The Keystone of Math


Have you ever been in a conversation that made no sense at all until a key fact showed up, often more or less by accident? In this post Occupy Math is going to reveal the central goal of the field of mathematics. If you don’t know what math is striving for, if our motives are obscure, then understanding collapses — like the arch shown above would if you removed the green keystone. The keystone of math is the search for patterns, commonalities that unite diverse topics and situations. For many people, math is a chore or a terror with much drudgery and ever-present fear of being judged. Occupy Math hopes that by presenting the following perspective on the purpose of math, math will become less scary for those of you who are not so sure about us.


Math is all about understanding patterns. Since math people are not penny-ante types, we want all the patterns. Absolutely all of them. Every one. We’re not going to get them, but it is truly said that “if you aim high, you’re less likely to shoot yourself in the foot”. It is also true that the more patterns you understand, the more chance you have of understanding the next weird pattern to come along. The great hope of mathematics is summed up by a quote from Albert Einstein:

The most incomprehensible thing about the world is that it is comprehensible.
-Albert Einstein

Studying patterns all the time sometimes backfires and handicaps you. The following image divides the letters of the alphabet according to a mathematical principle — but people with more training often take longer figuring out what that principle is. Try asking a sixth grader “how do you tell which side of the line a letter goes on?”


A nice example of a pattern that occurs in many places is the Fibonacci sequence. You start with 1,1 and then add the last two numbers to get the next one. That means that the sequence starts 1,1,2,3,5,8,13,21,34,55,89,… Where does this pattern show up?

This list could be much longer — but the point is that one simple mathematical pattern shows up again and again.

So why does math get a bad rap in so many quarters?

Math lacks well-known spokespersons!

Occupy Math googled “famous physicists” and tabulated the top five hits: Albert Einstein, Stephen Hawking, Niels Bohr, Sir Isaac Newton, and Nikola Tesla. Trying the same search for mathematicians yielded Sir Isaac Newton, Euclid, Pierre de Fermat, Carl Friedrich Gauss, and Leonhard Euler. Einstein and Tesla appear in movies and TV shows. Hawking is a cultural icon. The top hit for math is the fourth hit for physics. For whatever reason, people that do math don’t end up as popular culture icons the way that people in physics do.

There are portrayals of math in popular culture, like the show Numbers. While this show made some effort to include real math, it comes closer to portraying math as a type of psychic power. Advanced knowledge of math makes it hard to enjoy the show Numbers. Another appearance of a mathematically skilled character in popular culture is Mr. Parker Pyne, an Agatha Christie character that solves problems with statistics. Both these examples are detective fiction and they support Occupy Math’s thesis that mathematics is the search for patterns. Here is another example of a pattern. See if you can figure it out.

0, 1, 1, 2, 4, 7, 13, 24, 44, 81, 149, 274, 504, 927, 1705, 3136, …

There are people who do an excellent job of explaining math.

One of the benefits of the internet is that much smaller communities can have their own media. While the following examples of excellent speakers for math are not going to show up in People Magazine anytime soon, they are well worth a look. Occupy Math selected these three because they are very different from one another — all excellent, but approaching math along very different paths.

Vihart talks really fast. Her videos include excellent math, fun art projects, mythological references, and are simultaneously entertaining and informative. She manages to find explanations of fundamental features of reality in doodles. This is math at its coolest, if you can listen fast enough. The concluding thought in the video above is:

“This is why I love mathematics. The moment when you realize something seemingly arbitrary and confusing is really part of something. It is better than the cleverest possible ending to any crime show or mystery novel because that’s only the beginning.”

That realization Vihart speaks of is the moment you see the pattern.

This series of videos explain math with animation. Really, really well. Occupy Math will be linking many of these videos in the fall from the web page for his calculus class. The narrator says “Good math is nothing less than art” and he makes that idea live. His explanation of derivative rules is the most comprehensible one Occupy Math has ever seen. His attempt to come up with better notation for logarithms and exponents should be adopted. Why? It’s much easier to remember and connects the closely related exponential and log functions through notation. This man has a great talent at showing you the pattern to help you understand the math.

Numberphile introduces mathematical wonders with help from mathemeticians who are experts in the topic, and does it so well that most people will have no trouble understanding them. Occupy Math has already linked their videos on the Collatz conjecture. Most of their videos explain a pattern, at least incidentally. This is a channel for fans of math.

Conflict and stories

The thing that really brought science into the public consciousness was the Manhattan project. When some guys get together and invent a weapon that can end civilization, it merits some attention. The closest that math gets to this sort of recognition is in places like the Bletchley Park codebreaking effort that cracked the enigma code. This gave the Allies a much-needed edge in the Second World War. To place this in perspective, one of the best TV shows to come out of this is The Bletchley Circle. This is a BBC television series about women who were key in cracking the enigma code but had to keep not only the project but their own mathematical ability secret.

Enforced secrecy about math talent is not just in fiction. For decades, the largest employer of mathematicians has been the American National Security Agency. This organization is the one that maintains security on the information front. They are so secret that NSA was known for quite some time as the “No Such Agency”. A substantial fraction of the math talent in the United States vanishes into the NSA. This is probably the most cost-effective and least violent part of the US security apparatus. It also helps explain math’s public relations problem: many of the really good stories from the world of math require code word clearance to listen to.

Occupy Math tries to tell the good math stories. The YouTuber channels and puzzle sites linked in this post are examples of people that are trying to help math seem a little less like the troll under the bridge. If you know of stories or speakers that are part of the effort to help math’s standing in the world, please comment or tweet!

I hope to see you here again,
Daniel Ashlock,
University of Guelph,
Department of Mathematics and Statistics


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