There’s a scene in “A Beautiful Mind”, when Russell Crowe writes mathematical equations on a glass pane as it snows outside. There’s another scene in which he rides a cycle in the shape of $\infty$. These scenes have played a major part in making me want to become a mathematician….to discover ideas beautiful enough to write on glass panes as it snows outside.

But what does the life of mathematician actually look like? Spending countless hours editing latex documents in order to get the formatting right. Teaching calculus to mostly uninterested students. Trying repeatedly and failing to understand the motivation behind whole subfields. Getting daily emails from ArXiv full of papers that you’ll never even read the introduction of. Wondering whether any of this matters that much anymore, as Elon Musk sends rockets to the moon and OpenAI invents neural nets that may one day enslave the whole of humanity to maximize the number of paperclips.

Clearly, what I’d done was get inspired by an archetype of a mathematician, and devoted my life to embody that archetype. This, of course, turned out to be an inaccurate archetype. Don’t get me wrong. I love mathematics. And I do still want to come up with beautiful ideas. But I’m unlikely to scribble them on window panes on snowy days.

One of the most influential thinkers I’ve ever come across is Schopenhauer, who states that most of our desires and decisions are irrational. It was irrational of me to assume that my life as a mathematician would resemble that of the cinematic Nash’s. However, my imagination latched on to that, and held on to it despite all evidence pointing to the contrary.

Clearly, archetypes are extremely important in determining our ambitions, and consequently in shaping our lives. Let us explore archetypes that come up in other areas.

## Archetypes in other areas of life

When I work on a project on my own, I assume the archetype of the lone hero working on his project to make a dent in the world. However, when I work on something that my professor assigns me, or perhaps on a homework assignment for class, I assume the archetype of a faceless worker doing meaningless tasks under the yoke of a superior….doing things that will not distinguish me from others. When I work on things that I was not assigned, I assume the archetype of a being thirsty for knowledge. However, when I work on things that I am indeed assigned, I become a drone devoid of talent and motivation, who does menial tasks to make ends meet.

When I choose to help someone of my own accord, I embody the archetype of the benevolent hero who can and will save his people. But when somebody I don’t like expects regular help from me, I embody the archetype of the idiot who can be taken advantage of by anyone. I’m no neuroscientist, but it seems that our brains naturally attach an archetype to every possible action, and the rational mind chooses the action that has the most pleasing archetype. Of course bodily functions like eating, sleeping, etc are not included in this list.

What if we have unhelpful archetypes attached to some of our most important duties? How can we rectify this? We need to modify these archetypes, of course. Maybe the person who does projects on time is the one keeping the world sane and solving massive coordination problems? Someone like Gandhi?

We might just be able to change ourselves into whoever we want….as long as we have the right archetypes attached to them. Wanna get your laundry done on time?

Superman never skips laundry.