Lean to program. That's the only major that can help you in trading (computer science). Everything else will have only intangible, abstract benefits ("oh look my critical thinking was improved, so I can uh, make better decisions in trading!") ("oh look I know chaos theory, so I can tell myself the markets are too chaotic when I'm acting undisciplined...") ("I have a PHD in a hard science, so I'm going to come into the markets thinking I'm hot shit and thinking that a mess of instituional orders entered by algorithmic programs has some meaningful relation to natural phenomena").
Interesting, from my point of view (which is somewhat validated by being a computer science professional), both of these are the same. What exactly would a Programmer do but exactly what you say the scientist would do?
A computer programmer can automate his ideas. Nothing but screen time and the school of hard knocks can give one consistently profitable, valid trading ideas, including computer science. However, if one can program, when he has his valid ideas he can potentially automate, which is the direction the industry is going in (has gone in?).
I don't see this as being worthwhile to argue because you are extremely ignorant to the issue. I've read "How I Became A Quant and it is a severe simplification of what it means to be a quant. I don't know why quantum physics is relevant here? It is only one discipline, which you certainly don't need to be a genius to understand. Most physics majors @ MIT take the course their freshman or sophomore year of undergraduate instruction, and I can attest that very few of them are 'geniuses'. My point was that physics is the ultimate application of knowledge. It's more important to 'learn how to think' in order to excel in trading, rather than memorizing frivolous information throughout college. Calculus is one thing? Why? Because that's the highest level of mathematics that you've taken or truly understand? You better go check the continuity of the markets if you think that calculus will give you any advantage in trading. Furthermore, I will state the simple fact that the arguably top prop firms (Jane Street, DRW, SIG, Optiver, etc.) almost hire math, CS, and physics majors exclusively as traders. I don't have time to get into detail, but the continued progression of trading volume to becoming increasingly more automated is entirely obviously as to what the future will hold.
There's always going to be an emphasis on math, but you also need a simple sharp mind to understand trading. Ask yourself if you need some highly developed computer model to understand overpriced and undersold areas? Do you need math to recognize changes in volume, direction and fear? No, stick to the basics and transform yourself into a successful trader by continuing your own success. No firm wants some unknown joe who has zero track record of putting real dollars onto the table. Tell them you know nothing, you just do what the market tells you to do. Everyone is consistently looking for that golden "edge", unfortunately there are no real golden edges. If there were, then you would see more old bold traders, not just old traders. Furthermore, stick with finance, and grab a book on position management . If probability were all it took, why do some poker plays consistently dominate their opponents? everyone starts with the same odds, only few understand it's the severity of the odds and managing your choices within those odds that truly matter. Same goes with why Casinos are successful, the odds are on their side and they know the severity of a loss will always be small enough in the long run to remain profitable.