Probability is not the best the goal for undergraduate math education
I recently came across Arthur Benjamin's TED talk in which he claimed that math education needs a major change. He said that we need to refocus the goal of undergraduate education on probability and statistics instead of on calculus. I don’t agree with this, and here's why. Note that this doesn't mean that I think that probability and statistics isn't important. It just means that I disagree with the proposed change to math education.
Now it's certainly true that understanding some basic probability is an important part of a good education. Lots of the important policy decisions that we make are based on data of some sort. It's easy for politicians and special interests to distort or misrepresent data (lie) to support their positions, and one way to be able to see through these distortions and misrepresentations (lies) is to understand how to interpret data, and that's what a basic understanding of probability gives you.
But to understand enough probability to see through the misrepresentations isn’t really that hard. It just takes the background of a one-semester class for which the prerequisite is nothing more than an understanding of basic algebra. That's probably not the sort of class that should be ultimate goal of an undergraduate education. It's really the sort of thing that should be taught in high school. That's where I first learned probability, and the class that I took probably provided all of the background that the average person needs to have.
Another reason that I disagree with this is that calculus is really the foundation for all engineering and science. It's also the foundation for probability. So if you want to understand pretty much anything technical at a non-trivial level, including probability, you really need to understand some calculus to do that. That's not true for probability. It's definitely important background to have, but it's not as fundamental as calculus. Calculus is the language used to describe all engineering and science. Probability isn't. And undergraduate calculus is also an important step on the way to other important tools.
Functions of a complex variable is a fascinating subject and is inherently interesting (at least to me) to learn about, and it's essentially just an extension of undergraduate calculus to functions of complex numbers instead of functions of real numbers. That's where elliptic curves come from, so there are definitely lots of practical applications of it.
Measure theory is also inherently interesting (same disclaimer here), and that's essentially what you get when you try to push the definitions of undergraduate calculus to their limits and a bit beyond. You then see how calculus can fall apart and find what it takes to fix it. And the most important application of measure theory actually seems to be probability. A statistic is a measurable function of a random variable, after all, and probability theory seems to be the most important example of where you actually need to worry about whether or not sets or functions are actually measurable.
So it seems to me that probability is important background that everyone should know, but it's also not the sort of material that should be the ultimate goal of undergraduate education. Calculus is a much better goal for that. It's both the language of science and engineering and the next step towards more advanced topics. Probability isn't.
(Although quantum mechanics involves some probability, it really seemed more like applied functional analysis than applied probability to me. And calculus may not be very helpful in understanding algebraic geometry, but then I'm not sure that anything's really very helpful for that. But then does anyone really understand algebraic geometry?)