The Mathematics of History

“Those who cannot remember the past are doomed to repeat it.” – George Santayana

Most of us have heard the above quote or some form of it, but I don’t know if it really motivated any of us when having to memorize dates or fill out maps.  But, perhaps something else will motivate us.  It turns out that there are underlying patterns in history that can be modeled with mathematics.  Here’s a TED talk by Jean-Baptiste Michel, where he highlights a couple of such models and proposes an idea about the future relationship of history and mathematics.

The Mathematics of History

Talking Trees

Graph Theory is an area of mathematics that uses constructs called graphs to model many relations and processes found in real-world problems.  The graphs consist of vertices (points or nodes) connected by edges (segments or arcs or loops).  This area of mathematics has applications in computer science, biology, chemistry, linguistics, physics, chemistry, sociology, and more.  Can I dare say that Graph Theory is ubiquitous?  So, imagine my lack of surprise when I was watching a TED talk today and saw Graph Theory in action.  The link below takes you to the talk “How Trees Talk to Each Other” by Suzanne Simard.  The talk does not get into the mathematics, but there are some images that caught my attention.  One was that of a fractal, starting at 8:36 in the video.  (This grabbed me, as my Master’s thesis talked about using fractals to monitor the health of forests.  Sadly, the image had nothing to do with her mathematics.)  The next was a graph, which appears at 10:40 in the video.  She does talk about how that graph is used to model connections in a forest, giving me a bit of mathematical excitement.  Despite the lack of a whole lot of mathematics, this video is well worth a watch.  Check it out, and watch out for the bit of Graph Theory.

How Trees Talk to Each Other

Jim Simons: Renaissance Mathematician

Jim Simons is a man who has lived a full life as a mathematician.  While doing mathematical research and laying the foundation for string theory, he also cracked codes for the NSA.  He then went into cracking Wall Street, applying mathematics to investments and becoming wealthy.  He is now active with his Simons Foundation, which supports math and science education and autism research.  Watch this TED talk to find out more.

A Rare Interview with the Mathematician who Cracked Wall Street