Ranking top math-focus universities in the US difficulty-wise?

I'm really passionate about Math, and my goal is to get into one of the top universities for math. Based on the course-load and the curriculum, which would you say is the hardest math-centered university in the US?

When it comes to the most rigorous programs in Mathematics at U.S. colleges and universities, a few institutions are particularly known for their intensity and prestige. Keep in mind that defining difficulty can be subjective and can depend on a lot of factors such as individual preparation, workload, and the pace and depth of the curriculum. Here are some of the top schools known for their strong and challenging math programs:

1. Massachusetts Institute of Technology (MIT): MIT's undergraduate math program is tremendously respected and is considered quite intensive. Known for their Problem Sets (p-sets), students often find themselves facing complex and time-consuming tasks that they need to solve.

2. Princeton University: The undergraduate mathematics program at Princeton is one of the most rigorous in the country. The course-load here is heavy and the curriculum progresses at a very fast pace with a strong focus on proofs from first principles.

3. University of Chicago (UChicago): With a curriculum that stresses the appreciation of proofs and the purest form of mathematics, UChicago is known for its intense coursework in mathematics. The school offers honors sequences in analysis and algebra that are particularly challenging.

4. Harvard University: Harvard has a notoriously difficult curriculum in theoretical mathematics. Their Math 55 course, for instance, is often referred to as one of the most challenging undergraduate math classes in the country.

5. California Institute of Technology (Caltech): Caltech is small but mighty. The mathematics department offers rigorous course sequences in analysis and algebra that use textbooks written by faculty members.

Remember, each university has its unique teaching style and it's crucial to find a program that fits your learning style, not just one that's deemed the most 'difficult.' It's about thriving, not just surviving. Look at the way the curriculum is structured, the opportunities and support available, and the learning outcomes before making a decision. All these universities have highly regarded math programs, so you really can't go wrong wherever you choose to apply.