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Think Like a Maths Genius: The Art of Calculating in Your Head
Discover the secret of how to perform lightning calculations in your head, discover methods of incredible memorisation and other feats of mental agility. Learn maths secrets for the real world, from shopping to calculating a restaurant tip and figuring out gambling odds (or how much you've won). Learn how to solve sudoku faster.
304 pages, Paperback
First published January 1, 1993
1718 people are currently reading
7289 people want to read
About the author
Arthur T. Benjamin
22 books95 followersArthur Benjamin holds a PhD from Johns Hopkins University and is a professor of mathematics at Harvey Mudd College, where he has taught since 1989. He is a noted “mathemagician,” known for being able to perform complicated computations in his head. He is the author, most recently, of The Secrets of Mental Math, and has appeared on The Today Show and The Colbert Report. Benjamin has been profiled in such publications as the New York Times, the Los Angeles Times, USA Today, Scientific American, Discover, and Wired.
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Displaying 1 - 30 of 141 reviews
November 9, 2022
Oh I wish I had had this book in college. No, forget that. I wish I had had it in junior high. Maybe even earlier. Who knew that doing math in your head could be so easy
October 22, 2019
Some years ago, on a whim, I picked up Moonwalking with Einstein by Joshua Foer. In that book, the author—a hitherto unremarkable journalist—details how he learned memory techniques that allowed him to recall hundreds of digits of pi, to learn the names of dozens of strangers in minutes, and to memorize the order of an entire deck of cards in the amount of time it takes me to tie my shoes.
I was completely captivated. The idea that someone could so radically augment his mental prowess using ancient techniques appealed deeply to me. Soon I set about teaching myself some of these methods. The most famous and powerful is the so-called ‘memory palace’: converting information into images, and then placing these images in a familiar space. Using this method, I was able to memorize well over one hundred digits of pi. I even managed to learn the order of a few decks of cards.
This was impressive in itself, and a testament to the efficacy of these techniques. Even so, learning the techniques was itself time-consuming, and without significant practice I was sluggish both in committing to memory and recalling information. You cannot become a memory athlete without significant practice. What was worse, these systems only really worked with certain types of information. The technique for memorizing cards, for example, was useless when it came to remembering German vocabulary. So, after a few weeks, I gave it up.
I bought this book during my brief memory-trick craze, but my enthusiasm had worn off before I began it. Thus it languished on my shelves for many years—until now.
Though this book is technically co-authored, it seems obvious that Arthur Benjamin was the driving force behind it. Michael Shermer, the founder of the Skeptics Society, contributed an afterword in which he argues (unpersuasively) that these mathematical tricks and techniques somehow aid in being skeptical—though a quick-calculating conspiracy theorist strikes me as perfectly plausible. Benjamin, meanwhile, contributes the real meat of the book: ways to speed up mental calculation. He himself is a master of these techniques, which he uses for a sort of numerical magic show (there are many clips online).
Benjamin has done a wonderful job in compiling this little handbook. The mathematical tools are simple, easy to use, and effective. I had become so reliant on the calculator in my phone that it was a relief and, if you can believe it, a real pleasure to return to doing sums and products myself. The world of numbers can be unexpectedly fascinating, revealing unusual patterns, connections, and symmetries. I must admit, however, that I mostly skipped the last section on large multiplication problems, since the amount of practice required to properly execute them exceeded my interest in being a human calculator.
Benjamin’s feats in calculation, like Foer’s feats in memorization, show what the simple human brain can do when aided with techniques and training—achieving abilities so uncanny that it can seen like magic to the uninitiated. To me, this fact alone is cause for hopefulness, since it reveals to us the transformative power of expertise.
I was completely captivated. The idea that someone could so radically augment his mental prowess using ancient techniques appealed deeply to me. Soon I set about teaching myself some of these methods. The most famous and powerful is the so-called ‘memory palace’: converting information into images, and then placing these images in a familiar space. Using this method, I was able to memorize well over one hundred digits of pi. I even managed to learn the order of a few decks of cards.
This was impressive in itself, and a testament to the efficacy of these techniques. Even so, learning the techniques was itself time-consuming, and without significant practice I was sluggish both in committing to memory and recalling information. You cannot become a memory athlete without significant practice. What was worse, these systems only really worked with certain types of information. The technique for memorizing cards, for example, was useless when it came to remembering German vocabulary. So, after a few weeks, I gave it up.
I bought this book during my brief memory-trick craze, but my enthusiasm had worn off before I began it. Thus it languished on my shelves for many years—until now.
