The (Mathematical) Mind Is a Beautiful Thing
One month ago today, John Forbes Nash and his wife were killed in New Jersey while returning home from a trip in which he was honored with an award for his work. If they recognized the name, most people listening to the news associated him with the movie A Beautiful Mind. But you might ask, what did he do? What is he known for?
John Nash contributed to game theory and differential geometry, for starters. His theories are used in economics, artificial intelligence, military theory, and more. In computer science, there is an algorithm based on his Nash Equilibrium. The Nobel Prize he received in 1994 was based mainly on game theory results from his dissertation; he delineated between cooperative and non-cooperative games. In a non-cooperative setting, any cooperation that occurs is self-generated. In other words, it must be in everyone’s best interest to cooperate. A Nash Equilibrium is a situation in which no player can improve his position by choosing a different strategy. Using a mix of strategies guarantees at least one equilibrium exists.
Nash’s other major contribution was his theory about “the bargaining problem.” The bottom line is that how gains are divided depends on how much the deal is worth to each participant and what alternatives each participant has. Read this article to learn about an application of his work to decision making and policies on the global level.
Sadly, Nash spent a lot of his adult life struggling with mental health issues, too. What more could he have contributed without that interference? I shared an article on my course discussion board this past spring about a research project regarding intelligence and mental health. I took a look at many individuals that we consider to have possess(ed) great minds, and often times they were labeled as “odd” or “eccentric.” Is that because the brain cannot be neatly pigeonholed? We know more and more about the brain in recent years, yet in essence we only know a little.
We do know about neuroplasticity and the brain’s ability to create changes in neural pathways and synapses; these can be due to changes in behavior, environment, thinking, emotions, injury, etc. So if the brain is not static, then what can we do everyday to improve our critical thinking abilities? Fine-tune our focus skills? Read a book like Brain Rules and no pun intended, you’ll be thinking more about your brain and how to think outside the box, just a little bit like Nash.
About the Author
Diane Hollister has been teaching college courses since 1992. In June 2015, she resigned from her full-time position at Reading Area Community College in Reading, Pennsylvania, where all the math courses have undergone some level of redesign. She still teaches online there and now is part of Pearson’s Efficacy team, helping instructors to implement programs and strategies that bolster student success.
She is intrigued by neurobiological research and learning theory, and she was quick to adopt adaptive learning as a new tool in her courses. Not only does she strive to help her students succeed, but Diane enjoys the collaboration with her peers. She has taught a variety of courses and loves learning how new technology and resources can help students be more successful.
Read more of her articles about math, ICTCM, and quantitative reasoning.