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The Annotated Numberphile #3: The Second Anniversary

Table of Contents

This series on Numberphile continues. I’m annotating videos with my favorite memories. This time we tackle the second anniversary year. It features two of the great mathematicians, John Conway and Ron Graham. Numberphile was hitting its stride. Future years will have interviews with mathematician like Terrence Tao.

It’s this year that the channel hits 1 million subscribers and Brady unleashes the “Mile of Pi.”

SERIES TABLE OF CONTENTS

The Playlist

Here is the playlist of the second-anniversary videos. They are in order of publication date. The personal annotations are numbered by the video’s position in the playlist for easy reference. You can view this playlist on YouTube.

There are 73 videos and the total playlist time is about 10 hours and 40 minutes. In the top right corner of the playlist embed, there is a hamburger menu. Clicking this will allow you to navigate to any video in the playlist.

Personal Annotations

(2) 87,539,319

Simon Singh returns with this bit on Futurama (my favorite TV show of all time.) Singh reveals the abundance of references to the taxicab number, 1729. This is a reference to the mathematician Ramanujan. It is an excellent discussion of how the writers decided to insert these niche jokes that only a few would get.

If you love this story, you may like this cross stitch pattern for the taxicab number 1729.

(14) Why do people hate mathematics?

This is a video with Edward Frenkel. I like the comparison he makes early on to literature and art. Because I make this comparison all the time. He highlights many things I do when talking about math. We need to find ways to connect math to meaning in people’s personal lives. I would also add, that we need to help people process their math trauma and help them overcome math anxiety.

(15) Topology of a Twisted Torus

This is one of the few Numberphile videos that tackles the art of mathematics. Professor Carlo Séquin discusses the art of Keizo Ushio who did a sculpture of the twisted torus in this video. Ushio specializes in carving Mobius strips out of granite! Séquin took this idea further and imagined other ways you could cut a torus. Making more links and different twists. These prototypes are innovative and beautiful. My cross stitch patterns are my expression of math art.

(20)(21) Interviews with John Conway about the Game of Life

The Game of Life is one of those pop-culture math references that some people know. I find stories about it pop up from time to time in mainstream publications. People seem to find it fascinating. Unfortunately, Conway passed away in 2020 from Covid. We are fortunate that we have these conversations to remember him.

Conway discusses his friendship with Martin Gardner. This is how I learned that Gardner’s first great hit was an article for Scientific American on hexaflexagons. So popular that he became a regular columnist! (His column on the Game of Life was popular too.)

(23) Riemann Hypothesis

The Riemann Hypothesis is one problem in mathematics that has my full attention. Reading Music of the Primes was a revelation. It managed to find its way into the part of my subconsciou that understands mathematics. I had an epic math dream about it after I read about Reinmann’s analytic continuation of Zeta.

The passage talked about Reinmann walking the zeta function and I did so in my dream. I saw a magnificent hyperdimensional structure in the air. And well, after that it gets a little crazy. I don’t know if there is any significance to my dream. I have discovered that much of what I saw might be algebraic geometry. Hence my current obsession with it.

Professor Frenkel’s explanation of the Reinmann-Zeta function is the one that makes sense. It helped me understand the part about the complex numbers. There is also this bit I saw from Grant Sanderson (3blue1brown) as I was writing this. Updated this month as well. It can help you visualize what is going on with the function.

(37) Professors React to 2048

This video is a little silly. You will notice that most of these professors aren’t that impressed with 2048. It doesn’t offer anything for them that is more exciting than their actual work. But, it is something from popular culture related to mathematics. Which is nice.

I never got too far in the game myself. But, there is a 2048 speedrun that you can watch if you want to see the end. A similar game is Threes!. In fact, 2048 is a clone spawned from the popularity of Threes!.

(45)(50) Odd Equations

A little out of order, but these two videos do go together. They are both important to what I want to say. These videos are also the first to feature David Eisenbud. Who was the head of MSRI at the time. They are a sponsor of Numberphile. Brady goes to the US to interview the visiting mathematicians there. That is one of the reasons there is such a great variety of presenters.

I didn’t think much of these videos when I viewed them the first time. There was lingering math trauma that was preventing me from fully embracing mathematics. Fortunately, I’ve worked that all out, and there is no denying it now. It is more important to be myself than to make other people feel comfortable. I never want to stop talking about math with people.

These two videos speak to my math identity.

The first video on odd equations shows a process that I went through when I was younger. I spent hours in my room studying polynomials. Going through the same process Professor Eisenbud shows here. You start with the most basic equation you can then layer on the complexity. You add terms, coefficients, and degrees. Seeing each time how that changes the graph.

My goal was to sight-read equations. To become familiar with them. To see their graphs in my mind. Understand their subtleties.

It is the second video on the Fundamental Theorem of Algebra that brings it all home. As Profesor Eisenbud is doing the poof, you begin to see how these equations map out and define spaces. How the equations themselves offer us hints into their nature. We start to see the linkings between algebra and geometry. Or what we call algebraic geometry. I didn’t realize at the time that Eisenbud was an algebriac geometer. Turns out, I had to discover the field on my own.

Looking back, I find these videos delightful. This is the math that I truly love. Watch these videos if you want to understand how I think about math.

(49) Happy Ending Problem

This is the first interview with Ron Graham. Graham is also one of those mathematicians who have found their way into pop culture. Graham’s Number is unfathomably large. Surprisingly, that isn’t what this first video is about. It is a cute little theorem that he discusses here.

(53) The Mandelbrot Set

This is a video with Dr. Holly Krieger who is one of my favorite presenters. This isn’t her first video though. That didn’t make the cut. This is one of her first appearances. This video also has a special significance for me as it is about the Mandelbrot Set.

My first math dream was amazing. I saw what I described as a beetle with these funny edges. It started moving. It was as if a camera was zooming in and a three-dimensional pattern emerged. It was gorgeous. I woke up and didn’t know what I had seen. I was in Junior High at the time. I wasn’t familiar with anything like that. The next day, I was watching a documentary and there it was. What I saw in my dream. It was the Mandelbrot Set.

I don’t remember ever seeing it before that documentary. That dream perplexes me to this day. There is math in my subconscious that I don’t understand. But, it is nice having a channel like Numberphile that gives me some insight.

(71) The Making of a Mile of Pi

This is the longest video on the list at 30 minutes. This is the video that I wanted to share. Numberphile hit a million subscribers in three years. And this year in particular is a banger with so many great videos. It was hard to cut down on my choices. As you can tell, I have a lot to see about the videos for this year as many remind me of my own history with mathematics. Mile of Pi was quite the achievement for Brady. It is something that sticks out in my mind as one of the best videos of all time on the channel.

This year speaks to me more than any other year so far. I’m still looking forward to reviewing them all. There are sure to be more gems that I’ve forgotten about. You can read the next post in the series here.