Writing

How Can Infinitely Many Primes Be Infinitely Far Apart — Quanta Magazine

My latest column for Quanta Magazine ties recent news about “digitally delicate” primes to some simple but fascinating results about prime numbers.

You may have noticed that mathematicians are obsessed with prime numbers. What draws them in? Maybe it’s the fact that prime numbers embody some of math’s most fundamental structures and mysteries. The primes map out the universe of multiplication by allowing us to classify and categorize every number with a unique factorization. But even though humans have been playing with primes since the dawn of multiplication, we still aren’t exactly sure where primes will pop up, how spread out they are, or how close they must be. As far as we know, prime numbers follow no simple pattern.

There’s a tension among the infinitude of prime numbers — that there will always be primes close together and primes far apart — that can also be seen among digitally delicate primes, primes that become composite if any digit is changed. It may come as a surprise that any digitally delicate primes exist at all, but that’s just the beginning of their story. Find out more at by reading the full article here, and be sure to check out the exercises!

By MrHonner, ago

Why Claude Shannon Would Have Been Great at Wordle — Quanta Magazine

My latest column for Quanta Magazine uses the viral word game Wordle to explore the basic ideas of information theory, the branch of mathematics developed by Claude Shannon that revolutionized fields as diverse as digital communication and genetics.

Wordle is a perfect place to discuss the way Shannon defined “information” to posses certain important mathematical properties, like additivity and and inverse relationship with predictability.

For example, how would you proceed if your Wordle guess came back like this?

What you guess next says a lot about you both as a Wordle player and as an information theorist. To learn more, and maybe even level up your Wordle game, read the full article here.

By MrHonner, ago

Introducing Painless Statistics

I am thrilled to announce the release of my new book, Painless Statistics!

Painless Statistics, an entry in the Barron’s Painless series, is written to serve as both a supplementary resource for students taking statistics in school as well as a stand-alone resource for adults who are learning (or re-learning) stats on their own.

Painless Statistics begins with an example of working with data, and covers everything from summary statistics and representations of data to sampling distributions and statistical inference. The book also includes plenty of problems that get you thinking about and applying the important ideas in each chapter.

My hope is that Painless Statistics can be a useful resource for middle school, high school, and even college students learning statistics, as well as for lifelong learners interested in understanding the fundamental mathematical ideas at the intersection of statistics, probability, and inference.

I also think the book would be a great resource for any math teacher who might not see themselves as a statistics teacher but would like to better understand the fundamental ideas in statistics. If by reading Painless Statistics you learn 10% of what I learned by writing it, I think you’ll find it a worthwhile purchase.

If you or someone you know is learning statistics, or would like to learn statistics, please consider picking up a copy of Painless Statistics! It will be available in bookstores everywhere starting June 7th, and you can also order it online. I’ve included the Table of Contents below, and you can take a look inside at the first chapter here.

Painless Statistics Table of Contents

Chapter One: An Introduction to Data

Chapter Two: Data and Representations

Chapter Three: Descriptive Statistics

Chapter Four: Distributions of Data

Chapter Five: The Normal Distribution

Chapter Six: The Fundamentals of Probability

Chapter Seven: Conditional Probability

Chapter Eight: Statistical Sampling

Chapter Nine: Confidence Intervals

Chapter Ten: Statistical Significance

Chapter Eleven: Bivariate Statistics

Chapter Twelve: Statistical Literacy

By MrHonner, ago

What a Math Party Game Tells Us About Graph Theory — Quanta Magazine

My latest column for Quanta Magazine explores some deep (and recent!) results in graph theory using a simple mathematical party game. Trying to get your entire group of friends to each shake an odd number of hands leads to some fundamental and surprising results, like the impossibility of some simple configurations.

This also ties in to some recent research that has determined new bounds on the way a graph can be partitioned into subgraphs. You can read the full article here, which includes some fun and challenging exercises at the end.

By MrHonner, ago

Why Triangles are Easy and Tetrahedra are Hard — Quanta Magazine

My latest column for Quanta Magazine is a celebration of the Triangle Angle Sum theorem, a favorite result from high school geometry.

Do you think there’s a triangle whose angles measure 41, 76 and 63 degrees?

At first, answering this may seem easy. From geometry class we know that the sum of the measures of the interior angles of a triangle is 180 degrees, and since 41 + 76 + 63 = 180, the answer must be yes.

But there’s more to this question than meets the eye.

From triangles we move to tetrahedra, where a surprisingly simple question about angles wasn’t resolved until 2020. You can read all about it here.

By MrHonner, ago
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