# Not all Heroes Wear Capes

My first mathematical and overall nerd hero is John Forbes Nash. His life was explored in the book and the biopic *A Beautiful Mind.* The movie and then the book is where I became enthralled with math without even knowing it. It was probably in junior high when I first saw the movie and I became a fan of John Nash.

The movie does his life story better justice, and the book even better.

John Forbes Nash was born in 1928 in West Virgina and spent his math career at Princeton at the end of world war two when Princeton was home to the Institute of Advanced Mathematics where brilliant scientists and mathematicians like Einstein and Oppenheimer worked after the war. Nash wanted to have something completely original, and so he never went to classes, saying something along the lines of “classes dull original thinking”. He would spend all day walking campus and playing Go ( which is like chess but much more intense ) and trying to create mathematical explanations for the world around him.

One night when he went out to a bar with his friends he was working on a paper when a group of girls walked in, one blonde and the others brunette. Nash and his friends all had their eyes on the blonde, and the blonde gestured over to Nash.

Now this is the part where you can see math symbols floating around the persons head to see how they are thinking. He realized that if him and all of his friends were to go for the blonde none of them would have a date because they would all get in each others way. Then if they tried to ask out one of the blonde’s friends they would get rejected because nobody wants to be second pick. But if none of them go for the blonde, then they all get a date.

This was the moment where he created what is now known as the Nash Equilibrium. This concept won him a Nobel prize due to its applications in Economics, Evolutionary Biology, Politics ( it wasn’t a Nobel Prize in math because Nobel didn’t like mathematics or mathematicians so he did not involve the subject in the winning of a Nobel Prize. So mathematicians developed the Fields Medal which is awarded every 4 years). The field of mathematics that Nash’s work was in is known as **Game Theory **(which can be thought of as the math behind strategic choices). Video Game developers use it when making RPGs ( Role Playing Games ), it was used by countries when creating OPEC.

This is the Nash Equilibrium explained with an example. Imagine you and a friend committed a crime and are now being interrogated separately. The sentence is ten years, but if you confess then you go free and your partner goes to jail for life. They tell this to both of you. But if you stay quiet then it is only a one year sentence due to the evidence that they have. So what do you do?

Can you trust your friend to not snitch? The best option for both of you is to stay quiet and one year. But the best option for you individually is to snitch on your friend. But you don’t know if your friend will also snitch Nash’s Equilibrium says that the best option is to stay quiet but that both people will snitch and both of you will serve eight years.

We don’t think of our choices as being mathematically involved. Sure maybe not whether or not you have PBJ or Turkey for lunch, but those “tough” choices are. Choices made between groups of people, or in chess. Math made its way into your free will, no matter how much you hate it.

In the field of ethics, this sounds a lot like Utilitarianism, which is a ethical concept that the greatest good is that which benefits the greatest number. It was proposed by Jeremy Bentham and then made into a mode of ethics by John Stuart Mill. The choice that benefits the group as a whole is the choice that should be made, even if that puts a greater burden on some individuals. This has its political implications with healthcare and education, but can also be extended into ones personal choices. Nash’s work had philosophical implications in ethics which is not thought of as something math can do.

Another thing which hopefully makes you think of , do you have free will? Are you able to make choices for yourself? Or are you just a bunch of electrical impulses and mathematical equations?

One of my favorite parts of the John Nash story is that it shows math can be done by anybody. Nash was a schizophrenic, and not a savant by any means. He did nothing but work on his idea of an original idea, when you live in something like that for years, you get insights that normally would have passed you otherwise. Nowadays we call that “manifesting” something. But that is just the result of time in the chair.

Being original is a huge concept in mathematics, it is how we give credit too: who was original first. Nash lived this idea to the extreme and it was almost detrimental.

Next time on mathematically speaking, I will be diving into probability theory with the story of Blaise Pascal, how a young mathematician turned theologian gave us two of the largest principles in probability theory, and maybe an insight into the question of free will. Stay Tuned