Frustrated With Unhelpful, Mechanical Explanations?

I was too. I've spent years looking for the intuition behind the math concepts that seem to appear in every class, whether exponents or the Pythagorean Theorem.

Slowly, over a decade, I've condensed the key insights (and the analogies that explain them) into friendly, clear, easy-to-read lessons.

I want you to enjoy the Aha! moments in math, moving beyond memorization to experiencing an idea firsthand. Any idea becomes intuitive when explained correctly, and you will unlock your intuition for math.

“Most of the fundamental ideas of science are essentially simple, and may, as a rule, be expressed in language comprehensible to everyone.” — Albert Einstein

What You Will Learn

  • How To Grasp Math Concepts

    The theme of the book is that the intuition-first approach lasts, and ignites a love of learning. Get the specifics of how to apply this strategy.

  • The Pythagorean Theorem

    We've overlooked the meaning of this theorem all along. It's not about triangles, it's about any shape. The applications go far beyond geometry, from comparing movie preferences to colors

  • Exponents and Logarithms

    Exponents show up everywhere, from interest rates to bacteria colonies. But why e? What makes the natural log natural? Skip blind memorization and truly visualize the nature of exponents.

  • Imaginary and Complex Numbers

    How can a negative number have a square root? What does 'imaginary' mean? Using the analogy of rotations, this potentially confusing topic snaps into place.

  • Euler's Formula & Calculus Intro

    Euler's Formula is the jewel of math, linking exponents, radians, and imaginary numbers. And yes, it's understandable. The last chapter introduces calculus with the intuition-first approach.

  • Radians and Degrees

    What are radians, and why are they used in so many formulas? Learn to see radians as change of perspective, from the observer to the mover.

Join 4000+ Happy Customers

I purchased your Math, Better Explained recently. Your explanations have blown me away totally.  Like you, I work better if I understand what I am working with. Thank you for the wonderful explanations - I am really enjoying them. It is Wow after Wow.
Frank W.
via email
Great way to start cultivating math curiosity/intuition. This book is short, sweet, and to the point... Even if you have struggled with the concepts highlighted in the book, Kalid has a way of hitting the reset button in your mind. You let go of your past frustration and start seeing things from the p.o.v. of an open-minded novice.
Patrick Rolandelli
Math has no meaning to many people, it's just pointless shortcuts. This book makes that different. 

Sometimes important math concepts are belittled because they are too abstract. This book shows that abstract concepts can be explained.
Zac Rauschenberger
in a presentation to educators

Detailed Review From

Presh Talwalkar studied economics and mathematics at Stanford, and runs a popular blog about strategic thinking. When he introduced himself and asked to do a review, I wanted to see how a math fan liked the content. Here's a few excerpts:

Beautiful Illustrations

Math, BetterExplained has some of the best math charts and images that I have ever seen, period. You really have to see the images to get an idea of what I’m talking about.

The graphics are both creative and informative and definitely one of the best parts of the ebook.

Casual Tone and Funny

By no means is this a replacement for a textbook. And nor would you want it to be (I mean who reads a textbook for fun any way?).

I think about Math, BetterExplained as having a friend tutor you in a subject. The language is going to be casual and the overall mood light-hearted.

Clever and Practical

I really wish I had this book during high school. One of the strongest chapters is about why the Pythagorean Theorem is true. I give it to Kalid: the proof he offers is one that I had never explicitly read before, but it is so simple it made me wonder why it’s not taught that way.

Lessons For Lasting Intuition

The ebook was made with care, from a print-quality layout, to vivid diagrams, and analogies that help ideas click in seconds.

A lot of math lessons seem to present detail after detail, without an emphasis on visualization or lasting understanding.

These lessons are based on articles read by millions of readers, and evolved with thousands of comments and direct feedback. Here's what's you'll get in the course:

  • 12-chapter eBook with a professional layout (sample)
    • 1. Developing Math Intuition
    • 2. The Pythagorean Theorem
    • 3. Pythagorean Distance
    • 4. Radians and Degrees
    • 5. Imaginary Numbers
    • 6. Complex Arithmetic
    • 7. Exponential Functions & e
    • 8. The Natural Logarithm (ln)
    • 9. Interest Rates
    • 10. Understanding Exponents
    • 11. Euler’s Formula
    • 12. Introduction To Calculus
  • 12 video lessons walking through each chapter
  • Original PowerPoint slides and images for all diagrams
  • 3-part interview with learning expert Scott H Young on study techniques
  • Math concept worksheet to avoid common pitfalls, drawn from frequently asked questions for each topic


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Instant Download, For Any Device

The ebook is available as an instant download and can be read anywhere, including your computer, iPhone, iPad or Kindle. The PDF can be printed, and looks great.

For the techies, all files have zero Digital Rights Management.

Frequently Asked (& Imagined) Questions

  • What math background do I need?

    The book is written for a general high-school audience (you don't need to be a math wizard). The focus is on visualizing concepts so they click, not dry proofs.

    The main prerequisite is a familiarity with middle-school algebra, to follow along as a concept is worked out.

  • I'm a rocket scientist. Do I need this?

    Math must be internalized, not just understood at an intellectual level, and this is even more critical for someone who uses it daily.

    Can you intuit why an imaginary number raised to an imaginary power can be a real number? The goal is to work out this question in your head, without relying on a memorized formula.

  • Why did you write this book?

    I always enjoyed math in school. But during my first semester of college, I almost gave it up as I suffered through a horribly-taught class.

    While cramming, a few epiphanies ignited my understanding and enjoyment, and I was able to internalize (not memorize) the concepts. I want to share that understanding with you, because I know math can be taught better.

  • How does this compare to other math classes or books?

    I wrote this course because despite years of math lessons with the best schools and textbooks, I still didn't have the intuitive understanding I needed.

    The resources I've seen seem to march through details on how to do math with explaining the  why. (My opinion, of course.)

  • What if I don't like the book?

    That's no problem at all. Just contact me and I'm happy to offer an immediate and unconditional refund, even a year after your purchase.

    I created the explanations I dearly wish I'd found in school, but completely understand if they aren't a fit.

  • Can I email you with questions?

    You bet. If you purchase the course (at any level), feel free to contact me with questions for any of the topics covered.

Grasp The Essentials of Math Today

Basic Edition


eBook Only

  • 12-Chapter eBook (PDF, ePub, Mobi)

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Complete Edition


eBook, Videos, Slides

  • 12-Chapter eBook (PDF, ePub, Mobi)
  •  Original PowerPoint Slides & Images
  • 12 Video Lessons (2+ hours)
  • Concept Worksheet
  • 1 Hour Interview with Scott H Young

Buy now

The secure checkout takes a credit card. You may also use Paypal for the Basic and Complete Edition.


About The Author

Kalid Azad graduated from Princeton University with a degree in Computer Science.  He has been writing professionally for over a decade, from chapters in the best-selling "How to Program" textbooks (from Deitel, Inc.) to technical whitepapers for Microsoft, Corp.

Kalid has tutored math since high school (99% percentile for SAT/GRE/GMAT) and is enamored with finding the clearest, most intuitive insights on seemingly-complicated topics.

BetterExplained reaches 250k monthly visitors, is assigned as reading in dozens of university courses, and has been referenced in Science Magazine, along with the blogs for the New York Times, The Atlantic, O’Reilly Radar, Scientific American, and the National Academy of Sciences. 

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