I started my career at Five Rings Capital, a proprietary trading firm.
To anyone who loves math, I would highly reccomend startign your career with proprietary trading. Most prop shops take the general approach of if you get enough math and cs nerds in one place they will find ways to turn raw technical smarts into money. Here's what that looks like and why I would suggest it.
The Environment
Prop trading firms have a particular culture. You're evaluated on P&L (profit and loss), which provides immediate, objective feedback. There's no ambiguity about whether you're doing well.
This creates intense pressure but also clarity. Markets don't care about your intentions or how hard you worked. They care about whether you made correct predictions. This also really helps really bang in an important takeaway for any work. Work is not about time put in, work is not about the percieved effort, work is about what you produce. At a prop shop this is very clear, I could work a couple more hours during a lower volume time of day which would lead to sligfhtly more profit and therefore more money at the end of the year, or I could not do that. The tradeoffs are all about how much output I want to produce there is a very clear function where you can put in time, effort, skills, learning, etc and turn those into output. However, if I make a single important mistake all of that profit could be offset by the loss caused by that mistake. You can put in tremendous amount of time and effort and not actually produce anything, and on the flip side if you do something exremely clever you could turn very little time and effort into lots of value produced. Just like how everyones life was made just slightly better by whoever invented the tiny plastic stool that goes in the middle of a pizza box to stop the top of the pizza from connecting with the box.
This feedback loop is brutal but instructive. You learn quickly.
What I Learned
The lessons apply far beyond trading:
Rapid Updating: Markets punish you for holding outdated beliefs. You need to update constantly as new information arrives.
Probabilistic Thinking: Nothing is certain. Everything is probability distributions. "I think there's a 70% chance this works" is more honest than "This will definitely work." Trading trains you to think in probabilities. I certainly think the world would be significantly better if people were trained to think through and understand probabilities better.
Systems Thinking: Markets are complex systems. You can't understand them by looking at individual components. You need to see patterns, feedback loops, and second-order effects. Frequently the thing that matters most isn't what you think it is, in trading it could be something as simple as really understanding the way the exchange handles settlement.
Intellectual Humility: The market is smarter than you in so many ways. You need to relaly understand exactly where and why you disagree with the market. WHo is your likely coutnerparty and why do you know better than them in this specific case. Frequently you will be wrong and lose a lot of money, how do you update on that?
The People
Prop trading firms try to hire the absolute smartest people they can, and once you're hired it's mostly a flat hierarchy. Getting to learn from incredibly smart people and see how they think about the world is such a blessing. I certainly found working at a prop trading firm taught me significantly more than goign to an elite university. Everyone is smart, everyone is motivated, everyone shares the same goal.