As an aspiring mathematician and current math grad student, I am often confronted by students facing existential questions about life and the role mathematics p

As an aspiring mathematician and current math grad student, I am often confronted by students facing existential questions about life and the role mathematics plays in it. [For that matter, I also face these questions, just pitched a little differently] I think I can summarize the existential angst into a single question: does everyone need to learn mathematics? I waver on how I feel about this. On the one hand, the answer is clearly no. Not everyone needs to learn mathematics. Recently, there was a post on HN that prompted discussion about whether or not going to college was necessary to achieve "the American Dream." One of the higher comments also said no. But not going to college limits the paths one can take forward. This is parallel to my current thinking about general mathematics education. Being innumerate is bad for personal development. Numeracy is required for many professions while innumeracy is targeted and taken advantage of by news makers and, for lack of a better word, propagandists. That aside, this doesn't actually answer the question of whether or not everyone should learn math. I suggest that there are reasons for everyone to become numerate. Becoming numerate in the American education system is thought of as a byproduct of the mathematical system. Learning the quadratic formula by rote does not contribute to numeracy. It seems plausible that having the mental faculty to understand its derivation does. But I would also argue that becoming good at programming, physics, or chemistry (among others) also develops good numeracy. [I have thought about how "critical thinking skills," to use a buzzword, relates to basic numeracy. There are many studies, and the Math Wars is a battlefield]. In physics and chemistry, the quadratic formula might arise in the process of understanding something else. It doesn't bother me if a student sees a quadratic, knows there exists a formula to compute its roots, and then proceeds to look up/use this black box formula -- if the quadratic arose from good reasoning about some physical phenomenon (like finding orbits, or kinematics, or even making plans in games like KSP). To this, the author would reply that such a student is capable of understanding and perhaps even rederiving the quadratic formula on his or her own. I suppose I could summarize my view by saying that I have conflicting thoughts on the merits for or against rote memorization in early mathematics... or for that matter calculus (which I'm currently teaching).