Though this book is technically co-authored, it seems obvious that Arthur Benjamin was the driving force behind it. Michael Shermer, the founder of the Skeptics Society, contributed an afterword in which he argues (unpersuasively) that these mathematical tricks and techniques somehow aid in being skeptical—though a quick-calculating conspiracy theorist strikes me as perfectly plausible. Benjamin, meanwhile, contributes the real meat of the book: ways to speed up mental calculation. He himself is a master of these techniques, which he uses for a sort of numerical magic show (there are many clips online).
Benjamin has done a wonderful job in compiling this little handbook. The mathematical tools are simple, easy to use, and effective. I had become so reliant on the calculator in my phone that it was a relief and, if you can believe it, a real pleasure to return to doing sums and products myself. The world of numbers can be unexpectedly fascinating, revealing unusual patterns, connections, and symmetries. I must admit, however, that I mostly skipped the last section on large multiplication problems, since the amount of practice required to properly execute them exceeded my interest in being a human calculator.
Benjamin’s feats in calculation, like Foer’s feats in memorization, show what the simple human brain can do when aided with techniques and training—achieving abilities so uncanny that it can seen like magic to the uninitiated. To me, this fact alone is cause for hopefulness, since it reveals to us the transformative power of expertise.
January 16, 2012
I LOVE this book! It's a nerd's dream come true for me. I checked it out from the library and had it for at least two months. It pained me to give it back. I'm going to buy it soon as I get money. These tricks are so wonderful, it's a wonder they didn't use these in school.
I loved the Pi part. I can recite Pi to a hundred digits now! Always been a goal of mine too. I was content with knowing it for 20 digits, but this made it super easy to know it to a hundred. Then the figuring out the weekday when you have a date. Awesome!
The multiplying is really neat too. As you can tell I just LOVE this book! I'm cheesing writing this. lol! Go read it. If you only read one part, I suggest the Pi bit. :)
I loved the Pi part. I can recite Pi to a hundred digits now! Always been a goal of mine too. I was content with knowing it for 20 digits, but this made it super easy to know it to a hundred. Then the figuring out the weekday when you have a date. Awesome!
The multiplying is really neat too. As you can tell I just LOVE this book! I'm cheesing writing this. lol! Go read it. If you only read one part, I suggest the Pi bit. :)
August 19, 2015
As a nerd who is desperate for attention but also very lazy, this book was a godsend! Arthur Benjamin's mental math tips are very easy to learn, yet still appear impressive to the casual observer. Towards the end of the book, there are some real showstoppers, but even if one only gets halfway through the tricks, you could still impress people at a party (a very lame party).
December 27, 2012
This book helped me to re-build a fresh perspective on doing math in my head. He builds on a central idea of breaking down seemingly complex computations into simple, manageable ones. He then gives you new ways of seeing numbers such that, once these various patterns become familiar, you are able to employ tricks to getting the math done quickly. One of his first examples is how to square a two-digit number that ends in 5.
"... you need to remember only two things. 1. The answer begins by multiplying the first digit by the next higher digit. 2. The answer ends in 25. For example, to square the number 35, we simply multiply the first digit (3) by the next higher digit (4), then attach 25. Since 3 × 4 = 12, the answer is 1225. Therefore, 35 × 35 = 1225."
"... you need to remember only two things. 1. The answer begins by multiplying the first digit by the next higher digit. 2. The answer ends in 25. For example, to square the number 35, we simply multiply the first digit (3) by the next higher digit (4), then attach 25. Since 3 × 4 = 12, the answer is 1225. Therefore, 35 × 35 = 1225."
July 24, 2012
Foreword by Bill Nye?
BILL NYE?!?
Watching him was definitely the greatest time I had in science class. Knowing that he advocates this book (or was bought out to support it) is pretty much worthy of my attention.
No question there is definitely useful (to the point of being necessary) information in this book. In the first chapter (ironically Chapter 0), I was introduced to a smorgasbord of various tricks that became immediately useful: the rule of multiplying 11s, squaring numbers that end in 5, multiplying two digit numbers with the same first digit and second digits that sum to 10 (which, I admit was a little bit harder to have explained but as soon as I got it, it became ridiculously valuable). Beyond that, I learned how to do pretty much all math in my head. Squaring any two digit number above 30 was something I thought was reserved for savants (like the guy from Pi).
I feel nerdy as hell for praising the book this much but it really is that good. You might not want to be bogged down with explanations of how to square three digit numbers in your head but I would recommend anyone to read Chapter 0, then see how they like it, or evaluate if it's going to be useful to them.
BILL NYE?!?
