The Magic of Maths Book Summary - The Magic of Maths Book explained in key points

The Magic of Maths summary

Arthur Benjamin

Solving for x and Figuring Out Why

4.2 (32 ratings)
15 mins

Brief summary

'The Magic of Maths' by Arthur Benjamin is an inspiring and entertaining read that reveals the beauty and wonder of math. Benjamin shows how math can be fun and useful in our everyday lives, and he demonstrates some of his own incredible mental math tricks.

Table of Contents

    The Magic of Maths
    Summary of 8 key ideas

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    Numerical patterns are not only magic – they can lead to real applications too.

    Mathematics is more than just tedious textbooks and laborious calculations; it is a whole world of patterns that are not only magical, they can be really useful too.

    Consider the so-called numerical patterns – patterns made of numbers – and their surprising and beautiful properties.

    The author first discovered these patterns as a child, when he was playing with pairs of numbers that add up to 20:10 and 10, or 9 and 11, for instance.

    He wondered: what’s the largest possible product I can get by multiplying these pairs together?

    Let’s find out:





    So, the largest product is when both numbers are 10. Nothing extraordinary, right?

    But if you look closer, there’s something interesting about these numbers. Examine how far each product is from 100, counting downwards, and you’ll notice a pattern: 0, 1, 4, 9. These are the first square numbers, that is, the numbers that follow the sequence 1², 2², 3², and so on.

    This pattern applies all the way up and down the scale: if we calculate 5 x 15, we can get back to 100 by adding 5². And what’s more, the same pattern emerges no matter what number the pairs add up to!

    These numerical patterns aren’t only magical, they’re also useful in the real world. If we can learn their secrets, we can use them to increase the power of our mental arithmetic, that is, the calculations we make in our head.

    For example, we can use the above pattern to easily calculate the square of a number.

    Say you want to square the number 13. Instead of calculating 13x13– a nightmare to do mentally – we can perform the easier calculation 10*16 where both numbers add up to 26, just like 13 and 13.

    Now we’ve got 10x16=160, but we’re not quite there yet. Our previous pattern tells us that since we went up and down 3 from 13, we need to add 3² to the result. Thus we get 13²=(10*16)+3²=160+9=169.

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    What is The Magic of Maths about?

    The Magic of Maths (2015) reveals the magic hidden within the fascinating world of mathematics. These blinks will show you the beautiful and often surprising patterns of mathematical observations, expand your knowledge of geometry and algebra, teach you numerical party tricks and illuminate the mysterious properties of numbers like π (pi).

    The Magic of Maths Review

    The Magic of Maths (2015) by Arthur Benjamin is a captivating exploration of the power and beauty of mathematics. Here are three reasons why this book is worth reading:

    • With its practical applications, the book demonstrates how math can unlock solutions to everyday problems, making it relevant and intriguing.
    • Presented in an accessible way, the book uses clear explanations and real-world examples, ensuring that readers of all backgrounds can appreciate the wonders of math.
    • Through its fascinating puzzles and mind-bending concepts, the book challenges readers to think creatively and expand their understanding of the world.

    Best quote from The Magic of Maths

    And yet, we often dont get to see that numbers possess a magic of their own, capable of entertaining us, if we just look below the surface.

    —Arthur Benjamin
    example alt text

    Who should read The Magic of Maths?

    • Anyone interested in mathematical techniques, tricks and curiosities
    • Professional and hobby mathematicians

    About the Author

    Arthur Benjamin is a regular speaker at TED talks and is Professor of Mathematics at Harvey Mudd College. He holds a PhD from Johns Hopkins University and is also the author of Secrets of Mental Math.

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    The Magic of Maths FAQs 

    What is the main message of The Magic of Maths?

    Discover the enchanting world of numbers and unlock the power of mathematics in everyday life.

    How long does it take to read The Magic of Maths?

    The reading time for The Magic of Maths varies depending on the reader, but it typically takes several hours. The Blinkist summary can be read in just 15 minutes.

    Is The Magic of Maths a good book? Is it worth reading?

    The Magic of Maths is an engaging and enlightening read. With captivating examples and clear explanations, it's definitely worth your time.

    Who is the author of The Magic of Maths?

    The author of The Magic of Maths is Arthur Benjamin.