<p>Engineering is difficult no matter how good you are at the technical subjects. The truth is, they are all extremely tedious majors, and that requires work that no amount of talent can solve. The chemistry in ChemE is generally rather elementary, and the math does not come up that often. There’s a bit of physics too, but after a while you don’t really use that all that much either. The core of a ChemE major is generally the transport series, which has more formulas (“empirical equations” i.e. estimations that aren’t really explained to you) than conceptual knowledge, and design classes, which are pretty much by definition tedious attention to detail. If you are naturally good at the basics (chemistry, physics, and math), then you will be able to manage, but not easily. If you are truly talented (as in, just about the best mathematician you know and very good with physics), then perhaps you will be able to get away with what one might call a light workload (10-15 hours a week on homework, which is pretty much nothing since there’s much less school time than in high school), but then you would be wasting your talent if you gave yourself a light workload. However, engineering is good because it gives you a solid base in chemistry and physics that you can definitely build on depending on how you design your major, and on top of that you learn engineering. Knowing engineering would be a very useful skill for law school. For med school, it might be a problem in that it will hurt your GPA, but I’d caution away from med school if you don’t like biology, because the entire field is about memorizing facts (because you definitely can’t derive medicine from first principles in a physics-like manner).</p>
<p>Chemistry is a lot more about understanding why matter behaves the way it does, and most of the classes go into details on what you cover rather than, as in engineering, giving you endless equations and expecting you to just accept hand-waving explanations. You can take a more math-heavy route if you like physical chemistry, and you can definitely take a few more programming classes than an engineering curriculum would allow for. Lots and lots of labs though, because you just straight up have to do chemistry if you want to understand it. Also not a bad major for law school or med school. I will also note that chemical engineering puts more emphasis on the “engineering” than on the “chemical” side, so by taking a chemistry major, that part is basically lost on you. If you don’t like engineering, then chemistry definitely allows you to take a lot of other useful classes that will come in handy.</p>
<p>Math, as a major, is definitely different than math as a minor or as a part of another degree. As it is used in other majors, it is a lot of number crunching and equation solving. Math the major itself is about proofs, or more generally, about finding new ways to think about problems. The cornerstone class is advanced calculus, a class that basically derives the theory of calculus from a theoretical mathematical perspective; it’s really hard because the “most correct” way of thinking about calculus is far from intuitive (it is nothing like what a first year course in calculus is taught). Proofs have to be exactly correct, or else they really aren’t proofs, and that becomes difficult when you start proving something that is actually useful. Pure math is what the stereotypical mathematician does, as in doing a thesis on “finding ______ Numbers in ___ - space under ______ conditions” etc. Applied math can go a lot of ways - scientific computing, statistics, probability, computer science, finance, and many other paths that I don’t recall off the top of my head. Personally, I think that math makes for an excellent double major, but on its own you somewhat lose perspective on why it is actually important. The key skill you will learn is how to take problems and think about them in a new and useful way, but if you don’t have any perspective on significant other problems, then your skills are really quite wasted, and you quality to either be a math teacher or a pure math researcher.</p>
<p>Well, that was pretty long. Hope it helps.</p>