Watching him was definitely the greatest time I had in science class. Knowing that he advocates this book (or was bought out to support it) is pretty much worthy of my attention.
No question there is definitely useful (to the point of being necessary) information in this book. In the first chapter (ironically Chapter 0), I was introduced to a smorgasbord of various tricks that became immediately useful: the rule of multiplying 11s, squaring numbers that end in 5, multiplying two digit numbers with the same first digit and second digits that sum to 10 (which, I admit was a little bit harder to have explained but as soon as I got it, it became ridiculously valuable). Beyond that, I learned how to do pretty much all math in my head. Squaring any two digit number above 30 was something I thought was reserved for savants (like the guy from Pi).
I feel nerdy as hell for praising the book this much but it really is that good. You might not want to be bogged down with explanations of how to square three digit numbers in your head but I would recommend anyone to read Chapter 0, then see how they like it, or evaluate if it's going to be useful to them.
May 23, 2010
Two stars really isn't a fair rating. Had some fun adding and subtracting and then multiplying 3 digit numbers in my head.
But as the problems get more complex, my limitations became apparent. Couldn't read through the entire book. When I couldn't do what the book was suggesting, just gave up.
So no - reading this book wont suddenly make you a math genius.
There are some interesting stories with interesting perspectives, but not enough to inspire the me to practice the "tricks" and yes I expect the average person will need to practice.
So in fairness the 2 stars represents the bitterness I felt upon failing to become an overnight mathemagician...but who knows, maybe you can do it!
But as the problems get more complex, my limitations became apparent. Couldn't read through the entire book. When I couldn't do what the book was suggesting, just gave up.
So no - reading this book wont suddenly make you a math genius.
There are some interesting stories with interesting perspectives, but not enough to inspire the me to practice the "tricks" and yes I expect the average person will need to practice.
So in fairness the 2 stars represents the bitterness I felt upon failing to become an overnight mathemagician...but who knows, maybe you can do it!
June 13, 2011
I slowed down about half way through this book and was ready to give it 3 stars. In some cases I had discovered a fair number of the tricks on my own, or had learned them elsewhere. The processes described were sometimes just brute mathematics, requiring you compute, then hold numbers in your head and compute again.
However, the second half had some cool techniques that I didn't know, and while 4 or 5-digit multiplication problems are just plain difficult (as the author admits), 3 and 4 digit squares are more doable than I would've thought, and (perfect) cube roots of numbers with up to 6 digits are so easy it's fun. With the neat mathematical "magic tricks" at the end to cap it off, this book was back up to 4 stars for me.
However, the second half had some cool techniques that I didn't know, and while 4 or 5-digit multiplication problems are just plain difficult (as the author admits), 3 and 4 digit squares are more doable than I would've thought, and (perfect) cube roots of numbers with up to 6 digits are so easy it's fun. With the neat mathematical "magic tricks" at the end to cap it off, this book was back up to 4 stars for me.
July 27, 2007
"Special thanks to NATALYA ST. CLAIR for typesetting the initial draft, which was partly supported by a grant from the Mellon Foundation." :D
March 10, 2016
Contains techniques for lightning fast mental calculation and other things for elementary mathematics and random tricks. For instance, it includes the phonetic memory system for recalling numbers and a way to calculate dates in your head. The techniques listed in the book are a bit counter intuitive, but they work pretty well. The book also contains problems for you to do on your own in order for you to go and improve your abilities at this particular skill.
Also contained within are biographies of other historical lightning calculators and random bits of trivia which makes this book pretty interesting.
Also contained within are biographies of other historical lightning calculators and random bits of trivia which makes this book pretty interesting.
September 12, 2016
The author is enthusiastic, but somehow this enthusiasm doesn't transmit to the reader. The tricks work, but I am incredibly bored by this book regardless. (might have worked better with real-life examples, but I for one am hard-pressed to think of a good real-life reason to multiply a pair of two-digit numbers in your head)
December 20, 2014
I really liked this book, and its accompanying video CD. The author is full of enthusiasm and the mathematical tricks are really worth learning, and so simple.
I enjoyed teaching some of the tricks to my grandson, who, in turn, enjoyed showing them off to his friends and teachers at school.
I'd recommend this book to everyone. A lot of fun!
I enjoyed teaching some of the tricks to my grandson, who, in turn, enjoyed showing them off to his friends and teachers at school.
I'd recommend this book to everyone. A lot of fun!
August 18, 2021
Useful tips for speeding up the calculations, because math is in the understanding - the numbers are just the medium of choice.
