didn’t sit down & memorize them, I just find it easy to remember such things, and no doubt Benjamin does, too.)

    #2. He’s VERY good at addition, probably even with very large numbers.

    #3. For 3-digit squares, they aren’t too hard to compute if you already know the 2-digit ones. During the grand finale, he told us the pattern he uses: 329 [for example] = 300 squared (90,000: 9 is easy, and just remember that squaring always doubles the number of zeros) plus 29 squared (841: remember #1) plus 300*29*2 (8700 doubled = 17,400). Remembering #2, that gives 108,241. (Yes, I DID use a calculator. I’m not performing, and I’m not as good at these things as he is.)

    #4. Determining the missing digit presumably comes from the technique of summing the digits and “casting out 9’s” (as it is colloquially called, because 9 “equals” 0 in this system: sum-of-digits of 10-1 = 1-1 = 0). Remember, he already knows one of the factors of the big number, namely 8649, whose sum-of-digits is 0. When you multiply 8649 by absolutely ANYTHING (whole numbers only), the sum-of-digits of the answer is going to be 0 times the sum-of-digits of the other number. Try it yourself. (That’s right, he gets to multiply by 0. The second number is completely irrelevant. Cute!) So if you tell him a bunch of digits that add up to, say, 2, he knows that the missing one must be “negative 2″, or 9-2 = 7. Again, try it yourself.

    #5. The interesting part for me was the finale, when he revealed something else that I know other arithmetic whizzes use: “cookie fission”, i.e., a code that uses a different part of his brain for storage, so he can concentrate on the arithmetic. I heard of one whiz who thinks of all the 3-digit numbers as individual “friends”, rather than words. Same idea of using a technique that plays to the capabilities of a different part of the brain. (I do something similar with 2-digit numbers, thinking of them as distinct entities — not friends, though! Again, I’m not in their league, but I understand what they’re doing.)

    A nerd footnote for wolfmankurd: Whether numbers and other math concepts “really exist” is actually a point of philosophical disagreement among mathematicians themselves. It ain’t obvious. Some think they are “real”, waiting to be discovered. Some think they are just linguistic devices, special words and phrases that can be combined meaningfully in just certain ways (like, say, colors and nouns: “green barn” is fine, “green fear” is not). And some think they are constructed, existing precisely because we “built” them, just like a house.

    • joe
    • February 2nd, 2008

    Why Don’t play the lottery or stock market the odds are in your favor

  12. Now that is magic.

    • don
    • February 3rd, 2008

    no one notices but he makes a mistake at the 4 minute mark

    • Cnutz
    • February 4th, 2008

    The Guys an autistic sevant that’s not intimidated by people…..

    • JP
    • February 5th, 2008

    This guy is pretty good at what he does, but there are much more talented savants out there. This kid who is only 25 is brilliant and is the leading record holder for reciting Pi, which he did up to 22,500 places. Check him out and see some real magic.

    http://video.google.com/videoplay?docid=4913196365903075662

    • Josey Wales
    • February 9th, 2008

    HOLY SLIDE RULE BATMAN !!!

  13. This is a wonderful example of one human awakening to their potential………this is going to be happening more and more often……check out the canadian sky to see what’s been appearing there, there are several photo albums at my website.

    Keep an open mind and heart…..it’s how the Truth gets in.

  14. r u guys retarded, hes wering an earpeice

    • robort gassman
    • February 13th, 2008

    how do you do that !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

    • prsmama
    • February 14th, 2008

    Get off the earpiece, people, have you never heard of an in-ear monitor? He’s mic’d so he has to have a monitor, did you see any along the front of the stage?

    And religious freak up there needs to study the bible some, God (capital G for those of us who truly respect Him) applied significant numbers to countless things throughout scripture, not the least being Himself (7) and satan (6).

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