I know its EXTREMELY difficult to get into Princeton regardless of your intended major, but what are some toughest majors to get into Princeton with, purely in terms of admission rather than the actual workload, etc?
Princeton does not admit by major.
Princeton can review by major, to ensure a kid is prepared, aware, and to achieve balance in the class, initially, among majors.
OP, asking “purely in terms of admission” makes me wonder the purpose.
Here is an article from 2012 that lists the most popular majors at Princeton. Econ and politics top the list.
https://paw.princeton.edu/article/major-trends-math-hot-decline-social-sciences
As pointed out above, Princeton does not admit by major. But they do pay attention to what you put down on the application.
You’re either in or not. Princeton is not a public university with limited resources for majors with high demand, it can accommodate whoever qualifies.
At the same time, some majors are less demand so if you have excellent qualifications for a less in-demand major it might help on the margin.
Ie., just like a strong background in STEM is necessary to meet the basic qualification for a STEM major, if you apply for a Humanities major you better have AP Foreign Language, both AP English, at least 2AP history courses, perhaps dual enrollment classes, plus relevant ECs over three years.
In other words, don’t try to game this.
The one you’re applying to.
As others have said, Princeton doesn’t admit by major. However, selection of a major could have some influence on your application. Your selection, or even non-selection, should be consistent with your interests, activities, and overall presentation. There’s also one major, that I’m aware of, at Princeton that may be somewhat more difficult to get into and stay in. It’s the Operational Research and Financial Engineering major. You have to satisfy additional departmental core requirements and meet minimum departmental gpa, on top of engineering school core requirements. This is only relevant, of course, after you’ve been accepted.