Couldn’t digest all of the stuff (because school’s mentally-taxing enough), but will surely use it as a compendium for the future.
Couldn’t digest all of the stuff (because school’s mentally-taxing enough), but will surely use it as a compendium for the future.
February 12, 2018
Fantastic book! If you love math, or would just like to be able to struggle less with it, this book is a great tool. One caveat however: don't expect magically easy math abilities. Benjamin shows you the tools to make mental math problems exponentially easier, but at the end of the day you still need to calculate!
Now with that out of the way, can you calculate squares and square roots in your head? For two, three-no-five digit numbers? This book will show you the ways of these and many other fantastic mathematical prestidigitation techniques. Calculate the day of the week of any calendar date? Check. Estimate square roots to many decimal places? Check. Memorize Pi to hundreds of digits? Check. Use mod sums to check your answers? Check (digit)!
Bottom line: get this book if you want to nerd out and work your math muscles.
Now with that out of the way, can you calculate squares and square roots in your head? For two, three-no-five digit numbers? This book will show you the ways of these and many other fantastic mathematical prestidigitation techniques. Calculate the day of the week of any calendar date? Check. Estimate square roots to many decimal places? Check. Memorize Pi to hundreds of digits? Check. Use mod sums to check your answers? Check (digit)!
Bottom line: get this book if you want to nerd out and work your math muscles.
July 25, 2011
There were enough interesting math shortcuts in this book to keep my interest, especially those dealing with multiplication tricks, squaring, finding divisors (and why those tricks work), and figuring out any day of the week in the Gregorian Calendar. But, there were also many parts that just weren't feasible to me. Only certain people, like the author, are capable of doing all the mental tricks he covers. Some math problems were just too much to do with paper and pencil, and I'm a math person! The other cricism I have is of the last chapter, the epilogue. It doesn't seem related to the rest of the book.
February 15, 2014
الكتاب الاكثر فائدة في موضوع الحساب الذهني
انصح القراء العرب بقراءته اسلوبه سهل جدا
والحيل فيه مفيدة وعملية فالناس في حياتها ومعاملتها اكثر ما تستخدم الرياضيات البسيطة غير "المعقدة"
القدرة على حل العمليات بشكل مختصر جدا وذهنيا التي يعلمها الكتاب ستجعلك تحزن على عدم معرفتك السابقة بها
good book
انصح القراء العرب بقراءته اسلوبه سهل جدا
والحيل فيه مفيدة وعملية فالناس في حياتها ومعاملتها اكثر ما تستخدم الرياضيات البسيطة غير "المعقدة"
القدرة على حل العمليات بشكل مختصر جدا وذهنيا التي يعلمها الكتاب ستجعلك تحزن على عدم معرفتك السابقة بها
good book
March 27, 2013
I tremendously enjoyed both the book and the video course. I was familiar with Benjamin both from other courses and from his mental math tricks. Not only did I improve a lot just from watching, but I picked up some really neat new tricks that I know I can get with practice. Lots of fun.
July 7, 2015
An entertaining math book! Seriously. Easy to read and easy to understand strategies for improving number sense. I think my kids might also like how the author frames the equations as tricks or illusions. Of course, with my short memory, I had to buy a copy so I can refer back to it. Sorry library.
December 14, 2016
Helped me so much to make math easier. I shocked my friends into thinking I was a super genius and with this books helps I won't stop. I put it down because after a while it was starting to bore me but after a few months you can pick back up again.
April 28, 2010
I already knew/used a few of these tricks, but some were new and pretty smart. And there's nothing nerdier than doing math in you head on the train, so that was fun.
October 17, 2011
The first third of this book should be mandatory for all math and elementary educators. Gets a little unnecessary after that, but it was still a good read.
February 10, 2014
Some things in here I have no interest in mastering, but there are some neat tricks worth some study!
July 11, 2014
This was good. I learned some cool ways to do quick math, along with some ways that I can amaze my students.
August 25, 2018
I absolutely loved this lecture! The professor who taught it was, in my opinion, phenomenal. The secrets of mental math are, I find, very intriguing.
September 1, 2024
(Greitas) skaičiavimas mintyse žaliems. Kalkuliatorių ir kitokios velniškos technikos nemėgėjams ir šiaip anarchistams.
November 7, 2021
pretty good book, a bit niche. lots of tips and tricks to do math better to some degree. need to drill the exercises a lot to be the "genius" level though.
January 22, 2018
Starts out interesting. Loses its spark about four chapters in.
March 22, 2022
Practical methods and quick tricks to sharpen mental arithmetic.
December 18, 2012
En una època en la que tothom va amb un mòbil (amb calculadora) a les butxaques, vaig jo i llegeixo un llibre que només es dedica a explicar trucs per calcular (mentalment) més ràpid. Sembla que no té sentit, però... bé, jo sempre he sigut molt vaga per aquestes coses, i per no haver de treure la calculadora de la bossa, o el mòbil de la butxaca (i obrir la calculadora), o... sempre acabo calculant les coses de cap, que és més ràpid que buscar una calculadora. D'acord, pels càlculs llargs no, però... què és més ràpid: posar la mà a la butxaca, desbloquejar el mòbil, obrir la calculadora, introduir 31*27 i veure el resultat o dir 31*3=93*3=279*3=837? A mi em sembla molt més ràpida la segona. I més ara, que en comptes de multiplicar tres vegades per tres, calcularia 29²-4=30*28+1-4=840-3=837. D'acord, d'acord, què estic fent? Ara ho explico...
El llibre té molts trucs que ja feia servir (no pots dedicar-te a operar mentalment i no fer servir trucs o pararàs boig!), però n'hi ha algun que no havia fet servir mai (i que van molt bé!).
Per exemple, jo per fer els quadrats, com ara per calcular 71², sempre feia:
71²=(70+1)²=4900+140+1=5041.
Però el llibre proposa un mètode molt més ràpid, basat en una cosa que qualsevol podem observar:
n² = (n+k)*(n-k)+k²
Així, qualsevol quadrat de dues xifres, com ara el quadrat de 71, es pot reduir a multiplicar dos nombres de dues xifres (un d'ells acabat en zero) i sumar-li un quadrat d'una xifra:
71² = 70*72+1²=5040+1=5041.
No sembla que hi hagi massa diferència, però, què passa si vull calcular 87²?
Amb el meu mètode primer jo calcularia (90-3)² = 8100-540+9=7569.
I ara: 90*84+9=7569.
Bé, potser no hi ha tanta diferència, i el que he guanyat és agilitat mental...
El llibre continua amb coses més esotèriques, com calcular el quadrat d'un nombre de 3 xifres. He mirat com es fa, i ho sé fer en cas de necessitat (la idea és la mateixa que amb els quadrats de nombres de 2 xifres), però en aquests casos agafaria la calculadora... Tot i que si no tingués calculadora, és més senzill fer-ho així que de la forma natural. Que què vull dir? Doncs, per exemple,
238² = 200*276+38² = 55200+ 40*36 + 2² = 55200+1440+4 = 56644.
No és difícil, però si ho faig mentalment oblido el 55200, així que necessito llapis i paper. Però si algun dia he de fer el quadrat de 238 a mà tinc clar que no multiplicaré 238*238...
Hi ha algun capítol prescindible, i en algun moment se li'n va la bola (quadrats de 5 xifres mentalment?) Però, en general, una lectura agradable... i interessant!
June 29, 2013
This book was quite helpful for my uses but leaves many topics uncovered.
I used the book to prep for various interviews where I need to do math in my head FAST and without paper. This book was an excellent start. I would say that it is too brief to be exhaustive so I'd recommend consulting other materials if you're trying to learn mental math for a serious goal.
What the book does provide is a solid introduction into doing math in your head and if you get through it, you will probably end up wanting to learn more. For example, it teaches vedic division (on paper) but there are many more vedic concepts to learn than that. Note that the book stresses flexibility in how you look at numbers and if nothing else, will teach you to look at a math problem in several ways.
I ended up skipping a couple of the chapters that deal with very advanced multiplication (the pacing of the book leaves something to be desired.) and the Major System (you essentially memorize images as a peg system that makes long calculations easier to not forget as you're doing another step).
Great read overall - just make sure you know why you are reading it!
I used the book to prep for various interviews where I need to do math in my head FAST and without paper. This book was an excellent start. I would say that it is too brief to be exhaustive so I'd recommend consulting other materials if you're trying to learn mental math for a serious goal.
What the book does provide is a solid introduction into doing math in your head and if you get through it, you will probably end up wanting to learn more. For example, it teaches vedic division (on paper) but there are many more vedic concepts to learn than that. Note that the book stresses flexibility in how you look at numbers and if nothing else, will teach you to look at a math problem in several ways.
I ended up skipping a couple of the chapters that deal with very advanced multiplication (the pacing of the book leaves something to be desired.) and the Major System (you essentially memorize images as a peg system that makes long calculations easier to not forget as you're doing another step).
Great read overall - just make sure you know why you are reading it!
Displaying 1 - 30 of 141 reviews